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WORKS  OF 

PROFESSOR    F.  R.  BUTTON 

PUBLISHED    BY 

JOHN    WILEY   &   SONS 


The  Mechanical  Eng^ineering:  of   Power 
Plants. 

750  pages  and  500  illustrations.  8vo, 
cloth,  $5.00. 

Heat  and  Heat-engines. 

A  study  of  the  principles  which  underlie 
the  mechanical  engineering  of  a  power 
plant. 

576  pages  and  198  illustrations.  8vo, 
cloth,  $5.00. 


Digitized  by  VjOOQ IC 


n 


HEAT  AND  HEAT-ENGINES. 


A  STUDY  OF  THE  PRINCIPLES  WHICH  UNDER- 
LIE THE  MECHANICAL  ENGINEERING 
OF  A  POWER  PLANT 


BY 

FREDERICK   REMSEN    HUTTON,  E.M.,  Ph.D., 

professor  of  Mechanical  Bngtneenng  at  Columbia  University. 


FIRST   EDITION, 
FIRST   THOUSAND. 


NEW   YORK: 

JOHN   WILEY   &    SONS. 

London:    CHAPMAN    &   HALL,   Limited. 

1900. 


Digitized  by  VjOOQ IC 


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Copyright,  1899, 

BY 

FREDERICK  REMSEN   HUTTON. 


SOBKRT  DKUMMOND,   PKTNTSIt,  NKW  YORK. 


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PREFACE. 


The  effort  has  been  made  under  another  title,  **  The 
Mechanical  Engineering  of  Power  Plants,**  to  discuss  the 
steam-engine  and  the  steam-boiler  with  their  accessory 
apparatus,  so  as  to  enable  students  and  others  to  make  an 
intelligent  selection  of  successful  designs  for  a  set  of  condi- 
tions which  might  be  imposed.  The  object  of  the  author  was 
to  make  the  reader  familiar  with  accepted  solutions  of  the 
power-house  problem  in  all  its  details,  but  no  attempt  was 
made  to  discuss  the  questions  of  design  of  such  apparatus. 
It  was  intended  that  the  student  should  ask  at  the  end  of 
his  study  of  that  book:  What  are  the  principles  of  physics 
and  dynamics  upon  which  these  machines  depend;  and  how 
do  engineers  proceed  when  called  upon  to  design  such  power- 
house engines  ? 

This  book,  under  the  title  of  **  Heat  and  Heat-engines,** 
has  been  prepared  to  answer  these  questions  in  part.  It 
discusses  the  energy  resident  in  fuels,  and  the  methods  of  its 
liberation  as  heat  for  power  purposes;  the  transfer  of  such 
heat  to  convenient  media  whereby  it  can  be  used  in  heat- 
engines;  the  laws  and  properties  of  such  media,  and  the 
design  of  cylinders  of  the  necessary  volume  to  give  a  desired 
mechanical  effect  or  horse-power.  Then,  this  point  having 
been  reached,  and  relations  being  established  for  the  mutual 
variations  of  temperature  with  pressure  and  volume  in  such 
media  when  operated  in  a  cylinder  with  a  piston,  it  becomes 

ill 


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IV  PREFACE, 

easy  and  natural  to  go  farther  and  discuss  the  air-compressor 
and  its  complement,  the  air-engine;  and  to  extend  this  dis- 
cussion to  include  the  problem  of  mechanical  refrigeration. 
The  hot-air  engine  using  a  permanent  gas  as  a  medium 
naturally  leads  to  the  gas-engine  and  the  oil-engine;  and  the 
engine  using  steam  as  a  medium  leads  naturally  to  those 
using  other  media,  such  as  naphtha,  alcohol,  and  ammonia. 
The  chapter  on  the  Injector  as  a  heat-absorbing  and  energy- 
transforming  device  closes  the  book. 

If  the  distinction  were  a  conceded  one,  the  first  book 
designated  as  the  mechanical  engineering  of  power  plants 
might  be  said  to  lead  to  this  supplementary  discussion  upon 
the  dynamical  engineering  of  power  plants.  The  treatment 
assumes  and  does  not  attempt  to  prove  the  dynamic  or 
mechanical  theory  of  heat,  and  does  not  ask  nor  require  to 
know  whether  there  is  an  intermolecular  ether  or  not,  nor 
whether  the  energy  of  heat  manifests  itself  by  producing  a 
vibratory  or  undulatory  or  vortex  motion  of  matter,  or  is  an 
electro-magnetic  phenomenon.  These  discussions  belong  to  a 
transcendental  sphere  of  investigation  and  research  with  which 
the  practical  engineer  as  a  rule  need  not  concern  himself. 

It  is  somewhat  in  this  latter  view  also,  that  for  the 
purpose  in  hand  the  term  *' thermodynamics "  has  been 
largely  avoided,  as  well  as  the  attractive  development  of  the 
truths  of  the  science  of  heat-engine  design  by  the  methods  of 
exponential  equations  and  the  use  of  the  calculus.  No  one 
is  more  ready  than  the  writer  to  recognize  the  elegance  of 
the  deductive  method  from  fundamental  equations,  and  the 
delights  of  the  revelations  of  law  which  are  thus  secured. 
But  on  the  other  hand  it  must  not  be  overlooked  that  the 
very  ease  and  elegance  of  the  deductive  method  makes  it  an 
unsafe  tool  in  the  hands  of  the  inexperienced  who  are  without 
the  steadying  effect  of  long  familiarity  with  the  actual  con- 
ditions of  the  applications  of  theory,  which  should  prevent 
the  drawing  of  conclusions  which  the  mathematical  treatment 


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PKEFACE.  r 

alone  does  not  pronounce  unsound.  The  science  of  thermo* 
dynamics  has  this  singular  distinction^  that  it  has  been  devel- 
oped deductively  from  fundamental  equations  by  master- 
minds, using  the  methods  familiar  to  the  physicist  and  the 
skilled  mathematician.  But  it  has  often  moved  so  far  in 
advance  of  the  ordinary  attainments  of  the  practitioner 
in  the  power-house  on  the  one  hand,  and  so  far  in  advance 
of  the  experience  of  the  student  on  the^  other  hand,  that 
both  have  often  lost  the  connecting-link  between  the  ad- 
vanced theory  and  the  current  practice.  The  effect  on  the 
student  has  been  to  weaken  his  appreciation  of  the  subject 
if  he  was  not  of  a  mathematical  bent;  or  if  he  was  gifted  with 
facilit}'  in  this  method  of  thought,  he  failed  to  satisfy  his 
early  employers  because  he  applied  the  deductive  methods 
and  conclusions  with  a  zeal  not  always  according  to  knowl- 
edge. The  practitioner,  on  the  other  hand,  as  the  result  of 
years  of  training  in  the  inductive  method  of  generalizing  from 
particulars  in  his  daily  affairs,  is  out  of  touch  with  the  deduc- 
tive method  and  has  no  use  for  the  unfamiliar  process  and 
its  practitioner.  He  therefore  unjustly  undervalues  his 
young  technical  graduate  and  his  method  of  training. 

This  treatise  tries  to  occupy  a  middle  ground.  It  might 
wisely  be  used  as  a  groundwork  for  a  subsequent  treatment 
of  heat-phenomena  by  the  analytic  or  mathematical  method 
after  the  student  has  become  familiar  with  the  physical  facts 
of  which  the  equations  of  thermodynamics  are  condensed 
statements.  By  pursuing  this  middle  course,  however,  a  few 
places  may  be  detected  where  the  logical  mind  will  miss  the 
antecedent  premise  upon  which  the  conclusion  is  based,  or 
where  it  is  stated  upon  authority,  and  the  proof  is  not  given. 
This  is  the  result  of  trying  to  treat  thermodynamics  without 
the  calculus,  and  the  result  should  be  to  turn  the  student  to 
further  and  exhaustive  research  in  the  higher  field.  At  least, 
this  is  the  author's  desire. 

Equations  could   not  be  avoided,    nor  the  use  of    loga- 


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VI  PREFA  CE. 

rithms;  but  the  use  of  the  temperature-entropy  diagram  £or 
the  graphical  representation  of  relations  has  been  abundantly 
permitted.  The  appendices  also  open  doors  into  departments 
of  further  research  and  knowledge  beyond  the  scope  set  by 
the  limits  of  the  text. 

The  student  and  writer  of  to-day  is  the  heir  of  the  work 
and  thought  of  his  predecessors  who  have  inspired  and  guided 
him.  The  bibliography  in  the  appendix  will  show  how  many 
workers  in  these  lines  have  left  their  impress  upon  the  modern 
treatment  of  the  subject.  The  influences  most  felt  in  this 
book  are  those  from  Rankine,  Cotterill,  Ewing,  Peabody, 
Wood,  Reeve,  and  Richmond,  to  whom  heartfelt  acknowledg- 
ment is  extended  and  to  whose  treatises  the  advanced  student 
is  referred.  To  the  last  name  in  the  list  special  thanks  are 
due  for  valuable  suggestions  and  a  criticism  upon  certain 
parts  in  the  proofs.  To  Profs,  Thurston,  Carpenter,  and 
other  contributors  to  the  Transactions  of  the  American 
Society  of  Mechanical  Engineers,  and  to  Prof.  Reeve,  the 
author  is  indebted  for  use  of  helpful  illustrations. 

The  specialist  will  require  to  pursue  the  lines  of  his 
selection  by  supplementing  the  basal  treatment  of  this  book 
by  further  study  in  the  excellent  treatises  on  the  gas-  and 
oil-engine,  the  injector,  the  refrigerating-machine,  and  in  the 
field  of  the  application  of  compressed  air.  It  will  be  a  great 
pleasure  if  the  treatment  and  its  methods  shall  make  the  book 
useful  also  to  that  growing  class  of  persons  who  are  brought 
into  touch  with  engineering  matters  and  are  anxious  to  learn 
about  them,  and  yet  who  are  not  fitted  to  profit  by  an  ex- 
clusively mathematical  discussion.  The  object  which  has 
been  sought  in  its  preparation  will  be  secured  if  the  book 
shall  prove  helpful  and  useful  as  a  stimulus  to  further  study. 

Columbia  University,  New  York,  July^  1899. 


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TABLE  OF  CONTENTS. 


CHAPTER   I. 

INTRODUCTORY, 

PAR.  PA2B 

1.  Sources  of  Motor  Energy i 

2.  Limitations  of  Muscular  Force  and  the  Force  of  Gravity i 

3.  Importance  of  the  Motor  Energy  Liberated  on  Combustion 3 

4.  Analysis  of  a  Power  Plant 3 

5.  Scheme  of  Classification 5 

CHAPTER  H. 

GENERAL   NOTIONS  ON   THE  PHENOMENA    MANIFESTED  IN  HEAT- 
ENGINES. 

6.  General  and  Introductory 6 

7.  Graphic  Representation  of  the  Work  of  a  Piston-engine 8 

CHAPTER  in. 
GENERAL  NOTIONS  ON  HEAT. 

8.  Introductory X2 

9.  Mechanical  Theory  of  Heat 13 

10.  Mechanical  Equivalent  of  Heat 13 

ir.  The  British  Thermal  Unit 14 

12.  The  Specific  Heat 14 

13.  Temperature 15 

14.  Thermometers 16 

15.  Air-thermometer 17 

16.  Absolute  Temperature 18 

17.  Total  and  Intrinsic  Energy 19 

CHAPTER    IV. 
GENERA  TION  OR  LIBERA  TION  OF  HEA  T.    COMBUSTION. 

18.  Introductory 20 

JQ.  Heat  from  Combustion 20 

vii 


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VI 11  TABLE   OF  CONTENTS. 

PAR.  PACK 

20.  Certain    Phenomena  of   Combustion.  Ignition,    Flame,   Incandes- 

cence    21 

21.  Spontaneous  Combustion.     Explosion 23 

22.  Calorific  Power  of  a  Fuel 24 

23.  Coal-calorimeters 25 

24.  Air  Required  for  Combustion  of  Carbon 25 

25.  Air  Required  for  Combustion  of  Hydrogen 27 

26.  Air  Required  for  Combustion  of  Compounds 28 

27.  Combustion  of  an  Analyzed  Fuel 29 

28.  Weight  of  Products  of  Combustion  with  an  Analyzed  Fuel 30 

29.  Volume  of  the  Products  of  Combustion  with  an  Analyzed  Fuel 31 

30.  Dilution  of  the  Products  of  Combustion 32 

CHAPTER   V. 

FUELS, 

31.  Introductory 34 

32.  Solid  Fuels.     Anthracite  Coal 34 

33.  Bituminous  Coal 37 

34.  Lignite 39 

35.  Asphalt 40 

36.  Peat 40 

37.  Coke 41 

38.  Wood 42 

39.  Bagasse,  Straw,  Tan-bark 44 

40.  Charcoal 46 

41.  Artificial  or  Patent  Fuels 47 

42.  Liquid  Fuel.     Petroleum .  48 

43.  Kerosene 50 

44.  Alcohol 50 

45.  Liquid-fuel  Furnaces 51 

46.  Oil-vapor  Burners 52 

47.  Oil-gas  Systems 55 

48.  Advantages  of  Oil-fuel 56 

49.  Disadvantages  of  Oil-fuel 57 

5c.   Gaseous  Fuels.     General 58 

51.  Natural  Gas 58 

52.  Producer-gas 60 

53.  Water-gas.     Dowson  Gas 62 

54    Coal-gas  or  Illuminating-gas 67 

55.  Acetylene-gas 69 

56.  Comparison  of  Gaseous  Fuels 69 

57.  Powdered  Fuel 72 

58.  Calorific  Power  of  a  Hydrocarbon 73. 


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TABLE   OF  CONTENTS.  IX 

'AR.  PAGE 

59.  Evaporative  Power  of  a  Fuel.     Efficiency.  Heat-balance 74 

60.  Data  Concerning  Fuels 7^ 

CHAPTER    VI. 

TEMPERA  TURES  OF  COMBUSTION,    PYROMETERS, 

61.  Introductory 85 

62.  Temperature  of  the  Fire 86 

63.  Pyrometers.     General 89 

64.  Metal-ball  Pyrometer 90 

65.  Wiborgh's  Air-pyrometer 91 

66.  Uehling-Steinbart  Pyrometer 91 

67.  Le  Cbatelier  Thermo-electric  Pyrometer.     Siemens  Pyrometer  ...  92 

68.  Mesur6  and  Noel's  Pyrometric  Telescope 93 

69.  Some  Standard  Temperatures 93 

CHAPTER   VII. 
RATE  OF  COMBUSTION.     DRAFT, 

75.  Introductory 95 

76.  The  Rate  of  Combustion 95 

77.  Draft  for  Combustion.     General 96 

78.  Chimney-draft.     General 97 

79.  Theory  of  Chimney-draft  by  P6clet 98 

80.  Discussion  of  P6clet*s  Theory  of  Chimney-draft loi 

81.  Some  Accepted  Chimney  Formulae  and  Data 104 

82.  Cross-section  of  Chimney 106 

83.  Draft-gauges 107 

84.  Flue-gas  Analysis in 

85.  Stability  and  Structure  of  Chimneys 113 

85.   Artificial  or  Mechanical  or  Forced  Draft 117 

87.  Advantages  of  Mechanical  Draft 119 

88.  Disadvantages  of  Mechanical  Draft 121 

89.  Smoke-prevention 123 

90.  Mechanical  Stoking ' 129 

CHAPTER   VIII. 
TRANSFER  OF  HEAT,    HEATING-SURFACE. 

91.  Introductory 139 

92.  Transfer  of  Heat.     General 140 

93.  Transfer  of  Heat  by  Radiation 142 

94.  Transfer  of  Heat  by  Contact 145 

95.  Transfer  of  Heat  by  Conduction 148 

96.  Transfer  of  Heat  by  Convection.     Circulation 151 

97.  General  Remarks  on  the  Transfer  of  Heat 152 


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X  TABLE   OF  CONTENTS. 

rAH.  TAGB 

98.  Heating-surface 153 

99.  Ratio  of  Heating-surface  to  Grate-surface 157 

100.   Evaporation  in  Boilers  per  Pound  of  Coal 159 

loi.  Water  per  Horse-power  per  Hour 160 

102.  Ref rigerating-surface 162 

103.  Conclusion 163 

CHAPTER    IX. 
MEDIA    USED   TO   TRANSFER  HEAT  ENERGY. 

105.  Introductory 164 

106.  Solids,  Liquids,  and  Gases 164 

107.  General  Characteristics  of  a  Medium  to  be  used  in  a  Heat-engine  166 

108.  Some    Heat-carriers  which  have  been  used  as  Media  in  Heat- 

engines 171 

109.  Vapors : 172 

no.  Liquefaction,  Fusion  or   Melting.     Latent  Heat  of    Fusion    and 

Vaporization 172 

CHAPTER   X. 
PHYSICAL  LA  IVS,  EXHIBITING  EFFECTS  OF  HE  A  T  UPON  HE  A  T-CARRIERS. 

111.  Introductory 176 

112.  Law  of  Gay-Lussac,  or  Charles'  Law 177 

1 13.  Coefficients  of  Expansion 178 

114.  Law  of  Mariotte,  or  Boyle's  Law 179 

115.  Combination  of  Mariotte  and  Gay-Lussac  Law.     Value  of  Sym- 

bol i? 180 

116.  Specific  Heat  at  Constant  Pressure  and  at  Constant  Volume 183 

117.  Joule's  Law 18^ 

118.  Graphical  Representation  of  the  Thermal  Changes  in  a  Gas 185 

119.  Lines  of  Constant  or  Equal  Pressure.     Isopiestic  Lines  or  Isobars  186 

120.  Lines  of  Constant  or  Equal  Volume.     Isometric  Lines 187 

121.  Lines  of  Constant  or  Equal  Temperature.     Isothermal  Lines 187 

122.  Isodynamic  or  Iso-energic  Lines'. 188 

123.  Adiabatic  Lines 188 

124.  Iso-entropic  Lines.     Entropy 190 

125.  Plotting  of  Isothermal  and  Adiabatic  Lines 195 

CHAPTER    XI. 
I  'A  PORS  A  S  HEA  T^CA  RRIERS.    S TEA  M. 

130.  Introductory 198 

131.  Saturated  Vapor.     Saturated  Steam 199 

132.  Superheated  Vapor.     Superheated  Steam 200 


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TABLE   OF  CONTENTS.  XI 

PAR.  FACE 

133.  Relations   of    Pressure   and    Temperature   in    Saturated   Steam- 

vapor  (Regnault) 201 

134.  Rankine  Formula  for  Pressure  of  Saturated  Steam 203 

135.  Other  Formulae  for  Pressure  and  Temperature  of  Saturated  Steam  204 

136.  Steam  Tables 205 

137.  Saturated  Vapor  Pressures  and  Temperatures  for  Media  other 

than  Steam 210 

138.  Total  Heat  of  Steam 211 

139.  Heat  of  the  Liquid 211 

140.  Heat  of  Vaporization.     Internal  Latent  Heat 212 

141.  Specific  Volume  of  Hot  Liquids 213 

143.  Critical  Temperature 214 

143.  Increase  of  Entropy  of  a  Mixture  of  Liquid  and  Vapor  Entropy  of 

the  Liquid 215 

144.  Increase  of  Entropy  of  the  Vapor 217 

145.  Superheated  Steam,  Total  Heat  of 218 

146.  Specific  Heat  of  Steam 218 

147.  Negative  Specific  Heat  of  Saturated  Steam 219 

148.  Specific  Heat  of  Superheated  Steam  at  Constant  Volume 220 

149.  Specific  Volume  of  Superheated  Steam 220 

150.  Specific  Volume  of  Saturated  Steam 221 

151.  Condensation  in  Adiabatic  Expansion  of  Steam 222 

152.  Evaporation  from  a  Feed-water  Temperature 223 

153.  Evaporation  from  and  at  212''  Fahr 224 

154.  Rankine's  Factor  of  Evaporation 225 

155.  Theoretical  Evaporation  of  Water  per  Pound  of  Fuel 225 

156.  Output  of  a  Steam-boiler  in  Heat-units 226 

957.  Efficiency  of  a  Steam-boiler 226 


CHAPTER  XIL 

WORK  DONE  BY  ELASTIC  HEA  T  MEDIA    IN  CYLINDERS  OF  HE  A  T- 
ENGINES,  CYLINDER  DESIGN, 

160.  Introductory 228 

161.  Work  done  with  Constant  Pressure  in  the  Cylinder 229 

162.  Constant-pressure  Work  with  Air  or  Permanent  Gases 23 1 

163.  Constant-pressure  Work  with  St^am 232 

164.  Work  done  by  an  Elastic  Heat-carrier  Expanding  in  a  Cylinder. 

Cut-oflf  or  Degree  of  Expansion 232 

165.  Work  of  a  pv  Diagram  represented  by  an  Area 235 

166.  Work  of  an  Elastic  Heat  Medium  Expanding  Isothermally 237 

167.  Work  of  an  Elastic  Heat  Medium  Expanding  Adiabatically 239 

168.  Adiabatic  Work  in  Terms  of  Pressures 242 

169.  Temperature  Changes  in  Adiabatic  Expansion 243 


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XU  TABLE   OF  CONTENTS, 

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170.  Conclusions  regarding  Isothermal  and  Adiabatic  Expansion 245 

171.  Design  of  Cylinders  for  Piston-motors 245 

172.  The  Compound  or  Multiple-expansion  Engine 247 

173.  Advantages  of  the  Compound  Engine 250 

1 74.  Disadvantages  of  the  Compound  Engine 253 

175.  Design  of  the  Rotary  Engine 254 

1 76.  The  Steam  Turbine 255 

CHAPTER   XIII. 

MECHANICAL    COMPRESSION  OF  HEAT  MEDIA. 

i8o.  Introductory 260 

181.  The  Air-compressor  with  Pressures  Given 260 

182.  The  Air-compressor  with  Volumes  Given 263 

183.  Value  of  the  Factor  n  in  Air-compressing 263 

184.  Mean  Pressure  in  the  Compressing-cylinder 265 

185.  Isothermal  Compression 266 

1S6.  Effect  of  Clearance  in  Compressing-cylinders 267 

187.  Volume  of  Compressing-cylinder 269 

188.  Cooling  of  Compressing-cylinder 270 

189.  Compression  in  Two  or  More  Stages.     Compound  Compressors..  270 

190.  Fluid  Compressors 273 

191.  Conclusions  and  Remarks 273 

CHAPTER   XIV. 
TEMPERATURE-ENTROPY  DIAGRAMS  FOR  HEAT-ENGINES. 

195.  Introductory 276 

196.  The  Temperature-entropy  Diagram 277 

197.  Temperature-entropy  Diagram  for  an  Ideal  Heat-engine 279 

19S.   Deductions  from  the  Temperature-entropy  Diagram 28a 

199.  Entropy-temperature  Diagram  applied  to  a  Perfect  Steam-engine 

working  with  Complete  Expansion 284 

200.  Amount  of  Condensation  in  Adiabatic  Expansion 286 

201.  Temperature-entropy  Diagram  when  Expansion  is  Incomplete...  288 

202.  Temperature-entropy  Diagram  when  there  is  no  Expansion 290 

203.  Temperature-entropy  Diagram  when  Steam  is  Superheated 290 

204.  Plotting  of  Entropy-temperature  Curves  for  Water  and  Steam....  291 

205.  Transfer  of  the  Indicator-diagram  to  the  Entropy-temperature  Di- 

agram      294 

CHAPTER   XV. 
THE  IDEAL   CYCLE  HEAT-ENGINE. 

210,  Introductory 296 

211.  The  First  Law  of  Thermodynamics 297 


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»\R.  »*AGE 

212.  The  Second  Law  of  Thermodynamics 297 

213.  Carnot's  Cycle 298 

214.  Carnot's  Cycle  Reversed 301 

215.  Carnot's  Criterion  of  Reversibility 302 

216.  Efficiency  of  the  Carnot  Cycle 303 

217.  The  Rankine  and  Clausius  Cycles 305 

218.  Theoretical  Weight  of  Heat  Medium  for  a  given  Work 306 

219.  Recapitulation > 309 

CHAPTER   XVI. 
THE  CYCLE  OF  THE  ACTUAL   STEAM-ENGINE, 

220.  Introductory 311 

221.  Elements  of  Departure  of  the  Actual  Cycle  from  the  Ideal  Carnot 

Cycle 311 

222.  Progress  in  Steam-engine  Efficiency 316 

223.  Ideal  and  Actual  Efficiency  Compared 317 

224.  Methods  of  Reducing  Internal  Condensation 319 

225.  The  Steam-jacket 321 

226.  Conditions  and  Action  of  an   Effective  Steam-jacket 323 

227.  Gain  from  the  Use  of  the  Steam-jacket , . .   324 

228.  Non-conducting  Cylinders 325 

229.  Superheating,  to  Prevent  Cylinder  Condensation 325 

230.  Methods  of  Superheating 328 

231.  Objections  to  Superheating 330 

232.  Gain  or  Economy  by  Superheating 331 

233.  Loss  by  Clearance 331 

•234.   Probable  Amounts  of  Clearance 334 

235.  Clearance  Losses  Diminished  by  Compression 335 

^36.   Calculation  of  Mean  Effective  Pressure  when  Clearance  and  Com- 
pression are  Considered 335 

237.  Friction  in  Steam-pipes 337 

238.  Loss  of  Pressure  and  Temperature  from  Cooling  in  Pipes 337 

■239.   Efficiencies    Experimentally  Determined    in    Terms   of   Thermal 

Units 337 

CHAPTER   XVII. 
THERMAL   ANALYSIS  OF  HEAT-ENGINES. 

240.  Introductory 340 

241.  Pounds  of   Heat    Medium   per   Horse-power  Calculated  Theoret- 

ically from  an  Indicator-diagram 340 

242.  Hirn's  Analysis 343 

243.  Application  of  Hirn's  Analysis 349 

244.  Limitations  of  Hirn's  Analysis 351 


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245.  Thermal  Analysis  by  Temperature-entropy  Diagram 353 

246.  Losses  Revealed  by  the  Temperature-entropy  Diagram 357 

247.  Reeve's  Entropy-temperature  Chart 359 

248.  Conclusion 360 

CHAPTER   XVIII. 

COMPRESSED-AIR  ENGINES. 

250.  Introduction 361 

251.  Loss  of  Energy  in  Transmitting  Air  through  Pipes 363 

252.  The  D'Arcy  Formula  for  Compressed  Air 364 

253.  Compressed  Air-engine  with  Complete  Expansion 365 

254.  Compressed-air  Engine  at  Full  Pressure,  without  Cut-off 366 

255.  Compressed-air  Engine  with  Incomplete  Expansion..' 369 

256.  Compressed-air  Engine  with  Isothermal  Expansion 370 

257.  Volume  of  the  Cylinder  of  a  Compressed-air  Engine 371 

258.  Compound  Compressed-air  Engine 371 

259.  Combined  Efficiency  of  Compressor  and  Air-engine 374 

260.  Heat  Range  in  the  Air-engine  Cylinder 375 

261.  Preheating  the  Air  for  the  Air-engine 376 

262.  Temperature-entropy  Diagram  for  Compressed-air  Engine 377 

263.  Temperature-entropy  Diagram  for  the  Air-compressor 380 

264.  Temperature-entropy  Diagram  for  the  Combined  Air-compressor 

and  Air-engine 381 

265.  Concluding  Summary 384 

CHAPTER   XIX. 
HOT-AIR  ENGINES. 

266.  Introductory 386 

267.  Types  of  Hot-air  Engine 387 

268.  Regenerator  for  Hot-air  Engine 388 

269.  Hot-air  Engine  with  Temperature  Changes  at  Constant  Volume. 

Stirling's  Engine 389 

270.  Temperature-entropy    Diagram    for   a   Stirling   Hot-air   Engine.  391 

271.  Hot-air  Engine  with  Temperature  Changes  at  Constant  Pressure. 

Ericsson's  Engine 394 

272.  Other  Forms  of  Hot-air  Engine 396 

273.  Hot-air  Engine  with  Separate  Compressing  Cylinder 398 

274.  Temperature-entropy    Diagram  of  a  Hot-air    Engine  Changing 

Temperatures  Non-Isothermally 401 

275.  Joule's  Equivalent  Hot-air  Engine  with  Closed  Cycle 402 

276.  Internal  Combustion  Hot-air  Engine  Using  Solid  Fuel 403 

277.  Concluding  Summary 405 


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CHAPTER   XX. 

INTERNAL-COMBUSTION  ENGINES.     THE  GAS  AND   THE  OIL    ENGINE, 

PAK.  PACK 

280.  Introductory — Historical 406 

281.  Lenoir  Gas-engine  of  i860 •> 407 

282.  Hugon's  Gas-engine  of  1865 409 

283.  Otto  and  Langen  Atmospheric  or  Free-piston  Gas-engine  of  1867.  409 

284.  Brayton  Gas-engine  or  Ready  Motor  of  1873 41 1 

285.  Four-phase  Cycle  of  Beau  de  Rochas 412 

286.  Otto  Silent  Gas-engine  of  1876. 413 

287.  Dugald  Clerk  Gas-engine  of  1880 415 

288.  Atkinson  Di£ferential  or  Cycle  Gas-engine  of  1885 416 

289.  Classification  of  Gas-engines 420 

290.  Methods  of  Igniting  the  Gas-charge 421 

291.  Indicator-diagrams  from  the  Gas-engine 424 

292.  Some  Phenomena  of  Ignition  in  the  Gas-engine 427 

293.  Usual  Mixtures  of  Gas  and  Air 430 

294.  Thermodynamic   Efficiency  of  the  Otto  Engine  Considered  as  a 

Carnot  Engine 431 

295.  Temperature-entropy  Diagram  for  the  Gas-engine 433 

296.  Compound  Gas-engines 44a 

297.  The  Oil-engine  for  Kerosene  or  Non-volatile  Oils 441 

298.  The  Oil-engine  for  Gasoline  or  Light  Volatile  Oils 444 

299.  The  Diesel  Petroleum-motor 445 

300.  Performance  and  Economy  of  Direct-combustion  Engines 447 

301.  Advantages  of  the  Gas- and  Oil-engine ' 449 

302.  Disadvantages  of  the  Gas-  and  Oil-engine 451 

303.  Conclusion 453 

CHAPTER  XXI. 

VA  POR-ENGINES. 

305.  Introductory 454. 

306.  Formulae  for  the  Work  of  a  Vapor 455. 

307.  Experimental  Data  for  a  Problem  in  Vapors  as  Heat  Media 458 

308.  Efficiency  of  a  Volatile  Vapor  between  given  Temperature  Limits.  462 

309.  Efficiency  of  a  Volatile  Vapor  between  given  Pressure  Limits. .. .  464. 

310.  Efifect  on  Efficiency  of  Certain  Vapors  by  Adjusting  Back-pressure 

and  Expansion  Ratio 467 

311.  Effect  on  Efficiency  of  Certain  Vapors  by  an  Increase  in  Pressure 

Range 468 

312.  Usual  Vapor  Media.     Their  Disadvantages 471 

313.  Naphtha-  and  Gasoline-engines 473 

314.  Binary  Vapor-engines 474 


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XVI  »  TABLE   OF  CONTEXTS. 

I'AK.  »'AGB 

315.  Wellington  Series  Vapor-motor 476 

316.  Ammonia  Vapor-engines 479 

317.  Combined  Vapor-engines — Aero-steam  Engines 480 

318.  Storage  of  Energy  in  Liquefied  Vapors  480 1 

319.  Concluding  Remarks 481 

CHAPTER   XXII. 
MECHANICAL  REFRIGERATION. 

325.  Introductory 482 

326.  Analogy  between  the  Heat-engine  and  the  Ice-machine 483 

327.  Refrigeration   fcr  Ice-making  or  for  Cooling-chambers.     Brines.  484 

328.  Media  for  Use  in  Refrigerating-machines.     Advantages  and  Dis- 

advantages    486 

329.  Refrigerating-machines  using  Air  as  a  Medium 488 

330.  Ammonia  Refrigerating-machines.     Compression  Type 492 

331.  Hot  or  Cold  and  Dry  or  Hot  Systems  of  Ammonia-compression.  496 

332.  Ammonia  Refrigerating-machines.     Absorption  Type 497 

333.  Refrigerating-machines      on      Pictet     System.         Carbonic-acid 

Machines I 498 

334.  Temperature-entropy  Diagram  of  Refrigerating  Cycle 499 

335.  Efficiency  in  a  Refrigerating  Cycle 502 

336.  Refrigeration  by  a  Series  Process.     The  Step-by-step  Process....  505 

337.  Design  of  a  Refrigerating-machine 507 

.338.   Performance  of  Refrigerating-machines 510 

339.  Freezing  Mixtures.     Some  Low  Temperatures.     Liquid  Air 511 

CHAPTER   XXIIL 

THE  INJECTOR. 

340.  Introductory 514 

341.  The  Injector  Defined.     The  Ejector 514 

342.  Mechanical    Principles    Underlying  the  Injector.     The    Induced- 

current  Principle 516 

343.  Heat-transfer,  Work,  and  Efficiency  in  the  Injector 517 

344.  Mechanical  Principle  of  Impact  in  the  Injector 519 

345.  Double-tube  Injector.     The  Inspirator 520 

346.  Re-starting  or  Automatic  Injectors 521 

347.  Exhaust  steam  Injectors 522 

.348.   Advantages  of  the  Injector 522 

349.  Disadvantages  of  the  Injector :   522 

350.  Appendix.     Tables  of  Hyperbolic  Logarithms 525 

351.  "  Historical  Bibliography 528 

352.  '*  General  Bibliography -. ...   529 

353.  *'  Names  of  Scientists  and  Investigators 530 

354.  *♦  Notes,  Tables  and  References 530 


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LIST  OF'ILLUSTRATIONS. 


FIG.  FAGK 

1.  Indicator-diagram,  with  no  Expansion lo 

2.  "  '•  "      Cut-ofif ID 

3.  Hoadley's  Air-thermpmeter 18 

4.  Barrus'  Coal-calorimeter 25 

5.  Hollow  Grate-bar,  with  Forced  Draft 44. 

6.  Bagasse  Furnace 46 

7.  Thurman  Oil-burner 53 

8.  Urquhart  Oil-burner 54 

9.  Siemens  Producer 62 

TO.  Taylor   Producer 63,  64 

1 1.  Dowson  Producer 65 

12.  Lencauchez  Producer 66 

13.  Diagram  of  Chimney  as  a  Siphon 98 

14.  *'  Showing  Chimney  Capacity 105 

15.  U  Tubes  as  Draft-gauge 109 

16.  Wollaston-Prentiss  U  Tube   Draft-gauge 109 

17.  U  Tube  Draft-gauge,  with  Hook-gauge  Reading no 

iS.         **       Water-gauge no 

19.  Orsat  Apparatus  for  Flue-gas  Analysis iir 

20.  Chimney  Constructions 116 

21.  "  ••  116 

22.  *•  *•  '. 116 

25.  Induced-draft  System,  with  Pre-heating  of  Air,  S.  S.  Kensington..  118 

26.  Kafer's  Forced-draft  System,  U.  S.  S.  Swatara 119. 

27.  Mechanical  Draft  Arrangement,  Union  Traction  Co.,  Phila 122 

28.  Induced-draft  Plant,  American  Line  Pier 122 

29.  Ash-pit,  Hotel  Iroquois,  Buffalo 123 

30.  Hawley,  Down-draft  Furnace 126 

31.  Marston,  Down-draft  Furnace 127 

32.  Sellers  Extension  Furnace 12S 

33.  Roney  Step-grate 131 

34.  Coxe  Travelling-grate 132 

35.  Wilkinson  Mechanical  Stoker 133 

xvii 


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xvm  LIST  OF  ILLUSTRATIONS, 

FIG.  I'Ac.K 

36.  Columbia  Mechanical  Stoker.' 134 

37.  American  Under-fed  Stoker 135 

38.  "            ••          *•         "     Forced  Draft 136 

39.  Ringelmann  Smoke-scale 137 

40.  Radiation  Varying  with  Distance 143 

41 .  ' '         and  Contact  Compared 146 

42.  Heating-surface-  Increases  with  Initial  Temperature 155 

43.  Isopiestic  Lines 186 

44.  Isometric      '*       186 

45.  Isothermal  "       187 

46.  Adiabatic      '*       189 

47.  Isothermal  "       195 

48.  Isentropic     "      195 

49.  Drawing  of  Isothermal  Lines 196 

50.  '*         '*  Equilateral  Hyperbola  through  a  Point 196 

51.  Diagram  of  Regnault's  Relation  of  Temperature  to  Pressure 203 

52.  Fairbairn  and  Tate,  Apparatus  to  Determine   Specific  Volume  of 

Steam 221 

53.  Diagram  representing  a  Resistance  f,s 230 

54.  "                  "         anEffon/.v 230 

61.  "                   *•          a  Variable  Effort 235 

62.  "                   '*         a  Piston  Effort  with  Back  Pressure 237 

63.  **                   **          Isothermal  Expansion 238 

64.  *•                   ••          Steam  Effort  in  a  Woolf  Engine 247 

65.  "                   **                **           *•      in  a  Compound  Engine 248 

66.  "                   •*               ••           ••         ••              •'               '•      248 

67.  Diagram  representing  Steam   Effort  in   a   Receiver   Compound 

Engine 249 

68.  Typical  Rotary  Engine 255 

69.  De  Laval's  Steam  Turbine 258 

70.  Dow's  Out  ward-flow  Turbine 259 

75.  Isothermal  and  Adiabatic  Compression  Compared 267 

76.  Diagram  representing  Effect  of  Clearance  in  Compression 268 

77.  •*                   "                   *•        *' Multiple  Stage  Compression 271 

78.  Two-stage  Tandem  Air-compressor,  IngersolUSergeant 274 

79.  Diagram  representing  Isothermal  Expansion 280 

80.  **                   *'              Temperature-entropy 280 

8z.          *'                   "                         "                  '•         for  Actual  Engine...  285 
88.  Diagram  representing  Temperature-entropy  Vaporization  incom- 
plete   2S7 

83.  Diagram  representing   Temperature-entropy    Expansion  incom- 

plete    2i>9 

84.  Diagram    representing  Temperature-entropy,  no  Expansion 290 

85.  "                    **                          '*                  "         Steam  superheated. .  291 


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LIS  T  OF  ILL  US  TRA  TIONS.  X  l  X 

FIG,  l-AGB 

86.  Diagram    representing  Entropy  of  Water  and  Steam 292 

87.  "  **  Saturation  and  Adiabaiic  Curves 293 

88.  "  "  Transfer  of  Points  ixom  pv  to  ie  Diagram. .  295 

89.  "  *•  Carnot's  Cycle 299 

90.  **  "  Efficiency  of  Heat-engine 304 

91-  "  *•  *'  *'  "      304 

•92.   Diagram     representing     Duty    and     Economy    of    Steam-engines 

since  1800 316 

•93.  Diagram  representing  Efficiency  and  Water  Consumption 318 

94.  '•  "  "  '*         "         .       "  318 

95.  "  ••  "  "         "  "  319 

96.  Diagram    representing    Temperature   and    Pressure    Change    in 

Steam 327 

•97.  Diagram    representing    Temperature    and    Pressure    Change   in 

Steam 328 

9S.  Typical  Superheating 330 

100.         '•  *'  E£fect  of  Clearance 332 

loi.         *'  "  Calculation  of  Clearance  Volume 334 

102.  Diagram  to  illustrate  Calculation  of  Mean  Eflfective  Pressure 335 

103.  *•  *'  *'  Water  per  H. -P.  from  Indicator-diagram..  341 

104.  '*  *•  **  Hirn's  Analysis 345 

105.  **  **  **  Thermal  Analysis  of  Engine-test 354 

106.  ••  "  "  ••  "  ••  *'         356 

107.  *•  "  "  "  "  "  •'         357 

108.  ••  *•  •'  ••  ••  "  "         360 

109    Diagram  to  illustrate  Gain  by  Reheating   in  Multiple-expansion 

Air-engines 373 

no.  Re  heater  for  Compressed-air  Transmission 377 

715.   Diagram  representing  Complete  Expansion 378 

116.  '*  "      Temperature-entropy  in  Complete  Expansion.  378 

117.  Diagram    representing   Temperature-entropy    in   Partial  Expan- 

sion or  no  Expansion 379 

118.  Diagram  representing  Compression 380 

119.  "  "               Adiabatic  Compression 382 

120.  "  **                      '*           Expansion 38a 

121.  "  "               Combination  of  the  above 382 

122.  **  *•              Temperature-entropy  for  above 382 

125.  Stirling's  Hot-air  Engine 390 

126.  Pressure-volume  Diagram  of  Stirling  Air-engine 391 

127.  Temperature-entropy  Diagram  for  Ideal  Hot-air  Engine 392 

128.  "  *•  "    Stirling  Engine 392 

129.  Ericsson  Hot-air  Pumping-engine,  Perspective 395 

130.  '•  •'  •*  "      ,  Section 395 

131.  Pressure- volume  Diagram  of  Ericsson  Engine 396 


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X X  LIST  OF  IL L  US TRA  TIONS. 

no.  PAcr 

132.  Pressure-volume  Diagram  of  Ericsson  Engine 396- 

133.  Section  of  Rider  Hot-air  Pumping-engine 397 

134.  Pressure-volume  Diagram  for  Products  of  Combustion-engine 399- 

135.  Temperature-entropy    Diagram    for   a    Hot-air    Engine    heating 

non-isothermally 401 

136.  Joule's  Air-engine 403 

137.  Buckett's  or  Cayley's  Products-of-combustion  Engine 404 

140.  Lenoir  Gas-engine,  Sections 407,  408 

141.  "  "  "         Diagram...    , 408 

142.  Otto  and  Langen  Atmospheric  Gas-engine 410 

143.  Beau  de  Rochas  or  Otto  Cycle  Ideal 413 

144.  Otto  Engine  Section 414 

145.  Clerk  Engine  Section 415 

146.  Atkinson  Differential  Gas-engine 417,  418 

147.  '•  "  •'         *•       41S 

148.  '*        Cycle  Gas-engine 419 

M9-  "  "        "  "       419 

155.  Barnett  Igniting-cock 422 

156.  Indicator-diagram  Gas-engine 425 

157-  "  "  '•         "        425 

15S.  ••  •'  "         *•        425 

159-  "  "  "         •'        426 

160.  "  ••  "         •' 426 

i6r.  "  •'  "         "        426 

162.  "  *•        from  Separate  Cylinder 427 

163.  "  *•        Ideal 432 

164.  Temperature-entropy  Diagram  for  Gas-engine 433 

if^5.  ••  ' •        435 

166.  '•  ••  '*       "         ••       437 

167.  '*  "  •'       ••         ••        439 

168.  *•  ••       440 

169.  "  "  "       *•         **        446 

170.  Diesel  Gas   or  Oil  Motor 448 

171.  "         "     *'     "         "       Card 448 

173.   Section  of  Otto  Gas-engine  Slide-valve 453 

175.  Ideal  Indicator-diagram  of  Vapor-engine 456 

176.  ••  ••  "  ••  **  463 

177.  "  "  "  "  '•  466 

17S.       "  "  "  ••  •*  469 

179.   Naphtha-launch  Engine 474 

183.    Binary  Engine 475 

181.   Diagram  illustrating  Series  Engine 479 

185.  Type  Scheme  of  Heating  and  Refrigerating  Organs 483 

186.  '*  "         *'  Organs  Bell-Coleman  Ice-machine 490* 


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LIST   OF  ILLUSTRATIONS.  XXI 

TIG.  I'AGK 

187.  Pressure-volume  Diagram  of  Bell-Coleman  Ice-machine 491 

188.  Ammonia  Compression  Refrigerating-machine  495 

189.  "  Absorption  Refrigerating-machine 498 

190.  Temperature-entropy  Diagram  for  Refrigerating  Machine 499 

191-  "  "  "  "  "         501 

192.  "  "  **  "  " 501 

193-  **  •*  *•  *•  "         502 

194.  Wellington  Series  Engine 477 

195.  Temperature-entropy  Diagram^  of    Refrigeration   by  a   Step-by- 

step  Process 506 

196.  Type  Section  of  Injector 515 

197.  Self-adjusting  Injector 521 

198.  Double-tube  Injector 521 


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HEAT   AND  HEAT-ENGINES. 


CHAPTER    I. 
INTRODUCTORY. 

1.  Sources  of  Motor  Energy. — There  are  three  great 
sources  of  force  or  energy  for  industrial  uses.  The  first  to  be 
utilized  is  the  force  resident  in  the  contractile  tissue  of  the 
muscles  in  man  and  animals,  which  is  known  as  muscular  force. 
The  second  is  called  the  force  of  gravity  and  is  the  force  by 
^hich  the  earth  attracts  all  masses  toward  its  centre.  The 
third  is  the  group  of  forces  which  become  manifest  or  are  re- 
leased upon  chemical  reactions  such  as  combustion  or  oxida- 
tion ;  the  two  most  important  of  these  latter  are  the  forces 
of  heat  and  electricity. 

2.  Limitations  of  Muscular  Force  and  the  Force  of 
Gravity. — While  the  muscular  force  of  men  and  animals 
varies  with  the  race,  species,  size,  health,  training,  tempera- 
ment, and  muscular  endowment  of  the  individual,  yet  certain 
fixed  limits  are  set  to  the  amount  of  energy  to  be  gotten 
from  any  single  unit.  Large  powers  can  only  be  obtained  by 
aggregating  many  units,  which  is  inconvenient  and  costly; 
but  more  than  all,  a  limit  is  set  by  the  endurance  of  the  ani- 
mal unit,  which  must  have  periods  of  rest  and  recuperation. 
Speed  is  also  limited  by  the  ability  of  the  animal  motor  to 


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2  HEAT  AND   HEAT-ENGINES. 

maintain  a  maximum  effort  f^r  any  length  of  time.  Finally, 
there  is  no  considerable  reserve  store  of  energy  to  be  drawn 
npon  if  more  effort  is  required. 

The  force  of  gravity  becomes  available  as  a  motor  force 
v/hen  a  weight  or  mass  is  lifted  to  a  higher  level  and  is  per- 
mitted to  descend  to  a  lower  one.  Solid  weights  are  only 
serviceable  when  lifted  by  some  other  mechanical  force;  water 
and  air  are  the  only  weights  which  are  otherwise  lifted  further 
from  the  centre  of  the  earth  independent  of  man.  The 
former  is  lifted  by  the  sun  in  vapor  to  high  levels  of  land, 
whence  it  seeks  to  descend  to  tide-water  level  again ;  and  the 
winds  are  produced  when  colder  and  heavier  air  descends 
and  displaces  the  lighter  air  which  the  earth  has  warmed. 
Gravity,  therefore,  as  a  motor  force  is  dependent  upon  the 
availability  of  higher  levels  of  land  at  which  a  sufficient  mass 
of  water  can  be  accumulated,  and  an  adequate  reservoir  in  any 
particular  region  or  an  adequate  flow  from  a  source  is  a  neces- 
sary condition  for  the  use  of  water-motors;  and  while  there  is 
an  abundance  of  energy  present  in  the  atmospheric  ocean  at 
the  bottom  of  which  all  industry  is  carried  on,  yet  at  present 
the  reliability,  controllability,  and  capacity  which  must  be- 
long to  the  satisfactory  working  of  an  industrial  motor  are 
lacking  to  windmills  in  most  places  except  where  used  for 
pumping  or  where  they  can  be  used  to  store  some  other  form 
of  energy  in  accumulators. 

This  same  series  of  difficulties  has  beset  the  successful  ap- 
plication of  the  energy  stored  by  the  winds  and  other  disturb- 
ances in  the  ocean  waves.  Tide-motors  depend  upon  the 
lifting  of  the  ocean  level  by  the  stellar  or  planetary  attrac- 
tions, and  are  reliable  and  controllable,  although  only  made 
of  large  capacity  at  great  cost;  but  the  types  of  motors  as 
yet  devised  to  use  the  impact  or  lifting  force  of  coast-waves 
have  not  proved  reliable  or  permanent  enough  for  engineers 
to  venture  to  adopt  or  install  them. 

Since  it  is  the  sun's  heat    energy  which  lifts  the  water 


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IN  TKOD  ULTOR  Y.  3 

and  disturbs  the  equilibrium  of  the  strata  of  air,  it  would  ap- 
pear that  water-motors  and  windmills  are  in  this  sense  heat- 
motors  in  the  last  reduction. 

3.  Importance  of  the  Motor  Energy  Liberated  on  Com- 
bustion.— It  will  be  at  once  apparent,  on  a  moment's  thought, 
that  while  the  energy  resident  in  falling  water  is  most  ser- 
viceable and  is  destined  to  become  more  so  as  the  means  of 
transmitting  energy  are  improved,  yet  there  are  many  causes 
which  have  acted  to  make  the  use  of  the  steam-engine,  the 
gas-engine,  and  the  hot-air  engine  by  far  the  most  widespread 
at  this  time.  The  energy  in  falling  water  with  a  few  notable 
exceptions  is  limited  in  amount  both  by  the  weight  available 
and  by  the  height  of  fall;  while  in  combustible  fuel  or  oil  or 
gas  there  is  stored  an  amount  of  available  energy  which  is 
practically  unlimited  where  the  supply  of  combustible  is  not 
limited.  The  energy,  moreover,  is  in  a  compact  bulk;  fuel 
can  be  had  native  in  many  regions  where  there  is  no  head  of 
water,  and  where  fuel  is  not  native  it  can  easily  be  trans- 
ported. It  will  be  seen,  therefore,  that  the  study  of  those 
forms  of  motors  which  are  so  widespread  compels  the  study 
of  the  laws  and  principles  which  underlie  the  phenomena  of 
heat,  and  that  the  general  name  of  heat-engines  may  properly 
be  applied  to  such  engines. 

While  every  one  believes  that  the  near  future  is  to  reveal 
methods  for  generating  or  liberating  energy  directly  from  fuel 
in  the  form  of  electromotive  force,  and  this  is  now  done  by 
the  chemical  reactions  which  occur  in  various  electric  batter- 
ies, yet  at  this  writing  the  importance  and  extent  of  the  appli- 
cations of  such  methods  make  them  lie  in  the  province  of  the 
physicist  still,  rather  than  in  that  of  the  engineer. 

4.  Analysis  of  a  Power  Plant. — The  industrial  result  in  a 
pow^er  plant  is  the  production  of  something  which  shall  have 
a  commercial  or  salable  value.  This  may  be  a  manufactured 
article,  or  it  may  be  a  safe  transportation  of  goods  or  persons 
for  which  the  community  shall  be  willing  to  pay.     Hence  the 


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4  HEAT  AND   HEAT-ENGINES. 

last  link  in  the  power-plant  chain  will  be  as  extensive  as  the 
entire  field  of  industry. 

The  first  step  or  link  is  the  generation  or  liberation  of  en- 
ergy to  furnish  the  necessary  power.  In  the  heat-engine 
this  occurs  where  the  combustible  fuel  is  burned  in  a  proper 
furnace  or  fire-box.  This  liberated  or  generated  energy  must 
be  suitably  stored  in  a  reservoir  or  accumulator  from  which  it 
may  be  drawn  ofT  as  required.  In  a  steam  plant  this  function 
13  discharged  by  the  boiler;  in  gas-engines  this  storage  step 
is  lacking.  In  water-power  plants  the  liberation  and  storage 
are  done  for  the  engineer  either  before  his  work  begins,  or 
else  the  storage  reservoirs  or  dams  become  very  important 
features  of  his  undertaking.  The  third  step  or  link  is  the 
appliance  whereby  the  energy  stored  in  the  second  step,  and 
held  as  potential  energy,  shall  be  transformed  into  actual 
energy  by  being  permitted  to  act  through  a  prescribed  path 
under  the  control  of  a  capable  intelligence.  This  appliance 
is  the  engine  or  motor,  which  must  be  adapted  to  the  force 
which  is  to  be  utilized  both  as  to  capacity  and  as  to  form,  and 
which  demands  a  knowledge  of  the  laws  and  properties  which 
attach  to  the  medium  whereby  the  energy  is  revealing  itself. 
Fourth  in  the  chain  comes  the  machinery  of  transmission, 
whereby  the  motion  of  the  motor  or  engine  and  its  develop- 
ing power  shall  be  adapted  or  properly  transformed  to  meet 
the  uses  and  purposes  of  the  machine  whereby  manufacturing 
or  transportation  is  eflfected  at  the  industrial  end  of  the  series. 

The  subject  of  transmission  of  power  is  by  itself  so  im- 
portant and  extensive,  and  the  industrial  field  so  limitless, 
that  power-plant  study  may  properly  be  limited  to  the  other 
or  first  three  steps  for  convenience.  The  water-motor  and 
the  wind-motor  will  also  be  excluded  from  present  considera- 
tion for  the  sake  of  confining  the  scope  of  study.  The  field 
will  therefore  become  that  which  embraces  the  generation  or 
liberation  of  energy  in  the  form  of  heat,  and  the  utilization 
of  that  energy  in  the  heat-engine. 


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IN  TROD  UCTOR  K.  5 

5.  Scheme  of  Classification. — In  this  view  the  subject  of 
heat  and  heat-engines  will  group  itself  for  study  under  the 
following  heads: 

I.   General    Notions  on    the    Phenomena   manifested    in 
Heat-engines. 
II.  Sources  of  Heat,  or  Fuels;  Generation  or  Liberation 
of  Heat.     Combustion. 

III.  Transfer  of  Heat.     Heating-surface. 

IV.  Media  used  to  Transfer  Heat  Energy  to  Engine-orgars. 

Properties  and  Physical  Laws. 
V.  Work  done  by  a  Heat  Medium ;  Relations  of  Heat  and 
Force  in  Expansion  and  Compression,     Cylinder 
Design. 
VI.  Thermal  Analysis  of  a  Heat-engine.     Heat  Cycle  and 
Efficiency. 


VII.  Air-Compressor  and  Compressed-air  Engine. 
VIII.   Hot-air  Engines. 
IX.   Internal-combustion  Engine.      Gas-  and  Oil-engines. 
X.  Vapor-engine. 
XI.   Mechanical  Refrigeration. 
A  final  chapter  on  the  Injector  is  appended. 

It  will  be  observed  that  the  latter  sections  are  in  a  sense 
to  be  viewed  as  the  fuller  application  of  the  principles  dis- 
cussed in  the  first  six  headings. 


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CHAPTER    II. 

GENERAL    NOTIONS    ON  THE   PHENOMENA    MANIFESTED 
IN  HEAT-ENGINES. 

6.  General  and  Introductory. — In  order  that  the  en- 
gineer may  have  a  satisfactory  form  of  motor,  it  must  be  one 
in  which  an  adequate  force  acts  through  the  desired  space  in 
a  unit  of  time.  A  force  of  inimitable  extent  is  of  no  practi- 
cable value  unless  it  is  exerted  through  a  finite  and  measura- 
ble space.  Hence  every  real  engine  has  an  organ  capable  of 
receiving  the  action  of  a  force  or  effort,  and  capable  of  mov- 
ing through  a  constrained  path  under  the  action  of  that  eflfort, 
while  the  force  is  overcoming  the  resistance  moving  through 
the  required  distance.  In  countries  which  use  and  prefer  the 
metric  system,  the  unit  of  force  is  the  kilogram,  and  the  unit 
of  path  is  the  meter.  The  product  of  effort  into  its  path  is 
called  worky  and  the  unit  of  work  is  a  kilogrammeter.  Where 
the  pound  is  the  unit  of  force,  and  the  foot  is  the  unit  of  path 
traversed  by  the  effort,  then  the  work  will  be  expressed  by 
their  product  as  before,  but  the  work-unit  will  be  in  foot- 
pounds. For  a  large  output  of  work  from  a  motor,  the  foot- 
pound or  kilogrammeter  is  inconveniently  small ;  hence  mul- 
tiples are  usual.  The  accepted  standard  as  evaluated  by 
James  Watt  from  experiment  is  that  called  a  *'  horse^power," 
and  is  equivalent  to  a  work  of  33,000  foot-pounds  done  in 
one  minute.     The  equivalents  of  the  horse-power  are: 

6 


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PHENOMENA    MANIFESTED    IN  HEAT-ENGINES, 


Horse-power. 

English 
Foot-pounds 
per  Minute. 

French 

Kilogramroeters 

per  Minute. 

Austrian 
Foot-pounds 
per  Minute. 

English  and  American. . . . 
French 

33,000 

32,545.2 

33.034-2 

4,562.46 

4,500 

4,567.14 

25,233.6 
25,420.8 
25,800 

Austrian 

The  metric  horse-power  is  more  usually  expres.sed  as  75 
Icilogrammeters  per  second.  The  unit  of  electric  output  is 
known  as  the  Watt,  and  represents  a  work  in  foot-pounds 
equivalent  to  -^^-^  of  a  horse-power.  One  thousand  watts  or 
a  kilowatt  is  therefore  equal  to  1.34  horse-power. 

In  heat-engines  the  universal  practice  is  to  have  the  eflfort 
which  overcomes  the  resistance  take  the  form  of  a  pressure 
of  a  gas  or  vapor  exerted  upon  a  given  area.  It  will  appear 
hereafter  how  and  why  the  heat  produces  pressure.  If  the 
elastic  tension  of  the  gas  or  vapor  be  expressed  in  pounds 
per  square  inch,  and  its  pressure  is  exerted  upon  a  disk  or 
piston  which  fits  a  cylinder  without  leakage  and  which  has  an 
area  expressible  in  square  inches,  then  the  product  of  the 
pressure  into  the  area  in  these  units  will  give  a  total  effort  in 
pounds.  If  the  unit  be  the  kilogram  per  square  centimeter, 
-and  the  area  be  in  square  centimeters,  the  effort  will  be  in 
kilograms.  The  piston  therefore  must  move  through  the 
necessary  number  of  feet  or  meters  per  minute,  in  order  that 
the  horse-power  required  may  be  generated.  Hence  if  5 
-denote  the  space  in  the  desired  units  through  which  the  effort 
PA  in  the  corresponding  units  is  made  to  move  in  one 
minute,  then  the  total  work  of  one  minute  will  be  PAS  in 
the  required  compound  unit  of  foot-pounds  or  kilogrammeters. 
Since  the  usual  heat-engine  cylinder  is  of  comparatively  short 
length  for  convenience  of  construction,  the  common  require- 
ment is  that  the  piston  which  fits  it  must  traverse  its  short 
length  many  times  in  one  minute.  If  L  denote  the  length  of 
the  traverse  of  the  piston  in  meters  or  feet,  and  N  denote  the 
number  of  times  this  traverse  is  made  in  one  minute,  then  the 


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8  ffEA  T  AND   HE  A  T^ENGINES. 

initial  5  above  may  be  replaced  by  LN\  whence  the  work- 
expression  becomes 

Work  =  PALN 

in  whatever  units  are  used.  Since  the  horse-power  of  the 
engine  will  be  as  many  as  the  number  of  times  that  the  unit 
33,000  is  contained  in  the  total  work  in  foot-pounds,  the 
above  will  become 

Work_  PALN 

33000""      •    •  "■   33000' 

Furthermore,  if  A  be  expressed  in  square  feet  instead  of 
square  inches,  then  AL  represents  the  volume  of  the  cylinder 
in  cubic  feet  effectively  filled  at  the  end  of  each  traverse  of 
the  piston,  and  if  N  denotes  the  number  of  times  per  minute 
that  this  volume  is  filled,  it  follows  that  the  work-expressioa 
can  be  written 

Work  =  PZ:^iV=PF, 

when  V  denotes  the  volume  ^filled  in  a  unit  of  time  by  the 
working  vapor  or  gas  which  causes  the  pressure  P  in  the 
cylinder.  The  latter  now  must  be  given  in  pounds  per  square 
foot.  PV  is  therefore  a  very  general  expression  for  work  in 
foot-pounds  per  unit  of  time.  It  can  also  be  used  to  express 
the  foot-pounds  of  work  done  in  one  stroke  of  an  actual 
engine  if  N  be  called  unity,  or  the  work  done  by  one  unit 
weight  of  vapor  which  occupies  a  specific  volume  V. 

A  steam-»  gas-,  air-,  or  vapor-engine  operating  so  as  to 
make  the  foregoing  discussion  apply  to  it  may  conveniently 
be  designated  by  the  general  name  of  a  piston-engine,  and 
this  term  will  be  generally  used  for  such  machines  in  the 
discussions  which  follow.  It  applies  equally  well  to  a  pump 
in  which  a  fluid  resistance  represented  by  P  in  pounds  per 
square  foot  is  overcome,  and  a  volume  Fof  the  fluid  in  cubic 
feet  is  displaced  in  one  minute,  whether  by  piston  or  by 
plunger. 

7.  Graphic  Representation  of  the  Work  of  a  Piston- 
engine. — Since  the  work  of  a  piston-engine  is  the  product  of 


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PHENOMENA   MANIFESTED   IN  HEAT-ENGINES  9 

two  factors — feet  multiplied  by  pounds,  or  foot-pounds, — it 
is  obvious  that  a  closed  figure  can  be  drawn  enclosing  an 
area  which,  upon  an  assumed  scale  of  units,  shall  be  the  same 
*as  the  given  product  in  foot-pounds.  Furthermore,  what- 
ever the  shape  of  that  figure,  a  rectangle  can  be  drawn  the 
product  of  whose  base  into  its  altitude  will  give  the  same 
area,  or  represent  that  same  number  of  foot-pounds  of  work. 

In  piston-engines  it  will  become  manifest  later  that  the 
figure  representing  the  work  takes  a  small  number  of  typical 
shapes.  It  is  convenient  to  agree  to  represent  pounds  by  the 
vertical  ordinates,  parallel  to  the  coordinate  axis  of  F,  and 
to  represent  feet  by  the  horizontal  abscissae,  parallel  to  the 
coordinate  axis  of  X.  A  piston-engine  can  then  be  made  to 
draw  its  own  work-diagram  by  a  simple  device.  If  the  pres- 
sure P  from  the  storage  source  of  supply  which  is  to  force 
the  piston  forward  be  also  let  into  a  small  cylinder  of  known 
area  of  cross-section,  and  bear  upon  a  piston  in  that  cylinder 
whose  motion  is  resisted  by  a  calibrated  spring,  then  the  pis- 
ton effort  and  spring  distortion  will  balance  at  a  certain  point. 
If  a  marking-point  or  pencil  be  attached  to  the  spring 
piston,  the  position  of  equilibrium  of  pressure  and  spring  can 
be  marked  and  noted.  Further,  if  the  motion  of  the  engine- 
piston  be  given  to  a  board  or  drum  in  a  horizontal  direction, 
while  the  pencil  which  is  controlled  by  the  calibrated  spring 
travels  vertically,  the  condition  is  fulfilled  of  having  the  hori- 
zontal dimensions  of  the  traced  diagram  represent  feet  or  be 
proportional  to  feet,  while  the  vertical  dimensions  represent 
pounds  or  are  proportional  to  pounds.  An  instrument  em- 
bodying this  principle,  and  modified  to  conform  to  conditions 
of  convenience  and  accuracy,  is  called  the  Indicator. 

If  the  P.V.  form  of  the  expression  for  work  is  preferred, 
th^n  the  horizontal  lines  will  be  proportional  to  volumes. 
The  linear  length  of  the  engine-stroke  must  be  multiplied  by 
a  factor  representing  the  area  A  of  the  engine-piston.  In 
the  first  case,  the  area  of  the  work-diagram  gives  the  work 
per  each  square  inch  of  area  of  the  engine-piston,  and  must 


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10 


HEAT  AND   HEAT-ENGINES. 


be  multiplied  by  the  same  area  A  to  give  the  work  of  the 
entire  piston.  Hence  either  method  may  be  followed  as  is 
most  convenient. 

The  simplest  case  of  work-diagram  is  presented  in  Fig.  i. 

Here  the  pressure  P 

^ >w    from    the    boiler    or 

reservoir  is  constant 
throughout  the  stroke 
of  the  engine,  and 
the  diagram  is  es- 
sentially a  rectangle. 
If,  however,  the  pres- 
sure is  not  constant 
(and  it  will  be  seen 
hereafter  to  be  de- 
sirable that  it  should 
not  be)  throughout  the  whole  stroke,  then  the  general  form 
of  the  diagram  will  be  that  of  Fig.  2.     Here,  beginning  at 


Fig.  1. 


e 


MXNitfimK  I 


Pro.  2. 


the  upper  right-hand  corner,  there  is  an  admission  at  constant 
pressure   up  to  the   end   of   the   upper  horizonta;   line    and 


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PHENOMENA    MANIFESTED   IN  HEAT-ENGINES.         II 

then  a  fall  of  pressure  gradually,  as  given  by  the  curved  lines, 
indicating  a  variable  or  varying  pressure  down  to  the  lower 
left-hand  end.  The  curves  at  the  right  and  left  sides  of  Fig. 
2  indicate  a  variation  of  pressure  with  volume  of  cylinder; 
and  the  law  of  such  variation  (if  there  is  one)  has  obviously 
a  considerable  effect  on  the  work  done  in  a  piston-engine  per 
stroke.  It  further  deserves  study  to  ascertain  what  it  is 
which  causes  a  variation  in  the  vertical  distance  apart  of  the 
upper  and  lower  lines  of  the  work-diagram  and  what  are  the 
laws  of  its  action.  These  obviously  affect  also  the  power  to 
be  gotten  from  the  engine. 

Here,  then,  is  the  problem.  The  proportions  of  the 
work-diagram  in  a  heat-engine  as  to  size  and  shape  are 
aflfected  by  heat.  What  is  heat,  and  what  are  its  laws  and 
principles? 

There  are  other  diagrams  which  may  be  drawn  to  present 
the  operation  of  heat-engines,  besides  the  pressure-volume  dia- 
gram above  discussed.  These  will  be  referred  to  in  their 
proper  connection  hereafter,  and  after  the  indicator  (or 
P.V.)  diagram  has  been  considered. 


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CHAPTER    III. 
GENERAL  NOTIONS  ON  HEAT. 

8.  Introductory. — It  should  be  stated  at  the  very  outset 
of  study  that  the  essence  or  nature  of  what  is  called  heat  is 
not  known.  Like  the  nature  of  the  force  of  gravity  or  the 
vital  force,  a  mystery  as  yet  impenetrable  shrouds  every- 
thing concerning  it  except  the  phenomena  which  it  occasions. 
Hence  it  has  been  the  function  of  the  physicist  and  mathe- 
matician to  find  hypotheses  or  assumptions  which  shall  ex- 
plain and  agree  with  the  phenomena,  and  which  shall  further 
enable  predictions  to  be  made  as  to  the  results  to  be  antici- 
pated with  untried  combinations.  Such  hypotheses  or  theo- 
ries must  explain  and  agree  with  ^z// phenomena  if  they  are  to 
be  acceptable,  and  one  discordant  or  unexplained  phenome- 
non is  sufficient  to  throw  doubt  on  the  working  theory  then 
in  general  acceptance. 

It  belongs  to  the  province  of  the  physicist  rather  than  to 
that  of  the  engineer  to  review  the  theories  concerning  heat 
which  have  heretofore  prevailed.  Fortunately  it  is  not 
necessary  for  the  engineer  to  be  conversant  with  the  refine- 
ments of  theory  to  be  able  to  use  its  general  principles  with 
inteirigence. 

The  universally  accepted  theory  of  heat  is  based  upon  the 
postulate  which  is  known  as  the  Conservation  of  Energy. 
This  announces  that  force  is  as  indestructible  as  matter,  and 
that  the  most  which  happens  to  energy  when  apparently  dis- 
sipated is  its  conversion  into  other  forms  of  energy,  just  as 

12 


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GENERAL  NOTIONS   ON  HEAT.  1 3 

matter  is  converted  into  other  forms  of  matter  when  a  com- 
bination is  apparently  destroyed.  This  theory  is  known  as 
the  Dynamic  Theory  of  Heat  or  the  Mechanical  Theory  of 
Heat,  and  its  axiom  is  that  **Heat  is  a  Mode  of  Motion.** 

9.  Mechanical  Theory  of  Heat. — The  phenomena  of  the 
conversion  of  work  into  heat  have  been  long  observed  in  the 
effects  of  impact,  of  heat  from  rubbing  friction  and  abrasion, 
and  the  like.  Rumford's  historic  experiment  (1798),  Davy's 
investigations  (1799),  and  the  work  of  other  physicists  led 
up  to  the  work  of  Dr.  Julius  Robert  Mayer  of  Heilbronn 
(1832- 1 842)  in  Germany,  and  the  quantitative  research  into 
the  convertibility  of  work  into  heat  by  Dr.  Joule  of  Man- 
chester, England  (i?43).  Later  Sir  William  Thomson  (1850) 
extended  analogous  principles  to  electricity,  and  the  name 
Thermodynamics  has  been  applied  to  the  science  which  is 
concerned  with  the  relations  between  heat  and  mechanical 
energy  under  all  conditions. 

The  fundamental  law  of  thermodynamics,  sometimes  called 
the  first  law,  is  that  Heat  and  mechanical  ejtergy  are  mu- 
tually convertible;  and  heat  requires  for  its  production  and 
produces  by  its  disappearance  mechanical  energy  in  the  propor- 
tion of  yy8  foot'pou7ids  for  each  British  thermal  unit.  This 
law  is  physical  and  experimental:  it  is  a  deduction  from  phe- 
nomena and  tests,  rather  than  an  intuition  or  an  axiom. 

10.  The  Mechanical  Equivalent  of  Heat. — The  factor 
778  was  originally  determined  by  Joule  to  be  772 ;  later  de- 
terminations give  it  the  higher  value  (Rowland).  Joule's 
experiment  was  to  find  the  weight  which,  falling  through  one 
foot  in  height,  would  produce  an  amount  of  heat  sufficient  to 
raise  one  pound  of  water  one  degree  on  the  Fahrenheit  ther- 
mometer-scale. This  factor  is  called  the  mechanical  equiva- 
lent of  heat;  in  metric  units  it  has  a  similar  definition,  but 
the  value  of  the  factor  is  426.8  kilogrammeters  per  kilogram 
of  water  raised  1°  centigrade.  Out  of  respect  to  its  first 
investigator  it  is  usually  designated  by  the  first  letter  of  his 


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14  ffEA  T  AND   HEA  T-ENGINES, 

name,  and  is  represented  in  formulae  by  the  initial  y.     Its  re- 
ciprocal, or  -jy  is  often  designated  by  the  capital  letter  A, 

11.  The  British  Thermal  Unit. — In  enunciating  the  first 
law  of  the  accepted  theory  of  heat,  the  words  British  Ther- 
mal Unit  were  used.     What  is  a  thermal  unit? 

The  thermal  unit,  or  unit  of  heat,  is  the  quantity  of  heat 
or  the  corresponding  energy  in  foot-pounds  which  will  raise  a 
unit  of  weight  of  water  through  one  degree  of  the  accepted 
scale  of  a  thermometer.  The  British  thermal  unit  is  therefore 
the  quantity  of  heat  or  energy  which  raises  one  pound  of 
water  one  degree  Fahrenheit;  the  metric  unit  is  the  quantity 
of  heat  or  energy  which  will  raise  one  kilogram  of  water  one 
degree  on  the  centigrade  scale.  The  metric  unit  is  called 
the  calorie  and  is  3.968  (roughly  4)  times  the  B.T.U. 
Strictly,  the  B.T.U.  is  the  heat  required  to  raise  one  pound 
of  water  from  39°  to  40°  Fahrenheit,  and  the  calorie  is  the 
heat  necessary  to  raise  one  kilogram  of  water  from  4°  to  5° 
centigrade.  These  figures  are  those  at  which  water  has  its 
greatest  density  from  experiment.  Many  engineers  and 
writers  use  the  temperature  of  melting  ice  as  the  starting- 
point,  and  recent  British  and  French  authorities  prefer  to  use 
62**  Fahrenheit  or  15°  Centigrade  as  the  base.  This  differ- 
ence will  explain  some  discrepancies  among  accepted  authori- 
ties upon  these  questions. 

12.  Specific  Heat. — It  must  follow  from  §  9  that  if  heat 
and  energy  are  mutually  convertible,  then  different  bodies 
must  vary  with  respect  to  their  capacity  for  receiving,  stor- 
ing, and  giving  out  this  energy.  In  the  general  field  of  me- 
chanical science  it  has  been  found  that  the  measure  of  stored 
energy  in  a  moving  organ  of  a  machine  or  a  free  body  is  made 
up  of  the  product  of  its  Mass  by  the  half-square  of  its  veloc- 

ity  of  motion  1 1.      In  molecular  or  atomic  motions  such 

as  those  in  question  in  heat-motion,    the  same  conceptions 


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GENERAL  NOTIONS   ON  HEAT.  1$ 

are  supposed  to  apply,  the  only  differences  being  the  infin* 
itesimal  character  of  the  atomic  mass,  and  the  probably  in- 
conceivably great  velocity  of  the  motion — whatever  it  may 
be.  Hence  the  mind  is  ready  to  accept  the  observed  fact  of 
such  great  differences  in  the  thermal  capacities  of  different 
bodies,  and  also  the  differences  in  the  same  body  in  different 
states. 

Speaking  generally,  then,  the  quantity  of  heat  or  energy 
which  is  required  to  raise  a  unit  mass  of  a  substances  by  one 
heat-unit  will  be  called  its  specific  heat.  It  will  be  seen  here- 
after that  this  general  statement  needs  to  be  guarded  in  cases 
where  any  other  change  occurs  by  heat  applied  to  a  body  be- 
sides an  increase  in  its  temperature  (see  §  1 16).  The  specific 
heat  of  bodies,  solids,  liquids,  vapors,  and  gases  requires  to 
be  experimentally  determined  by  the  physicist  in  the  labora- 
tory. Tables  of  specific  heats  appear  in  an  Appendix. 
Water  has  a  specific  heat  of  unity  by  agreement  among  ex- 
perimenters, both  because  its  value  is  so  large,  and  also 
because  it  is  so  conveniently  used  in  comparisons  and  trans- 
fers. 

13.  Temperature. — It  follows  from  the  mechanical  theory 
of  heat  and  the  above  discussion  that  temperature,  as  meas- 
ured by  the  appliance  called  a  thermometer  or  by  the  human 
sensorium,  is  not  a  measure  of  the  amount  of  heat  energy 
resident  in  any  two  or  more  different  bodies  or  masses.  It  is 
an  indication  of  its  intensity,  however,  and  of  that  portion  of 
the  total  energy  which  can  affect  the  senses  of  the  observer. 
An  experiment  to  show  this  is  made  by  taking  equal  weights 
of  two  bodies  like  iron  and  water  at  the  same  temperature, 
and  putting  them  into  another  quantity  of  some  liquid  at 
another  temperature.  The  water  will  transfer  much  the  more 
heat  to  the  liquid. 

It  will  appear  shortly,  however,  that  the  product  of  the 
mass  or  weight  by  its  specific  heat  and  by  its  temperature 
(the  latter  being  properly  observed)  will  give  a  measure  of  the 


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l6  HEAT  AND   HEAT-ENGINES. 

heat  energy.  Of  two  bodies  of  the  same  substance  and 
therefore  having  the  same  specific  heat,  but  being  at  different 
temperatures,  and  near  each  other,  the  hotter  body  tends  to 
become  cooler,  and  the  cooler  body  becomes  hotter  by  the 
receipt  of  transferred  heat-motion.  Heat  passes  of  itself 
from  a  hotter  to  a  cooler  body,  but  this  process  does  not 
reverse  except  by  introducing  a  factor  of  mechanical  energy 
to  cause  it  to  do  so. 

14.  Thermometers. — Appliances  for  measuring  or  ob- 
serving differences  in  temperature  (but  not  differences  of  heat 
necessarily)  are  called  thermometers.  Most  of  them  depend 
upon  the  property  of  a  liquid — mercury  or  alcohol — whereby 
it  expands  equally  for  constant  increments  of  temperature 
(see  §  113).  If  the  liquid  is  confined  in  a  tube  of  fine  calibre, 
the  expansion  is  easily  read  on  a  properly  graduated  scale. 
Solids  have  this  same  property  of  expansion  by  heat,  and  can 
be  used  for  higher  temperatures.  They  are  then  often  called 
pyrometers.     Gases  can  also  be  used  in  thermometry. 

Without  entering  too  deeply  into  this  subject,  there  are 
two  fixed  points  of  temperature  which  are  used  in  graduat- 
ing thermometers:  the  point  at  which  ice  melts,  and  the 
point  at  which  water  boils  under  a  pressure  of  one  atmos- 
phere.^'. Thp  latter  is  that  given  by  Regnault's  determina- 
tions, of  14.7  pounds  per  square  inch  above  vacuum,  or 
2 1 16.2  pounds  per  square  foot. 

The  Fahrenheit  scale  calls  melting-ice  temperature  that 
denoted  by  32°  on  its  scale,  and  boiling- water  temperature  is 
212".     Its  zero-point  is  thus  32  degrees  lower  than  melting  ice. 

The  centigrade  scale  divides  the  180  degrees  Fahrenheit 
between  melting  ice  and  boiling  water  into  100  parts,  and 
places  its  zero  at  the  melting-ice  point. 

The  Reaumur  scale  divides  the  100  degrees  of  the  centi- 
grade scale  into  80  parts. 

The  transformations  from  one  scale  to  the  other  are  not 
difficult.     See  Appendix. 


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GENERAL  NOTIONS   ON  HEAT,  1/ 

15.  Air-thermometer. — At  high  temperatures  the  liquids 
used  in  thermometer-tubes  become  vapors,  and  at  low  tem- 
peratures the  liquids  freeze.  This  change  of  state  of  the 
registering  body  is  not  only  inconvenient,  but  is  accompanied 
by  inaccuracy  and  uncertainty  near  both  limits.  Hence  it 
has  been  sought  to  use  a  permanent  gas  as  a  thermometer, 
and  air  has  been  most  used  by  reason  of  its  convenience  and 
adaptability. 

In  principle  the  air  thermometer  consists  of  a  perfectly 
cylindrical  tube,  closed  at  the  bottom,  and  containing  a  quan- 
tity of  air  below  a  bubble  or  drop  of  mercury  in  the  tube, 
which  is  to  serve  as  a  register  for  the  expansion  of  the  air 
below  it.  If  the  air- volume  below  the  mercury  be  exposed  at 
the  pressure  of  one  atmosphere  (the  barometer  reading  29.922 
inches)  to  the  temperature  of  melting  ice,  and  the  position  of 
the  bottom  of  the  mercury  telltale  is  marked,  and  then  to  the 
temperature  of  boiling  water,  and  a  similar  mark  made  there, 
the  range  for  the  100  or  180  degrees  of  the  usual  thermonieter 
is  given,  and  the  fixed  points  are  determined.  Regnault's  in- 
vestigations showed  that  for  a  length  of  air-column  below  the 
lower  mark,  represented  by  unity,  the  length  from  the  bot- 
tom to  the  upper  mark  would  be  1.3665 — that  is,  the  expan- 
sion between  these  limits  is  0.3665  of  the  original  volume. 
Hence  it  would  appear  possible  to  graduate  such  a  tube  by 
means  of  this  property,  assuming  that  no  changes  in  other 
properties  occur  at  wide  ranges  beyond  the  range  of  experi- 
ence. The  graduation  upward  for  high  temperatures  offers 
nothing  unusual,  but  the  graduation  below  the  point  of  melt- 
ing ice  leads  to  an  interesting  inference. 

If  the  Fahrenheit  degrees  be  used  for  the  length  of  0.3665 
times  the  unit  length,  then  each  degree  of  the  air-thermom- 
eter has  a  length 

0.3665 

—^ —  =  0.0020361 1 

180  ^ 


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HEA  T  AND   HEA  T-ENGINES. 


Fig.  li, 
Ing-point  of 


of  the  unit  length  below  the  line  marked  for 
nnelting  ice,  or  for  each  degree  Fahrenheit  of 
increase  in  temperature  or  decrease  the  air- 
volume  increases  or  decreases  by  that  fraction 
of  its  length.  If  it  decreases  by  .i^TrW^TrTT  ^^  *^s 
length  for  each  degree  Fahrenheit,  then  at  a 
temperature  Fahrenheit  represented  by  491.13 
below  32°,  or  459.13  below  zero,  a  temperature 
must  be  reached  at  which  the  property  of  fur- 
ther reduction  of  volume  by  withdrawing  heat  or 
heat  energy  disappears.  In  other  words,  the 
body  appears  to  have  no  heat  energy  at  that 
point.  This  is  called,  therefore,  the  absolute 
zero  of  the  air-thermometer.  If  the  degrees  be 
numbered  from  this  point,  ice  melts  at  491.13** 
and  boils  at  671.13°.  For  centigrade  scale  of 
degrees  the  air-thermometer  zero  is  273°  below 
the  zero  of  the  ordinary  scale  at  melting-ice  tem- 
perature. Fig.  3  illustrates  a  form  of  air-ther- 
mometer, the  result  of  effort  by  Mr.  Fred  W 
Prentiss  and  the  late  J.  C.  Hoadley. 

16.  Absolute  Temperature. — If  air  were  a 
perfect  gas,  or  one  which  would  expand  exactly 
so  that  its  rate  of  expansion  would  be  the  same 
as  that  at  which  it  absorbs  heat,  the  air-thermom- 
eter scale  could  be  used  as  an  absolute  tem- 
perature scale.  It  is  practically  so,  and  will  be 
so  used  hereafter.  The  only  error  comes  in  de- 
termining the  zero  of  the  absolute  scale.  The 
work  of  Joule  and  Thomson  (1854)  and  that  of 
Rowland  (1879)  have  shown  the  discrepancies 
between  the  real  and  ideal  readings  (see  Ap- 
pendix). 

The  absolute  zero  as  computed  for  a  perfect 
gas  is  492.66°  F.,  or  273.7°  C,  below  the  melt- 
ice. 


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GENERAL   NOTIONS  ON  HEAT.  IQ 

The  significance  and  usefulness  of  the  absolute  scale  is 
very  great  in  work  with  heat  and  heat-engines.  In  fact  it  is 
indispensable.  From  what  has  preceded  (§§  9,  12,  13)  the 
total  heat  energy  present  in  any  body  at  any  time  will  be  the 
product  of  its  weight  by  its  specific  heat  by  its  absolute  tem- 
perature, when  no  energy  or  heat  is  in  process  of  absorption 
in  doing  work  upon  the  body  itself.  If  the  mass  is  a  unit  of 
weight,  and  two  differing  states  of  the  same  body  are  com- 
pared, then  the  difference  in  absolute  temperature  measures 
the  heat  energy  which  has  been  given  out  or  absorbed  under 
the  same  limitations. 

17.  Total  and  Intrinsic  Energy. — It  will  appear  finally 
from  the  foregoing  discussion  that  the  total  energy  resident 
in  a  body  is  not  always  to  be  evaluated  by  its  temperature 
or  by  the  thermometer  alone.  Part  of  it  may  be  measured 
when  changes  of  such  energy  occur,  when  the  specific  heat 
is  known,  and  the  initial  and  final  temperatures  absolute  or 
ordinary.  But  such  parts  of  the  heat  energy  as  are  taken  up 
in  changing  the  molecular  motion  of  the  atoms  of  the  body 
are  said  to  become  latent  or  hidden  because  the  usual  ap- 
pliances do  not  record  them,  and  by  certain  other  parts  of 
an  applied  heat  energy  an  external  work  in  foot-pounds 
may  be  done  which  the  thermometer  will  not  reveal  (§  in). 
It  is  obvious,  therefore,  that  some  attention  must  be  directed 
to  the  effects  of  heat  energy  upon  the  substances  upon  which 
it  acts,  and  the  means  of  producing  that  energy  or  liberating 
it  if  stored. 

The  latter  will  be  taken  up  first. 

Intrinsic  energy  in  a  body  is  its  capacity  for  performing 
work  by  virtue  of  the  heat  energy  resident  in  it,  without 
addition  of  such  energy  from  without.  The  zero  of  heat 
energy  is  at  the  absolute  zero.  The  inner  or  intrinsic  energy 
at  any  other  absolute  temperature  will  be  the  product  of  its 
weight  into  its  specific  heat  into  the  range  of  its  absolute 
temperature  above  absolute  zero. 


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CHAPTER    IV. 

GENERATION    OR    LIBERATION    OF    HEAT. 
COMBUSTION. 

18.  Introductory. — To  supply  the  energy  in  foot-pounds 
required  to  overcome  a  considerable  resistance,  and  to  do  this 
for  a  heat-engine  in  which  778  foot-pounds  shall  correspond 
to  one  heat-unit,  requires  that  there  shall  be  continually  in- 
troduced into  the  heat-engine  through  a  proper  organ  the 
necessary  supply  of  heat-units  in  each  unit  of  time.  From 
what  source  or  sources  shall  this  heat  and  energy  be  drawn  ? 
While  heat  appears  as  a  transformation  of  mechanical  energy 
in  friction,  impact,  abrasion,  attrition,  and  in  overcoming 
electrical  resistances,  these  sources  are  excluded  when  the 
object  sought  is  heat  which  may  itself  be  transformed  into 
mechanical  energy. 

19.  Heat  from  Combustion. — The  most  widespread,  con- 
venient, and  cheap  source  of  heat  has  been  found  as  the 
result  of  causing  the  oxygen  of  the  atmosphere  to  combine 
chemically  at  a  sufficiently  rapid  rate  with  certain  other  of 
the  chemical  elements.  Oxygen  combines  with  many  of  the 
metals  or  bases  or  elements  as  with  iron,  manganese,  boron, 
phosphorus,  and  the  like,  but  these  are  either  too  costly  to 
ser\'e  as  convenient  sources  for  heat,  or  else  the  process  of 
oxidation  is  so  slow  that  sufficient  heat  cannot  be  derived 
from  them  in  a  short  time. 

Combustion  may  be  defined  as  a  combination  with  oxygen 
which  takes  place  with  sufficient  rapidity  to  be  accompanied 
by  the  phenomena  of  heat  and  light.  The  elements  which 
are  found  to  possess  the  affinity  for  oxygen  which  is  required 

20 


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GENERA  TION  OR  LIBERA  TION  OF  HEA  T.  21 

for  combustion  are  Carbon  and  Hydrogen,  as  elements  or  as 
compounds.  Sulphur  often  enters  into  compounds  of  carbon 
and  hydrogen,  but  has  an  unimportant  position,  so  as  to  be 
usually  negligible.  A  carbon  or  a  hydrogen  element  or  a 
hydrocarbon  compound,  found  native  or  manufactured  so  as 
to  be  obtainable  in  sufficient  quantities  and  at  a  low  cost  to 
be  used  as  a  source  of  heat,  will  be  called  a  /ue/. 

20.  Certain  Phenomena  of  Combustion. — It  is  desirable 
to  secure  a  greater  exactness  of  conception  concerning  cer- 
tain facts  in  connection  with  the  generation  of  heat  from 
fuel. 

In  order  that  practical  combustion  of  a  fuel  may  occur,  it 
must  be  **  set  fire  to."  Ignition  is  the  beginning  of  active 
chemical  action,  and  the  first  step  in  a  combustion.  Most 
combustibles  require  to  be  raised  at  their  surface  to  a  certain 
temperature  before  this  ignition,  or  **  taking  fire  "  will  occur, 
or  if  kept  cooled  below  this  temperature  of  ignition  the  com- 
bination of  oxygen  will  not  occur,  or  will  cease  if  it  has  be- 
fore been  in  progress.  This  temperature  of  ignition  is  quite 
high  for  many  fuels,  and  its  maintenance  has  an  important 
bearing  upon  smoke-prevention.  Ignition  is  most  easily 
secured  by  a  flame,  and  a  flame  is  one  of  the  indications  of 
such  ignition. 

A  flame  is  a  body  or  current  of  gas  carrying  in  it  solid 
particles  at  such  a  temperature  as  to  glow  or  give  out  heat 
and  light.  These  solid  particles  are  usually  carbon  in  a 
finely  divided  state,  and  the  heat  of  the  flame  is  roughly 
measured  by  the  degree  of  the  incandescence  or  glowing  of 
these  particles.  A  red  flame  is  not  so  hot  as  a  yellow  flame, 
and  a  white  flame  is  the  hottest  of  all.  Flame  is  produced, 
when  the  supply  of  oxygen  at  the  place  where  ignition  oc- 
curs is  not  quite  sufficient  to  form  at  once  a  gaseous  product 
of  the  combustion.  When  the  supply  of  oxygen  is  copious 
and  means  are  taken  to  heat  it  and  mix  it  thoroughly  with 
the  combustible  matter,  then  the  heat  is  very  great  at  the 


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22  HEAT  AND   HEAT-ENGINES. 

point  of  combustion,  but  there  is  little  or  no  flame.  The  gases 
are  blue  or  colorless  and  have  little  heating  power  except  by 
contact.  The  heat  from  the  particles  glowing  in  the  flame  is 
given  off  from  a  large  extent  of  surface,  and  for  many  pur- 
poses the  flame  is  preferred  to  the  non-luminous  gas-current 
of  theoretically  perfect  combustion.  Purely  gaseous  sub- 
stances do  not  as  a  rule  become  luminous  by  heat. 

If  by  means  of  preheating  the  air  or  by  other  expedients 
a  great  elevation  of  the  temperature  of  ignition  be  secured, 
it  has  been  found  possible  to  exceed  the  limit  at  which  oxy- 
gen will  combine  with  carbon  or  hydrogen.  The  gases  move 
separately  without  uniting,  or  if  united  they  seem  to  sep- 
arate. This  excessively  high  temperature  is  called  the  *'  tem- 
perature of  dissociation  of  the  gases.*' 

In  the  combustion  or  ignition  of  solid  fuel  it  is  probable 
that  the  first  effect  of  the  heat  of  the  igniting  flame  is  to  dis- 
til off  from  the  surface  or  render  gaseous  a  thin  external  film, 
which  gas  combines  with  the  oxygen.  All  ignition  or  inflam- 
mation takes  place  at  the  surface  of  large  bodies  whether 
of  solid,  liquid,  or  gaseous  combustibles.  Hence  the  imper- 
ative necessity  of  intimate  mixture  of  oxygen  with  the  com- 
bustible gas  if  combination  is  to  take  place  in  a  short  period 
of  permitted  contact. 

Incandescence  is  strictly  to  be  defined  as  a  condition  of 
great  heat  energy,  accompanied  by  light  and  heat,  without 
-chemical  action.  True  incandescence  is  that  of  the  filament 
jn  an  incandescent  or  glow  electric  lamp.  The  so-called  in- 
candescence of  the  glow-worm  and  that  which  appears  in 
•forms  of  phosphorescence  and  fluorescence  are  so  called  only 
by  a  permitted  extension  of  the  term.  True  incandescence 
involves  the  idea  of  light  due  to  heat.  Incandescence,  how- 
ever, is  often  extended  to  include  the  condition  in  which  the 
chemical  action  is  quite  relatively  slow.  It  is  in  this  sense 
that  the  particles  of  glowing  carbon  in  a  flame-current  are  in- 
candescent, or  the  bed  of  coke  or  carbon   free  from   volatile 


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GEXEKATIOX  OR  LIBERATIOX  OF  HEAT,  23 

compounds  is  incandescent  when  undergoing  slow  combus- 
tion without  appearance  of  flame  or  gas. 

It  is  the  slowness  or  reluctance  of  the  combination  with 
oxygen  on  the  part  of  the  incandescent  particles  in  flame 
which  makes  perfect  combustion  of  luminous  flames  a  trouble* 
some  problem  in  some  cases.  If  the  carbon  particle  does  not 
burn  to  gas  while  hot  enough  to  unite  with  oxygen,  it  cools 
to  black-carbon,  lampblack,  or  soot.  A  current  of  gas  car- 
rjMng  such  solid  black  particles  in  it  is  called  **  smoke'*  in 
the  engineering  use  of  that  word, 

21.  Spontaneous  Combustion.  Explosion.  —  While  it 
usually  requires  the  heat  of  a  flame  to  start  combustion  by 
ignition,  yet  the  absorption  of  oxygen  by  a  body  in  a  favor- 
able condition  for  this  action  may  be  so  rapid  that  this  chem- 
ical combination  will  raise  the  temperature  of  a  combustible 
up  to  the  point  at  which  it  will  burst  into  a  flame.  This 
action  is  called  spontaneous  combustion.  Spontaneous  igni- 
tion would  be  a  better  term  and  more  exact.  The  condition 
favorable  for  it  is  the  presence  of  a  readily  oxidizable  body, 
<listributed  in  a  finely  divided  state  over  some  material  where- 
by a  great  surface  is  exposed  to  action  by  the  oxygen.  Oily 
Tags  and  greasy  waste  fill  this  condition,  and  both  are  par- 
ticularly liable  to  the  accident.  The  more  oxidizable  the  oil, 
the  worse  the  danger.  Vegetable  oils  are  particularly  liable 
to  this  rapid  action.  Coal-dust  in  bunkers,  by  reason  of  the 
oxidation  of  the  sulphur  in  it,  also  may  'set  fire  to  itself.  If 
the  heat  of  oxidation  can  be  conducted  off  as  fast  as  gener- 
ated, spontaneous  ignition  is  less  likely  to  occur,  but  as  a 
rule  the  porosity  which  exposes  a  large  surface  to  oxidation  is 
unfavorable  to  the  transfer  of  the  heat.  Capillary  action 
may  also  act  to  help  the  oxidizing  process. 

An  explosion  is  a  form  of  combustion  or  ignition  which  is 
practically  instantaneous,  or  so  rapid  that  a  large  volume  of 
gas  is  generated  and  fills  the  volume  previously  occupied  by 
the  material  which  has  been  transformed  into  gas  from  some 


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24  HE  A  T  AND   HE  A  T-ENGINES, 

less  bulky  form.  This  great  increase  of  volume  forces  the 
air  in  every  direction,  and  its  concussion  outward  or  its  return 
inward  causes  the  report  or  noise.  The  conditions  for  an  ex- 
plosion are  the  presence  of  combustible  gas  mixed  with  air 
and  brought  by  flame  at  some  one  point  to  the  temperature 
required  for  ignition;  or  the  combination  of  gasifying  solids 
with  others  rich  in  oxygen  and  ready  to  give  it  up,  and  the 
bringing  of  one  point  up  to  ignition  by  heat  or  friction  or  per- 
cussion. 

A  phenomenon  essentially  identical  with  an  explosion 
appears  when  an  atmosphere  is  full  of  a  combustible  dust  in 
a  finely  divided  state.  The  fine  division  produces  a  condi- 
tion analogous  to  that  when  spontaneous  combustion  is  prob- 
able; the  large  surface  for  oxidation  makes  the  gas  from 
combustion  form  so  copiously  and  rapidly  that  the  ignition 
is  practically  an  instantaneous  gasification  when  a  spark  or 
flame  is  introduced  into  such  an  atmosphere.  Coal-dust  in 
mines,  and  flour-dust  in  mills,  are  liable  to  this  form  of  rapid 
gasification. 

22.  Calorific  Power  of  a  Fuel. — It  will  be  obvious  that 
different  elements  and  different  compounds  will  differ  from 
each  other  in  their  ability  to  supply  heat  for  use  in  a  heat- 
engine.  The  Calorific  Power  of  a  fuel  is  the  amount  of  heat, 
expressed  in  thermal  units,  which  is  liberated  upon  the  com- 
bustion of  a  unit  of  weight  of  the  combustible  material.  The 
calorific  power  of  a  fuel  does  not  depend  upon  the  rapidity 
of  the  combustion  nor  on  the  time  taken  in  the  process  of 
absorbing  the  total  heat  of  the  combustion.  The  tempera- 
ture produced  by  the  combustion  does  depend  upon  the  rate 
of  combustion,  as  will  be  seen  in  the  next  paragraph. 

The  calorific  power  of  a  compound  is  the  sum  of  the 
calorific  powers  of  its  constituents.  If,  therefore,  the  calo- 
rific power  of  the  elements  carbon  and  hydrogen  have  been 
carefully  and  exhaustively  determined  in  the  physical  labora- 
tory, the  calorific  power  of  a  natural  fuel  or  an  artificial  mix- 


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GENERA  TION  OR  LIBERA  TION  OF  HE  A  T. 


25 


ture  may  either  be  computed  from  the  percentage  or  weight 
of  each  constituent  in  the  analyzed  fuel,  or  the  fuel  may  itself 
be  exposed  to  experimental  determination  of  its  calorific 
power  as  the  elements  were.  This  latter  method  is  the  most 
satisfactory. 

23.  Coal  calorimeters. — The  calorific  power  of  a  fuel  is 
found  experimentally  by  causing  a  known  weight  of  the  fuel 
to  burn  in  a  closed  vessel  surround- 
ed by  an  observed  weight  of  water. 
The  number  of  heat-units  absorbed 
by  the  rise  of  that  weight  of  water 
through  its  observed  range  of  tem- 
perature gives  the  calorific  power. 
The  apparatus  used  in  this  experi- 
ment is  called  a  calorimeter  or 
heat-measurer,  and  rightly.  Fig.  4 
illustrates  Mr.  Geo.  H.  Barrus'  ap- 
pliance. To  eliminate  errors  caused 
by  introducing  the  nitrogen  of  at- 
mospheric air,  oxygen  gas  is  usually 
supplied  to  support  combustion. 
It  would  be  foreign  to  the  present 
purpose  to  pursue  the  subject  of 
calorimetry  fully,  but  references  to 
more    exhaustive    treatises   will  be 

found  in  the  Appendix.     Values  for 

.  u         I      •/:  •      ^        J      J.U  BARRU8'  Coal  Calorimctcii 

the  calorific  power  are  given  under  the 

data  concerning  fuels  (§§  58  to  60).  ^^-  ^ 

24.  Air  Required  for  Combustion  of  Carbon. — Since 
combustion  is  the  chemical  union  of  oxygen  with  the  com- 
bustible elements,  it  must  take  place  according  to  the  laws  of 
chemical  combinations,  and  the  weights  of  air  for  each  ele- 
ment will  be  those  which  will  furnish  the  oxygen  weight  de- 
manded by  the  relations  of  the  atomic  weights  in  the  chemical 
compounds  which  are  formed. 


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^6  HEAT  AND   HEAT-ENGINES. 

Atmospheric  air  contains  oxygen  and  nitrogen  in  the  fol* 
lowing  proportions,  at  a  temperature  of  melting  ice: 

By  Weight.       By  Volume. 

Oxygen 0.236  0.213 

Nitrogen 0.764  0.787 

1. 000  1. 000 

Whence  a  given  quantity  of  air  weighs  ^^^-i-  =  4.25  times  the 
weight  of  the  oxygen  which  it  contains,  and  ^^y£- =  1.3 1 
times  the  weight  of  nitrogen  which  it  contains. 

By  volume  a  given  quantity  of  air  will  occupy  VtV"  = 
4.69  times  the  volume  of  oxygen  which  it  contains;  and  Ysr 
=  1.27  times  the  volume  of  the  nitrogen  which  it  contains. 

When  carbon  burns  to  carbonic  acid,  which  is  the  normal 
and  preferred  combustion  process,  the  chemical  equation  for 
the  process  and  result  is 

C  +  O.  =  CO., 
12  +  32  =  44, 

in  which  C  is  the  symbol  for  one  part  by  weight  of  carbon; 
O,  is  the  symbol  for  the  two  parts  of  oxygen  required  to 
burn  the  carbon  to  carbonic  acid,  whose  symbol  is  CO,. 
The  figures  below  each  are  the  respective  multiples  of  their 
atomic  weights  for  combination ;  whence  it  appears  that  the 
oxygen  weight  needed  will  be  given  by  the  proportion : 

Weight  of  oxygen  I   ,  j  Weight  of  carbon )    . .  ^2  •  12 
required  \   '   (  furnished         )    * 

or  2.66  pounds  of  oxygen  must  be  furnished  to  burn  the  one 
pound  of  carbon  completely.  The  weight  of  the  carbonic 
acid,  CO,,  will  be  the  sum  of  the  weights  of  carbon  and  oxy- 
gen, or  I  +  ^'^^  =  3'66  lbs. 

When  the  combustion  is  effected  by  supplying  atmos- 
pheric air,  there  must  be  supplied  from  the  foregoing  calcula- 
tion concerning  atmospheric  air  2.66  X  4.25  =11.3   lbs.  of 


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GENERA  TION  OR  LIBERA  TION  OF  HE  A  T.  2/ 

^ir.  Add  i.o  lbs.  of  carbon.  The  products  of  the  combus- 
tion will  weigh  12.3  lbs.  and  will  consist  of  carbonic  acid  and 
nitrogen. 

Sinnilarly  the  volunne  of  air  in  cubic  feet  to  burn  one 
pound  of  carbon  can  be  calculated  from  the  weight  of  it. 
At  atmospheric  pressure  and  at  the  temperature  of  melting 
ice  a  pound  of  air  occupies  12.39  cubic  feet.  Hence  11.3 
pounds  of  air  will  occupy  11.3  X  12.39  =  '4^  cubic  feet  at 
32°  F.,  or  152  cubic  feet  at  62°  F. 

When  carbon  (C)  burns  to  carbonic  oxide  (CO)  instead  of 
to  carbonic  acid  (CO,), 

C  +  O  =  CO, 

12  -j-  16  =  28, 

whence  the  oxygen  is  jf  of  the  unit  weight  of  the  carbon, 
and  1.33  pounds  of  oxygen  or  1.33  X  4.25  =  5.65  pounds 
of  air  are  required.  The  products  of  the  combustion  are  2.33 
pounds  of  carbonic  oxide.  The  weight  of  air  for  this  com- 
bustion will  be  1.33  X  4.25  =  5.65  pounds  of  air,  or  5.65 
X  I2-.39  =  70  cubic  feet  of  air  at  32**  F.,  or  76  at  62°  F. 

If  the  CO  "burns  as  a  combustible  gas  to  CO,,  the  addi- 
tional supply  of  air  is  required  as  in  the  preceding  case. 

25.  Air  Required  for  Combustion  of  Hydrogen. — Hy- 
drogen burns  to  water-vapor  or  steam-gas,  whose  chemical 
symbol  is  H.O.     The  chemical  equation  is 

H.  +  O  =  H,0, 
2  +  16  =    18, 

whence  one  pound  of  hydrogen  requires  ^^  =  8  pounds  of 
oxygen,  and  8+1  =  9  pounds  of  water- vapor  result  as  prod- 
ucts of  the  combustion,  if  oxygen  is  used  alone. 

Eight  pounds  of  oxygen  need  8  X  4.25  =  34  pounds  of 
air,  making  34+  i  =  35  pounds  of  water  and  nitrogen  as 
the  actual  weights  of  the  products  of  combustion.  The  vol- 
ume of  air  for  hydrogen  combustion  is  34  X  12.39  =  4^1 
cubic  feet  of  air  at  32"*  F.  or  457  cubic  feet  of  air  at  62**  F. 


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28  HEA  T  AND   HEA  T-ENGINES. 

26.  Air  Required  for  Combustion  of  Compounds. — In 

the  burning  of  compounds  of  carbon  and  hydrogen  each  acts 
as  though  the  other  did  not  exist,  and  the  air  required  is  the 
sum  of  the  requirements  of  the  constituents.  Marsh-gas»  for 
instance,  known  also  as  light  carburetted  hydrogen  or  methane, 
of  composition  CH^,  requires 

C  +  O,  =  CO.       =  12  +  32  =  44 
H,  +  O.  =  2(H,0)  =  J  +  32  =  36 

Total  =  16  +  64  =  80 

The  added  oxygen  is  four  times  the  weight  of  the  original 
gas,  or  one  pound  of  gas  gives  five  pounds  of  carbonic  acid 
and  water  if  no  nitrogen  is  added.  Four  pounds  of  oxygen 
will  be  furnished  by  4  X  4.25  =  17  pounds  of  air  at  32°,  or 
17  X  12.39  =  208  cubic  feet  of  air  at  32°,  and  giving  18 
pounds  of  CO,,  H,0,  and  N. 

The  proportions  of  the  CO,  and  H,0  were  respectively 
1^  of  the  former  and  \\  of  the  latter ;  or  there  was  one  part 
of  water  to  1.22  parts  of  carbonic  acid,  since 

36  :  44  : :  i  :  1.22. 

Similarly  for  olefiant  gas,  ethylene,  C,H^,  the  equations  will  be 

C,  +  O,  =  2CO.  =  24  +  64  =    88 

H,+  0.=  2H,0  =_4  +  3^=  ^ 

Total  =  28  +  96  =  124 

That  is,  for  a  weight  of  gas  (28)  will  be  required  a  weight  of 
oxygen  (96),  or  3.43  pounds  for  one  pound  of  gas,  making 
4.43  pounds  of  CO,  and  H,0,  and  calling  for  3.43  X  4.25  = 
14.58  pounds  of  air,  or  14.58  X  12.39  =  ^^^  cubic  feet  of  air, 
at  32°. 

The  products  of  combustion  will  be  14.58+  ^  =  I5«58 
pounds  of  CO,,  H,0,  and  N,  and  in  this  combustion  one  part 
of  water  goes  to  244  parts  of  carbonic  acid. 

If  there  is  sulphur  enough  in  the  fuel  not  to  be  negligible. 


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GENERA  TIOAT  OR  LIBERA  TIOX  OF  HE  A  T.  29 

then  an  additional  chemical  equation  is  required  and  more 
oxygen;   S  burns  to  SO,,  or  32  +  32  =  64. 

One  pound  of  oxygen  is  required  for  each  pound  of  sul- 
phur, corresponding  to  4.25  pounds  of  air  or  12.39  X  4.25  = 
52.65  cubic  feet  of  air  at  32°  or  57  cubic  feet  at  62°  F. 

27.  Combustion  of  an  Analyzed  Fuel. — The  chemical 
anaU'sis  of  a  fuel  gives  the  percentage  or  weight  of  C,  H,  S, 
and  O  in  a  pound.  Hence  the  calculation  for  the  weight  or 
volume  of  air  is  identical  with  the  foregoing,  except  by  rea- 
son of  the  provision  for  satisfying  the  oxygen  in  the  fuel  itself. 
The  investigations  of  Dulong  and  Despretz  and  others  have 
shown  the  principle  to  hold,  that  when  oxygen  and  hydrogen 
exist  in  a  compound  in  the  proper  proportions  to  form  water 
by  union  with  each  other,  these  constituents  have  no  effect 
either  in  affecting  the  calorific  power  or  the  demand  for  out- 
side oxygen  for  combustion.  It  is  only  the  surplus  hydrogen 
above  that  necessary  to  form  water  with  the  oxygen  which 
need  be  considered ;  or  instead  of  using  the  total  per  cent  or 
weight  of  hydrogen,  the  latter  is  diminished  by  one  eighth  of 
the  weight  of  oxygen,  since  one  part  of  hydrogen  by  weight 
goes  to  eight  weights  of  oxygen. 

By  volume 
each  per  cent  of  C  requires  140  X  C  -r-  lOO  cu.  ft.  of  air, 
*«    H        **        421  X  H-T-  100       **      '*    '' 

*'  *'        **   S        *'  52  X  S  -^  100      **      **    *• 

so  that  the  above  principle  gives 

140C  +42i(h-  g)+  52S 

Volume  of  air  =  . 

100 

By  weight,  for  a  fuel  containing  C  and  H, 

Weight  of  air  ==  1 1.3C  -f  34(h  >-  -). 
This  is  more  usually  written : 

Weight  of  air  =  12C  +  36(h  -  j)^ 


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30 


HEAT  AND   HEAT-ENGINES. 


28.  Weight  of  Products  of  Combustion  with  an  Ana- 
lyzed Fuel. — Bringing  together  the  data  and  results  of  the 
preceding  paragraphs: 

One  pound  of  C  makes  2.66  +  i  =  3.66  pounds  of  CO,; 
' *  H        *     8        +1=9  *»        *^  H,0; 

<<  S       ^      I        +1=2  '^        *'  SO,. 

Hence  if  C,  H,  and  S  denote  the  respective  percentages 
of  these  elements  in  the  fuel  in  question,  then 

3.66  -5-  100  =  .0366C  =  weight  of  CO,, 
9  -^  100  =  .09H  =  •*  **  H,0, 
2        -I-  100  =  .02S       =       **       **  SO,, 

if  the  combustion  were  in  oxygen.  Being  effected  by  air, 
however,  the  weight  of  the  products  of  combustion  will  be 
greatly  increased,  since  the  nitrogen  weighs  i||or  3.23  times 
the  wei'ght  of  oxygen  it  contains.      Hence  for 

I  pound  of  C  are  added  2.66  X  3.23  =     8.59  pounds  N, 

I  '*       '*   H  *'        **      8        X  3.23  =  25.84       •*  .      N, 

I  **       *^  S    **        -       I        X  3-23  =     3.23       ''       N, 

I  **       **   N  **        **      I                      =1             "        N, 

if  the  fuel  analysis  shows  nitrogen  in  it.  So  that  if  these 
weights  be  reduced  to  percentages  of  each  by  multiplying 
the  weight  of  each  constituent  by  the  above  weight  of  N  and 
dividing  by  lOO,  the  weights  of  CO,,  H,0,  SO,,  and  N  be- 
come  increased  as  shown  in  this  expression : 


Weight  of 
Products 
of  Com- 
bustion 


( .0859 

«    N 

.  = 

<  i 

"  H  X  1  -"^ 
(.258 

<« 

"  S  X  { -"^^ 
/  .032 

*'      0 

«« 

"NX     .oi 

**    N    =  .oioN; 

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GENERA  TION  OR  LIBERA  TION  OF  HE  A  T,  3  r 

in  which  C,  H,  S,  and  N  in  the  last  column  are  the  respect- 
ive percentages  as  given  by  the  analysis. 

29.  Volume  of  Products  of  Combustion  with  an  Ana- 
lyzed Fuel. — While  the  foregoing  calculation  is  most  general^ 
since  the  weight  is  independent  of  the  temperatures  of  the 
products  of  combustion,  the  practical  form  of  the  problem  is 
more  often  concerned  with  their  volume,  and  this  varies  with 
the  temperature.  With  the  same  conditions  of  pressure,  if 
F,  denote  the  volumes  at  the  temperature  of  melting  ice  as 
given  hitherto,  and  7J,  the  corresponding  absolute  tempera- 
ture, while  Fand  7"  are  the  volume  and  absolute  temperature 
corresponding  to  the  state  of  the  hot  and  expanded  gases,  a 
later  discussion  will  show  that  V^T •=  VT^y  or  the  volumes 
will  be  proportional  to  the  absolute  temperatures,  whence 

VT 
'^-     To' 
Similarly  if  the  initial  volumes  be  observed  or  taken  at 
62**  F.,  the   final  or  expanded   volumes  can  be  calculated. 
For  example, 

CO,  at  62°  occupies  8.594  cu.  ft.  to  the  pound; 

IT  <  '        I  <  *  *         I QO  *  *  *  *        *  *         *  *  *  * 

so,  **    **  **        5.848  **     **    **    **        ** 

|a         it     <i  it        I^.COI    **      **     **      *'  ** 

whence 

.0366C  X  8.594  =  .315C  =  cu.  ft.  of  CO,  at  62®; 

.090H    X  190      =  1.9H  =    ''     **    ^*  H      **    *' 

.02S       X  5.85     =  .117S  =    ''     ''    •*  SO,  ''    ** 

.2584H)  ^  3-49H  ) 

Adding  and  neglecting  the  smaller  weight  of  SO,,  the  vol* 
ume  at  62°  F.  becomes 

F,  =  1.475C  +  5.39H, 

and  the  volume  F,  at  any  greater  temperature  will  be  found 


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32  HEAT  AND   HEAT-ENGINES, 

T 
by  multiplying  the  above  expression  by  the  fraction  -~,  in 

which  Z",  is  the  absolute  temperature  corresponding  to  62°  F., 
and  T^  the  absolute  temperature  at  which  the  volume  is 
sought. 

30.  Dilution  of  the  Products  of  Combustion. — Where 
the  arrangements  for  the  air-supply  to  the  combustible  fuel 
are  inadequate,  and  where  proper  mixture  of  oxygen  and  the 
combustible  gases  is  lacking,  it  may  come  about  that  the 
spaces  in  and  above  the  fire  are  so  filled  with  CO,  or  carbonic 
acid  gas,  which  is  not  a  supporter  of  combustion,  that  an  ex- 
cess of  air  has  seemed  to  be  required  to  dilute  the  excess  of 
CO,  and  to  secure  a  complete  combustion.  This  difficulty 
has  appeared  at  its  worst  with  fuels  containing  volatile  com- 
bustible gases,  or  which  contain  moisture,  and  which  are 
burned  with  the  natural  draft  caused  by  a  short  chimney. 
The  excess  of  gas  distilled  off  from  the  coal  after  freshly 
charging  it  upon  the  fire  finds  difficulty  to  get  oxygen  enough 
at  temperature  high  enough  under  these  conditions,  when 
the  provision  for  the  supply  of  oxygen  is  abundant  for  a  later 
period  in  the  combustion.  Water-vapor  also,  from  damp 
fuels,  keeps  oxygen  away  from  the  combustible  gases,  by 
simple  mechanical  displacement,  if  the  temperature  is  not 
high  enough  to  dissociate  the  oxygen  and  hydrogen  of  which 
it  is  composed.  It  may  act  also  to  sweep  along  with  it  par- 
ticles of  carbonaceous  matter,  which  show  as  smoke  when  un- 
consumed. 

Hence  as  far  back  as  the  investigations  of  Prof.  Johnson 
for  the  U.  S.  Government  (1844),  the  principle  was  advocated 
•of  introducing  twice  as  much  air  into  a  furnace  as  the  theo- 
retical computations  demanded ;  or  where  12  pounds  of  air  per 
pound  of  carbon  fuel  were  theoretically  required,  the  engineer 
should  arrange  to  introduce  24  pounds.  This  rule  has  also 
been  followed  and  urged  by  British  engineers,  who  were 
familiar  with  gaseous  coals  and  other  fuels. 


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GENERA  TION  OR  LIBERA  TION  OF  HE  A  7\  33 

A  better  understanding  of  the  proper  conditions,  and 
attention  to  the  matter  of  minutely  dividing  and  distributing 
the  air-supply,  have  reduced  this  excess  from  twice  the  theo- 
retical weight  to  one  and  one  half  times,  or  i8  pounds  where 
12  is  needed.  And  the  best  modern  practice  with  the  regu- 
lar feeding  of  fresh  fuel  by  mechanical  stokers,  and  the  prin- 
ciples and  applications  of  forced  mechanical  draft  in  furnaces, 
have  reduced  this  excess  of  diluent  air  to  its  lowest  terms, 
and  in  many  successful  cases  only  the  theoretical  quantity  is 
supplied.  This  feature  is  specially  an  advantage  of  firing 
with  gas  as  fuel  to  be  discussed  hereafter.  The  excess  of  air, 
and  especially  its  nitrogen,  has  to  be  heated,  and  by  its  pres- 
ence lowers  the  average  temperature  prevailing  at  or  near  the 
fire.  It  may  even  check  combustion  of  any  gas  which  it  can 
cool  below  the  ignition-point,  and  modern  designers  are  seek- 
ing to  improve  practice  along  these  lines  and  to  approach 
more  nearly  to  the  requirements  of  the  chemistry  of  combus- 
tion. Data  for  weight  of  air  and  the  effect  of  excess  of  air  on 
the  temperature  of  the  fire  will  appear  with  the  discussion  of 
fuels  in  a  succeeding  chapter. 


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Coal 


CHAPTER   V. 
FUELS. 

31.  Introductory. — A  fuel  has  already  been  defined  (§  19) 
as  a  carbon  or  hydrogen  element  or  a  hydrocarbon  compound 
found  native  or  manufactured  so  as  to  be  obtainable  in  suffi- 
cient quantities  and  at  a  low  cost,  so  as  to  be  used  as  a  source 
of  heat.      Fuels  are  solid,  liquid,  and  gaseous. 

32.  Solid  Fuels.    Anthracite. — The  solid  fuels   include: 

Anthracite 
Semi-anthracite 

{Dry  bituminous 
Caking  bituminous 
Long-flaming  bituminous,  or  cannel 
Lignite 
Asphalt 
Peat 
Coke 

Tree-wood  and  slabs 
Bagasse 
Tan-bark 
.  Straw  and  stubble 
Charcoal 
Artificial  Fuel  Briquettes 

Such  fuels  all  seem  to  have  been  of  vegetable  origin,  and 
the  differences  between  the  coals  seem  to  have  been  mainly 
due  to  varying  conditions  during  their  formation  in  geologic 
periods,    varying    pressures    after    formation,    and    varying 

34 


Wood 


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FUELS. 


35 


antiquity.  The  following  table  shows  a  relation  between  the 
fuels  on  the  basis  of  the  completeness  of  the  carbonization 
of  the  wood  fibre  or  cellulose: 


Description. 


Carbon. 


Hydrogen. 


Oxygen. 


Wood-fibre  (cellulose) 

Peal 

Lignite ■ 

Lignite  (brown  coal). . 

Coal  (bituminous) 

Coal  (semi-anthracite) 
Anthracite 


52.65 
60.44 
66.96 
74.20 
76.18 
90.50 
92.85 


5-25 
5-96 
5-27 
5.89 
5.64 
5.05 
3.96 


42.10 
33-60 
27.76 
19.90 
18.07 
4.40 
3.19 


From  their  vegetable  origin  the  solid  fuels  usually  contain 
a  proportion  of  incombustible  mineral  matter,  sometimes  fusi- 
ble and  sometimes  not,  which  is  known  by  the  general  name 
of  ash.  The  ash  from  wood  is  mainly  composed  of  the  alka- 
lies: coal-ash  may  be  iron,  clay,  alkaline  earths,  etc. 

Anthracite  is  often  called  hard  coal — sometimes  blind  coal, 
or  stone  coal, — and  consists  almost  entirely  of  fixed  or  free 
carbon,  with  inorganic  matter  or  slaty  material.  It  was  formed 
at  high  heat  and  great  pressure  in  geologic  periods,  and  has 
little  if  any  volatile  matter  or  hydrocarbons.  It  is  this  pres- 
sure which  gives  it  its  greater  hardness  and  density  as  com- 
pared  with  a  coke  which  has  the  same  carbon  analysis. 

Its  hardness  and  compact  structure  cause  it  to  break  up 
or  decrepitate  when  charged  upon  a  hot  bed  of  fuel,  and  the 
small  chips  are  liable  to  loss  by  falling  into  waste  with  the  ash, 
or  to  be  carried  away  with  strong  draft  of  air  through  or  over 
the  fire.  The  English  and  French  anthracites  are  worse  ia 
this  respect  than  the  American. 

Anthracite  is  hard  and  lustrous,  with  vitreous  fracture; 
does  not  break  in  transportation ;  is  not  easily  ignited ;  burns 
with  a  short  flame  (unless  damp)  and  little  or  no  smoke; 
gives  an  intense  fire;  is  readily  extinguished  by  cutting  off 
the  air,  or  by  cooling  the  fire-temperature.  Its  hardness  and 
strength  make  it  possible  to  break  and  screen  anthracite  to 


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HE  A  T  AND   HE  A  T-ENGINES. 


size  without  excessive  loss,  and  in  Pennsylvania  the  recog- 
nized sizes  are,  from  the  smallest  downward: 


Designation. 


Dust 

Barley 

No.  3  buckwheat 

Bird's-eye 

No.  2  buckwheat,  or  rice  . 

No.  I  buckwheat 

Pea 

Chestnut 

Small  stove 

Large  stove 

Egg 

Broken 

Steamboat 


Diameter  of 

Perforation  over  which 

Coal  will  pan. 


Diameter  of 

Perforation  throufph 

which  Coal  will  pass. 


3/32  inch 

1/16  *• 

3/16  •• 

5/16  " 

3/8  •' 

9/16  •* 

7/S  " 

1%  - 

2H  - 

4 
7 


What  passes  through  a  sieve  of  -j^  inch  mesh  is  called 
waste  or  culm  or  dust.  Anthracite  shades  off  into  graphite 
on  the  one  side — Rhode  Island  anthracites  are  so  hard  as  to 
be  difficult  to  burn  alone — and  into  the  softer  varieties  on  the 
other.  The  semi-anthracites  have  some  volatile  matter, 
break  with  a  lamellar  or  conchoidal  fracture,  and  are  more 
readily  ignited.  Their  flame  is  short,  however.  The  analy- 
ses of  typical  anthracite  average : 

Per  cent. 

Pixed  carbon 90  to  94 

Volatile  matter  j  "y'^^een,  I  to  3  )  ^^ 

(  Oxygen  and  nitrogen,  I  to  3  ) 

Water i  to    2 

Ash 4  to     3 

with  a  specific  gravity  of  1.57. 

The  semi-anthracites  will  average  (Wilkesbarre) : 

Fixed  carbon 88.90 

Volatile   matter 7.68 

Earthy  matter  or  ash 3.49 

with  a  specific  gravity  of  1.4. 


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37 


The  anthracites  do  their  work  of  heating  mainly  by  the 
radiant  heat  of  the  incandescent  or  glowing  carbon.  They 
will  therefore  be  burned  in  furnaces  with  a  large  grate-area, 
and  the  fire  will  be  as  thin  as  consistent  with  having  no  holes 
in  it»  The  use  of  water  in  ash-pits  of  such  fires  often  increases 
the  apparent  flame  by  decomposition  of  the  steam-gas,  which 
cools  the  fire  by  the  heat  required  to  decompose  the  water, 
but  which  same  heat  is  regained  beyond  the  fire  upon  the  re- 
composition  of  the  dissociated  gases. 

American  anthracites  are  mainly  found  in  the  eastern 
parts  of  the  Allegheny  Mountains  and  in  the  Rocky  Moun- 
tains of  Colorado. 

33  Bituminous  Coals.  — Bituminous  coals  are  separated 
from  the  anthracites  by  the  possession  of  varying  amounts  of 
volatile  matter,  which  distil  off  as  gases  upon  the  application 
of  the  heat  of  the  fire  upon  which  the  coal  is  charged.  The 
semi-anthracites  or  semi-bituminous  coals  form  a  wide  class 
intermediate  between  those  which  have  the  characteristics  of 
their  several  groups  strongly  marked.  They  have  from  15 
to  20  per  cent  of  gaseous  matter,  a  high  heating  or  calorific 
power,  but  are  of  little  value  for  making  illuminating-gas  by 
the  retort  process.  They  are  valued  for  steam-making, 
because  while  burning  with  a  good  flame  they  do  not  give  so 
long  a  flame  as  to  be  inconvenient  in  a  boiler-setting.  The 
following  analyses  of  Maryland  and  Pennsylvania  types  will 
illustrate  these  properties: 


Locality. 

Specific 
Gravity. 

Fixed 
Carbon. 

Volatile 
Matter. 

Sulphur. 

Ash. 

Cumberland.  Md 

Blossburir    Pa 

1. 41 
1.32 

68.44 
73.11 

17.28 
15.27 

0.71 
0.85 

13.98 
10.77 

The  true  bituminous  coals  are  softer  than  the  anthracites, 
have  less  lustre  on  the  fracture,  break  into  layers  or  lamellae 
or  splints,  and  are  the  most  widely  distributed  of  the  fuels. 


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38  HEAT  AND   HEAT-ENGINES, 

Their  fragility  makes  it  inconvenient  to  sort  them  into  sizes 
as  can  be  done  with  anthracite,  so  that  but  three  grades  are 
usual:  lump,  nut,  and  slack.  When  no  attempt  is  made  to 
sort  by  size  the  coal  is  known  as  the  **run  of  the  mine,"  or 
is  used  as  extracted  from  the  bed  in  which  it  lay. 

Dry  bituminous,  open-burning,  free-burning,  or  furnace 
coal  is  a  class  of  coal  which  can  be  used  native  in  the  blast- 
furnace, because  of  the  absence  of  pitchy  or  **  fat  *'  material 
in  its  composition  which  would  cause  it  to  cake  together  and 
agglomerate  into  lumps  upor  exposure  to  heat. 

Caking  or  coking  coals  have  this  property  of  caking  to- 
gether, and  after  the  distillation  from  them  of  the  30  to  50 
per  cent  of  volatile  matter  which  they  contain  the  residue  is 
a  valuable  coke,  available  for  furnace  or  other  industrial  use. 
These  usually  have  sulphur  in  them,  but  when  free  from  it 
a  valuable  gas-coal  is  the  result. 

The  long-flaming  or  cannel  coals  have  more  gas  than  the 
foregoing,  but  are  usually  lower  in  calorific  power,  and  are  of 
less  industrial  importance  because  their  coke  is  not  so  valu- 
able. They  lack  a  certain  pitchy  brilliancy  found  in  the 
other  varieties,  and  are  usually  higher  in  ash. 

Splint-coal  is  a  variety  of  cannel  with  a  high  per  cent  of 
carbon,  high  calorific  power,  but  less  percentage  of  gas. 

The  bituminous  coals  are  easily  ignited,  and  by  reason  of 
the  readily  oxidizable  character  of  the  pyrites  usually  con- 
tained in  them  are  liable  to  spontaneous  ignition  (§21)  in 
their  bunkers  or  bins.  They  form,  however,  the  basis  of 
successful  industry  in  England  and  America  and  elsewhere. 

Typical  proximate  compositions  are  as  follows: 

Fixed    carbon 52  to  84  per  cent. 

Volatile  matter 48  to  12         ** 

Earthy    matter 2  to  20        ** 

Sulphur I  to     3         ** 


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FUELS, 


39 


Ultimate  analyses  of  representative  coals  would  show: 

Carbon 75  to  80  per  cent. 

Hydrogen 5  to    6        *' 

Nitrogen i  to    2        '* 

Oxygen 4  to  10        ** 

Sulphur 0.4  to     3         '* 

Ash  or  earthy  matter 3  to  10        ** 

Cannel-coals  would  be  fairly  represented  by  the  following 


table : 


COMPOSITION 

OF    CANNEL-COAL. 

Locality. 

Specific 
Gravity. 

Fixed 

Carbon. 

Volatile 
Matter. 

Earthy 
Matter, 

Franklin,  Pa 

40.13 

55.1 
32.0 
42.0 

44.85 
42.9 

55.7 
52.0 

15.02 
2  0 

Dorton's  Branch.  Kv 

1.25 

Breckenridge,  Ky 

12.3 

6  0 

Davis  Countv    Ind    «. 

1.23 

34.  Lignite. — The  lignites  are  coals  of  more  recent  geo- 
logic period  than  the  previous  fuels,  the  process  of  carboniza- 
tion of  the  wood  not  having  proceeded  so  far  nor  under  so 
great  pressure.  Lignites  are  brown  or  black.  The  brown 
lignite  is  sometimes  of  a  woody  texture,  while  the  black  is 
either  woody  or  of  a  homogeneous  structure  with  a  resinous 
fracture.  They  occur  in  California,  Utah,  Colorado,  Wyo- 
ming, Arizona,  Alaska,  New  Mexico,  and  Oregon.  Their 
iieating  capacity  will  be  from  one  half  to  two  thirds  that  of 
the  older  bituminous  coals,  and  they  are  tender  to  transport. 
Their  coke  is  either  powdery  or  fibrous  like  that  of  the  orig- 
inal wood.  Lignites  contain  more  oxygen  than  coal.  The 
following  table  will  show  their  composition: 

COMPOSITION    OF    LIGNITE, 


Locality. 

Specific 
Gravity. 

Fixed 
Carbon. 

Volatile 
Combusti- 
ble Matter 

Water. 

Ash. 

Total 

Volatile 
Matter. 

Coke. 

Kentucky 

Washincrton  . . 

1. 201 

40.00 
52.85 
41.25 

23.00 

31-75 
46.00 

30.00 
7.00 
3.50 

7.00 
3.00 
9.25 

53.00 
61.25 
50.50 

47.00 

38.75 
49.50 

•Colorado 

1. 271 

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HEA  T  AND   HE  A  T-ENGINES, 


35.  Asphalt. — Asphalt  as  a  fuel  has  a  large  proportion  of 
hydrogen  and  burns  like  a  tar  or  fat  bituminous  coal.  It 
yields  a  porous  coke,  and  in  comparison  with  lignite  shows 
the  following  average  composition: 

Lignite.  Asphalt. 

Carbon 69  per  cent.     79  per  cent. 

Hydrogen 5         **  9  ** 

Oxygen  and  nitrogen .  .      20        **  9  ** 

Ash 6        '*  3  '* 

100  100 

Coke  from  analysis. .  .      47  per  cent.       9  per  cent. 
Heating  power 13,108  B.T.U.     17,040  B.T.U. 

36.  Peat. — Peat  is  derived  from  the  bituminization  of 
mosses,  grasses,  and  similar  matter,  as  lignite  is  derived  from 
more  massive  wood.  It  occurs  in  bogs,  in  which  the  upper 
part  is  turf,  and  peat  occurs  below.  As  piled  and  dried  in 
the  air  after  digging  it  contains  from  25  to  30  per  cent  of 
water  and  from  7  to  1 1  per  cent  of  ash.  RegnauJt's  stand- 
ard analysis  of  dry  peat  shows: 

Carbon 58  per  cent. 

Hydrogen 6        '* 

Oxygen 31         '  * 

Ash 5 

100 
Freshly  dug  peat  will  show  75  to  80  per  cent  of  water. 
It  is  little  used  in  America,  but  is  of  importance  in  England, 
Belgium,  Germany,  and  Sweden,  on  account  of  its  low  cost. 
A  typical  composition  of  ordinary  Irish  peats,  both  exclu- 
sive and  inclusive  of  the  moisture,  which  they  always  contain 
in  their  natural  condition,  would  give: 

EXCLUSIVE    OF    MOISTURE. 


Description. 

Moist- 
ure. 

C 

H 

0             N 

S 

Ash. 

Coke. 

Good  air-dried 

59.7 
59-6 
59.5 

6.0 
4.3 
7.2 

31.9 

29.8 

24.8  1    2.3 

"0:% 

2.4 
6.3 
5.4 

Poor  air-dried 

Dense,  from  Galway 

44.3 

Averages 

59.6 

5.8 

29.6 

0.3 

4-7 

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FUELS. 
INCLUSIVE    OF    MOISTURE. 


4t 


Good  air-dried 

Poor  air-dried 

Dense,  from  Galway 

Averages 


24.2 
29.4 
29.3 

45.3 
42.1 

42.0 

4.6 
3.1 
5.1 

27.8 

43.1 

4.3 

24.1 

21.0 

17-5  1   1.7 

"o!6' 

1.8 
4.4 

3.8 

21.4 

0.2 

3.3 1 

31.3 


The  average  composition  of  Irish  peat,  disregarding  sul- 
phur, which  is  seldom  present,  at  least  in  quantity  sufficient 
to  have  any  appreciable  influence,  may  be  taken  to  be  as 
given  below: 

AVERAGE    COMPOSITION    OF    IRISH    PEAT. 


Constitueots. 


Includini;  25  per  cent;  Including  30  per  cent 
of  Moisture.  of  Nioisiure. 


Carbon. . . 
Hydrogen 
Oxygen 

Nitrogen  . . 

Ash 

Moisture 


44.0 
4-5 

22.5 
i.o 
3-0 

25.0 


41.2 
4.2 

21.0 
0.8 
2.8 

30.0 


The  thermal  value  of  dry  Irish  peat  would  be  (§  22): 

Carbon 14,650  X        0.59        =      8,643.5  B.T.U. 

Hydrogen.  .   62,100  X  (.06  —  ^j  =     1,397.25  B.T.U. 

Total     =  10,040.75  B.T.U. 

37.  Coke. — When  a  coal  containing  a  proportion  of  vola-^ 
tile  hydrocarbon  or  other  gas  is  exposed  to  a  distilling  action 
by  heat,  either  in  a  retort  or  an  oven,  the  residue  is  called 
coke  after  the  distillation  is  complete.  It  is  usually  dark 
gray  in  color,  porous,  vi^ith  a  slight  metallic  lustre,  hard  and 
brittle.  It  is  likely  to  contain  from  80  to  93  per  cent  of  fixed 
carbon,  from  17  to  5  per  cent  of  ash,  and  the  remainder  sul- 
phur or  other  impurities.  The  weight  of  coke  ranges  at 
about  66  per  cent  of  the  coal  charged,  with  an  increase  ia 
bulk  of  about  one  fourth.      It  will  absorb  moisture  with  avid- 


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HEAT  AND  ^HEAT-ENGINES. 


ity,  up  to  even  20  per  cent.  It  gives  a  nearly  smokeless 
combustion,  with  short  or  no  flame  if  dry,  and  burns  with  a 
steady  constant  fire. 

Modern  coke-ovens  condense  and  recover  the  gases  from 
the  distillation,  and  give  most  valuable  by-products  of  the 
coke  manufacture.  The  two  best  known  are  the  Semet- 
Solvay  and  the  Hofman-Otto,  saving  tar  and  sulphate  of 
ammonia,  and  if  possible  using  the  excess  of  combustible  gas 
as  fuel. 

Coke  is  less  used  in  America  as  a  source  of  motor  energy, 
but  more  in  metallurgy.  Its  absence  of  flame  in  combustion 
lessens  its  convenience  for  the  one  use  and  increases  it  for 
the  other. 

The  following  standard  figures  for  the  making  of  coke  are 
due  to  Mr.  A.  L.  Steavenson  (Iron  and  Steel  Inst,  of  Great 
Britain): 


Element. 

Original  Analysis 
of  Coal. 

Loss  in  Coking. 

Yield  of  Coke. 

Oxvfifcn.  ••...•••••• 

6.7 
84.9 
4.5 
I.O 
0.6 
2.0 

16.6 
68.1 
II. 2 

2.5 

1.6 

Osrbon  ..••••■••■«••••••• 

96.2 

H  vdrocren 

Nitroccn  ....  . ........... 

Siiluhur 

Ash 

3.8 

38.  Wood. — In  the  older  countries  and  the  more  thickly 
settled  parts  of  the  new,  wood  is  becoming  less  and  less  used 
as  a  source  of  heat  energy,  by  reason  of  its  growing  scarcity 
and  the  proper  opposition  to  deforestation  for  the  sake  of  the 
country  as  a  whole.  It  is,  however,  of  importance  still  as 
refuse  in  chips  and  dust  from  a  wood-working  process  of 
manufacture,  and  for  the  disposition  of  stalks  or  similar  an- 
nual product  of  tillage. 

Fire-wood  or  slabs  may  be  either  of  the  soft  woods,  such 
as  pine,  birch,  or  poplar,  or  the  hard  woods,  like  oak,  hickory, 
ash,  elm,  or  beach.     Ash  is  small  in  woods  and  varies  from 


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FUELS, 


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1  to  5  per  cent.  Fresh-cut  fire-wood  usually  holds  about  40 
per  cent  of  moisture,  which  upon  air-drying  for  several 
months  will  diminish  to  15  to  25  per  cent.  If  dried  in  kilns 
or  ovens  and  exposed  afterward  to  the  air,  the  wood  absorbs 
water  rapidly  in  the  first  few  days — perhaps  5  per  cent  in  the 
first  three — and  thereafter  will  absorb  slowly  till  the  normal 
percentage  of  dry  wood  is  reached,  and  this  will  fluctuate 
according  to  atmospheric  conditions.  Various  tree-woods  are 
much  alike  chemically,  averaging  as  follows: 


Kind  of  Wood. 


Beech. . 

Oak.... 

Birch.. 

Poplar. 

Willow 


Averages,  kiln-dry 
Average,  25)^  water 


I       Asli.         Moisture. 


49  36 
49.64 
50.20 
49-37 
49.96 


50.0 
37.5 


6.0T 
5-92 
6.20 
6.21 
5  96 


42.69 
41. 16 
41.62 
41.  (>o 
39-56 


0.91 

1.29 
1. 15 

0.96 


6.0 

4-5 


41.0 

i   30.75 


1. 00 
0.75 


1 .06 

1.97 

o.8r 
1 .86 
3-37 


2.0 
1.5 


25 


The  heating  power  of  wood  is  usually  called  7838  B.T.U. 
dry  or  5879  when  wet.  This  would  be  about  four  tenths 
that  of  an  equal  weight  of  coal,  or  in  other  words,  2\  pounds 
of  wood  are  equivalent  to  one  pound  of  coal.  In  substi- 
tuting wood  for  coal  as  a  fuel,  the  furnace  usually  has  to  be 
enlarged,  principally  in  its  height,  perhaps,  so  that  it  may 
carry  an  equal  weight  of  combustible  at  any  one  time  as  it 
formerly  did  with  coal.  Wood,  like  the  gaseous  coals,  distils 
off  volatile  or  tarry  matters,  which  are  often  sticky  and  brown 
in  color,  and  are  combustible  if  a  high  enough  temperature 
can  be  commanded.  These  do  not  constitute  a  true  smoke 
as  heretofore  defined  (§  20),  but  are  often  judged  to  be  one, 
and  should  be  as  avoidable. 

When  sawdust  from  manufacturing  processes  is  to  be  used 
as  a  fuel,  the  conditions  of  intimate  mixture  of  the  oxygen 
required  for  the  combustion  have  to  be  secured  by  special 
forms  of  grate,  and  usually  by  a  forced  draft  (§§  24  to  26,  and 


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HEA  T  AND   HEA  T-ENGINES, 


86  to  88).     Hollow  grate-bars  form  a  usual  method  of  meet- 
ing this  requirement  (Gordon's  or  Gadey's),  with  a  fan  forcing 


air  into  the  cored  passages  and  out  and  up  through  the  fuel- 
bed  (Fig.  5). 

39.  Bagasse,  Straw,  Tan-bark. — The  three  most  usual 
forms  of  woody  fibre  used  as  refuse  for  fuel  are  the  residue 
from  crushing  the  sugar-cane  to  press  out  its  juice,  which  is 
called  bagasse;  the  stalks  or  stubble  from  cotton,  wheat,  or 
barley  harvests;  and  the  spent  bark  from  tan-pits  out  of  which 
the  tan-liquor  has  dissolved  the  desired  acids  and  left  the 
woody  fibre  behind.  The  accepted  analyses  of  tropical  cane 
and  the  resulting  bagasse  after  crushing  give: 


Cane. 

f65f  Bapasse. 

7ojt  Bagasse. 

^3%  Baj^asse. 

Woody  fibre 

12.5 
73-4 
14.1 

37 
53 
10 

40 
10 

45 
■6 

Water 

Combustible  salts 

9 

100. 0 

100 

100 

100 

The  figures  6(i^  70,  and  72  refer  to  the  proportion  of  mill 
extraction  of  the  juice  from  the  cane. 


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FUELS,  45 

Dry  Louisiana  bagasse  will  analyze: 

Constituents.  Percentage. 

Volatile  matter 81.37 

Fixed  carbon 14.26 

Ash 4.6 

If  the  woody  fibre  contains  50  per  cent  of  carbon,  and  the 
combustible  salts  42  per  cent,  as  has  been  found,  then  the 
calorific  power  of  bagasse  would  be  about  1200  B.T.U. ;  or 
one  pound  of  coal  equals  5  or  6  pounds  of  wet  bagasse,  or  2  J 
to  3  pounds  if  dry.  In  burning  it,  it  is  fed  continuously 
into  a  very  hot  fire-brick  chamber,  and  generous  space  must  be 
provided  to  take  care  of  the  volume  of  steam  and  gas  gener- 
ated. 

Straw  is  composed  in  its  ordinary  and  air-dried  condition 
^ls  follows: 


Carbon . . . . 
Hydrogen. 
Oxygen  . . . 
Nitrogen   . 

Ash 

^ater 


Dry 

Wheat  Straw. 
Russia. 


46.1 
5.6 

43-7 
0.42 
4.18 


Wheat  Straw. 
Head. 


35.86 
5.01 

37.68 
0.45 
5.00 

16.00 


Barley  Straw. 

36.27 
5.07 

58.26 

.40 

4.50 

15.50 

100.00 

Mean. 


36.00 
5.00 

38.00 
.425 
4.75 

15.75 


100.00 


The  calorific  power  of  such  straw  would  prove  to  be  8144 
B.T.U.,  or  I  pound  of  coal  equals  2f  to  3f  pounds  of  cotton- 
stalks  or  straw. 

Tan-bark  containing  30  per  cent  of  water  has  a  calorific 
power  of  a  little  over  4200  B.T.U.  and  contains  15  per  cent 
of  ash.  That  is,  one  pound  of  coal  equals  2\  to  3  pounds  of 
dry  tan-bark,  or  6  to  8  pounds  if  the  latter  is  wet.  The  evap- 
orative capacity  of  tan-bark,  expressed  in  pounds  of  water 
evaporated  from  and  at  213°,  is  given  as  follows: 


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HEAT  AND   HEAT-ENGINES. 


With  30  per  cent 
of  Moisture. 


Perfectly  Dry. 

Water  supplied  at   ^i"",,,,   5.46  pounds      3.84  pounds 
Water  supplied  at  212°..  ..  6.31  pounds      4.44  pounds 

The  conditions  of  success  in  burning  tan,  as  is  the  case 
with  all  wet  fuel,  consist  in  completely  surrounding  it  with 
heated  surfaces  and  burning  fuel  so  that  it  may  be  rapidly 
dried,  and  then  so  arranging  the  apparatus  that  thorough 
combustion  may  be  secured.  Here  again,  as  with  sawdust, 
the  hollow  grate-bar  and  forced-blast  systems  in  combination 
with  the  hot  fire-brick  furnace  seem  to  meet  the  conditions 
most  satisfactorily.     Fig.  6  shows  the  overhead-hopper  feed- 


FiG.  6. 

ing  plan  to  secure  automatic  stoking  of  the  furnace  (§  90),  as 
applied  to  a  water-tube  boiler  with  the  forced  current  of  air 
from  a  fan  entering  the  fuel-bed  from  below,  and  the  furnace 
is  arched  over  with  fire-brick,  which  becomes  very  hot  and 
secures  the  necessary  conditions. 

40.  Charcoal. — Charcoal  is  the  product  of  distillation  from 
wood  to  expel  its  volatile  constituents  as  coke   is  produced 


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FUELS, 


47 


from  bituminous  coal.  It  is  done  in  heaps  or  pits  or  ovens 
at  about  600**  to  800°  F.  So  much  of  the  heat-making  prop- 
erties of  native  wood  are  expelled  in  the  process  of  making 
charcoal  that  it  is  of  little  moment  for  motive-power  pur- 
poses. It  is  easily  ignited  and  burns  with  a  flameless  and 
smokeless  incandescence.  Charcoal  has  its  quality  improved 
as  the  temperature  of  its  distillation  is  increased.  The  re- 
sults of  this  process  when  applied  to  black  alder,  previously 
dried  at  about  300°,  are  as  follows: 

COMPOSITION  OF  CHARCOAL   PRODUCED  AT   VARIOUS  TEMPER- 
ATURES. 


Temperature 

Constituents  of  the  Solid  Product. 

of 
Carbonization. 

Carbon. 

Hydrogen. 

Oxygen. 

Nitrogen  and 
Loss. 

Ash. 

302'  F. 
392 

482 
572 
662 
810 
1873 

47-51 

51.82 

65.59 
73.24 
76.64 
81.64 
81.97 

6.12 

3-99 
4.81 

4.25 
4.14 
4.96 
2.30 

46.29 
43.93 
28.97 
21.96 

18.44 
15.24 
14-15 

o.o3 

0.23 
0.63 

0.57 
0.61 
1. 61 
1.60 

47.51 
39-SS 
32. 9S 
24.61 
22.42 
15.40 
15.30 

Peat  charcoal,  produced  by  the  carbonization  of  ordinary 
air-dried  peat,  is  very  friable  and  porous,  and  extremely  diffi- 
cult to  handle  without  reducing  it  to  very  small  particles 
almost  powdery  in  their  character.  Although  it  is  easily 
ignited  and  burns  readily,  its  physical  characteristics  are  such 
as  to  prevent  its  general  use. 

41.  Artificial  or  Patent  Fuels. — Combustible  materials  in 
the  form  of  dust  or  grains  which  in  that  state  are  ill  adapted 
to  convenient  use  for  heat-making  can  be  made  into  a  practi- 
cable and  salable  fuel  by  agglomerating  such  loose  particles 
into  blocks  or  bricks  by  means  of  some  tarry  or  bituminous 
compound  such  as  pitch,  resin,  or  even  glue.  The  fine  dust 
or  grains  would  clog  a  fire  or  be  lost  in  ashes  or  by  the  draft, 
and  would  burn  too  rapidly  and  unsteadily  if  fed  irregularly 


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48  IfEA  T  AND   HEA  T-ENGINES. 

or  by  hand.     By  moulding  into  briquettes  the  combustion  is 

made  gradual  and  from  their  outer  surfaces  inward,  and  the 

larger  mass  is  not  so  readily  extinguished.     This    plan   is 

much  used  in  Belgium  and  in  some  other  places  in  Europe, 

and  has  been  tried  in  America  as  an  expedient  to  work  over 

the  heaps  of  waste  coal  in  the  dumps  of  mines.     Mechanical 

stoking  with  proper  travelling  grates  has  been  found  a  more 

successful  method  of  using  such  material. 

42.  Liquid  Fuel.    Petroleum. — The  second  great  class  of 

fuels  (§  31)  are  those  which  can  be  supplied  in  a  liquid  state 

and  burned  to  a  gas  with  the  consequent  liberation  of  stored 

.heat.      These  liquid  fuels  are  hydrocarbons  and  are  called 

oils.     Oils  of  animal  origin  are  now  supplied  to  such  a  limited 

extent  as  scarcely  to  deserve  consideration,  and  the  cost  of 

extracting  vegetable  oils  from  the  seeds  or  other  products 

which  carry  it  preclude  the  use  of  such  oils  for  fuel.     Hence 

the  mineral  oil,  or  petroleum,  is  the  principal  source  of  heat 

from  liquids,  either  in  its  crude  form  as  it  comes  native  from 

the  oil-well,  or  after  a  part  of  the  constituents  of  natural  oil 

have  been  eliminated  by  the  refining  process.     The  average 

•composition  of  crude  petroleum  is  usually  given  as: 

From  To         Average. 

Carbon 82  87.  i  85 

Hydrogen 1 1.2  14.8  13 

Oxygen  and  impurities 0.5  5.7  2 

100 
Its  specific  gravity  is  from  0.79  to  0.82.  Lima  oil  from 
the  Ohio  wells  is  of  a  dark  green  color,  is  quite  fluid  and  vol- 
atile, and  has  a  disagreeable  odor.  Its  volatility  makes  it 
ilame  easily,  and  give  off  an  explosive  vapor  in  a  confined 
space.  These  two  properties  have  resulted  in  restrictions 
upon  its  use  in  many  cities;  the  health  boards  object  to  the 
odor,  and  the  fire  departments  to  the  danger  of  fire  from  ex- 
plosions. Hence  the  refining  companies  have  introduced 
what  is  called  fuel-oil.     This  is  the  residue  after  a  part  of  the 


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FUELS. 


49 


fractional  distillation  process  has  been  completed, 
summary  of  this  process  is  as  follows: 


A  tabular 


-^      I  Temperature 
^o-       Fahrenheit. 


Distillaie, 


I 


"3 
113  to  140 
140  to  158 

158  to  248 


5     ,  24S  to  347  ^ 


338 -f 
482 


Rhigolene  ) 
Chymogetie  J" 
Gasolene 

Benzine,  naphtha  C 
B 

PoHshing-oils 
'  Kerosene 
I  Lubricating-oil 

Paraffine  wax 

Residuum  and  loss 


Probable 
Per  Cent. 


Specific 
Graviiy. 


traces 

1.5 
10. o 

2.5 

2 


50 

15 

2 

16 


.590  to  .625 

.636  to  .657 
.680  to  .700! 
.714  to  .718 
.725  to  .737 


Flashing.point* 


14 


.802  to 
.850  to 


820 
915 


32 


100  to  122 
230 


The  distillation  for  fuel-oil  is  stopped  after  the  kerosene 
has  been  obtained.  In  many  refineries  only  the  three  prod- 
ucts of  crude  naphtha,  burning  oil,  or  kerosene,  and  the  dis- 
tillate are  recognized,  the  latter  being  the  fuel-oil.  Its 
average  specific  gravity  is  about  .818  or  40**  Baum^  at  60°  F., 
so  that  a  gallon  weighs  7.3  pounds,  as  against  6.81  pounds  for 
the  crude  oil.  It  flashes  at  218**  F.,  or  just  above  the  boil- 
ing-point of  water.  It  is  thick  in  consistency.  The  calorific 
power  of  crude  oil  is  from  20,000  to  21,000  British  thermal 
units,  and  that  of  the  fuel-oil  is  from  17,000  to  19,000  heat- 
units.  Fuel-oil  is  called  **astatki  "  by  the  Russians.  Thos, 
Urquhart  of  Russia,  in  considering  the  use  of  petroleum  for 
locomotives,  gives  the  following  table  of  the  theoretical  evap- 


Pud. 

Specific 

Gravity 

at 

^atcr 

B    I.OOO. 

Chemical  Composition. 

Heating- 
power, 
British 
Thermal 
Units. 

Thcorct. 
Evap.,  Lbs. 
Water  per 

c. 

H. 

0. 

Lb.  Fuel, 
from  and 
at  aiao  F. 

Penna.  heavy  crude  oil.. 
Caucasian  light  crude  oil 
heavy     **      " 

Petroleum  refuse.. 

<70od  English  coal,  mean 
of  98  samples 

0.886 
O.S84 
0.938 
0.928 

1.380 

84.9 
86.3 
86.6 
87.1 

80.0 

13.7 
13.6 
12.3 
II. 7 

5.0 

1.4 
0.1 
I.I 
1.2 

8.0 

20,736 
22,027 
20,138 
19,832 

I4»ii2 

21.48 
22.79 
20.85 
20.53 

14.61 

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50  HEA  T  AND  HEA  T-ENGINES. 

orative  power  of  petroleum  in  comparison  with  that  of  coal, 
as  determined  by  Messrs.  Favre  and  Silbermann. 

The  further  details  of  refining  for  elimination  of  coloring 
matter,  and  the  steps  of  acid  and  alkaline  agitation,  are  aside 
from  the  present  purpose. 

43.  Kerosene. — Kerosene  has  already  been  referred  to  as 
the  **  burning  oil  *'  or  No.  6  in  the  process  of  fractional  dis- 
tillation of  petroleum.  Usually  3J  parts  of  crude  oil  render 
one  part  of  kerosene. 

The  heat  of  combustion  ranges  between  27,000  and  28,000 
B.T.U.  The  quicker  the  distillation  the  poorer  the  product, 
albeit  more  abundant;  but  the  more  abundant  the  lighter 
elements  the  less  safe  is  the  kerosene. 

The  flashing-points  at  which  an  ignitible  vapor  is  given 
off  by  heating  will  range  between  115°  and  125°  F. ;  the  oil 
will  itself  ignite  and  burn  when  heated  to  130°  to  140°  F. 
This  is  called  its  burning-point.  Besides  its  use  as  a  lamp-oil, 
kerosene  is  used  in  certain  forms  of  oil-engine  to  supply  the 
heat  for  motive  power.  The  limited  use  of  the  more  volatile 
petroleum  liquids  will  be  referred  to  in  Chapter  XX  (g§  297 
to  299). 

44.  Alcohols. — There  are  two  kinds  of  alcohol  used  in  the 
arts  and  as  sources  of  heat:  methylic  alcohol  or  wood-alcohol, 
which  has  the  chemical  symbol  CH^O,  and  ethyl  alcohol,  the 
ordinary  form,  which  is  represented  by  CaH.O. 

Wood-alcohol  is  formed  by  dry  distillation  of  wood  in  iron 
retorts  (usually  horizontal)  at  a  heat  not  above  900°  F.  It 
has  a  strong  characteristic  odor  and  boils  at  150°  F.  It 
would  be  a  most  popular  source  of  heat  in  many  places  where 
corn  is  abundant  if  there  were  no  restrictions  upon  its  man- 
ufacture. 

Ethyl  alcohol  is  obtained  by  distillation  from  the  fer- 
mented infusions  of  the  cereal  grains,  which  contain  either 
sugar  or  starch.      It  has  a  specific  gravity  of  0.792  and  boils 


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FUELS,  ST 

at  173°  F.,  but  will  freeze  only  at  200°  below  zero  when 
pure.  It  expands  3^  times  as  much  as  water  between  32° 
and  173^  F. 

Hydrated  alcohols  contain  water  ranging  from  50  per  cent 
by  volume  (proof  spirits)  to  93  per  cent  (cologne  spirits). 
The  affinity  for  water  is  very  strong. 

Pure  alcohol  is  very  inflammable  and  burns  with  a  pale- 
blue  smokeless  flame.  Its  calorific  power  is  about  28,500 
B.T.U.,  which  runs  down  to  12,000  with  greater  hydration. 

45.  Liquid-fuel  Furnaces. — The  heat  may  be  derived 
from  burning  oil  by  setting  fire  to  it  in  the  presence  of  oxy- 
gen while  the  oil  is  a  liquid,  or  is  a  finely  divided  mist  or 
vapor  of  liquid  particles  in  a  current  or  stream  of  air  or 
steam, «or  the  liquid  may  be  made  into  a  gas  and  then  ignited. 

The  heat  of  combustion  may  furthermore  be  utilized  di- 
rectly in  a  motor  cylinder  (the  oil-engine,  Chapter  XX),  or 
the  heat  may  be  used  as  the  heat  of  combustion  of  solid  fuels 
IS,  in  a  furnace  or  fire-box  from  which  it  is  transferred  by  a 
medium  to  the  cylinder. 

The  American  methods  have  been  the  vapor  or  gas  sys- 
tems exclusively.  The  liquid  systems  are  Russian  or  Indian 
in  the  main.  Four  general  plans  have  been  tried.  First, 
bowl-  or  pan-furnaces,  in  which  the  liquid  oil  was  delivered 
through  a  series  of  pipes  into  shallow  vessels  in  the  fire-box, 
and  burned  from  their  surface.  This  plan  is  old  and  prim- 
itive, and  gave  difficulty  from  smoke  because  air-supply  was 
difficult.  Second,  step-furnaces,  in  which  a  series  of  shallow 
troughs  was  arranged  across  the  furnace  in  steps,  and  the  oil 
fed  into  these  troughs  from  above  overflowed  into  the  one 
below  and  met  the  air  for  combustion  in  flat  strata  betweea 
the  steps.  This  answered  for  stationary  conditions.  Third,, 
drop-furnaces  had  the  oil  fed  in  thin  streams  from  many 
pipes  over  a  grooved  plate,  whereon  it  met  the  air  and  was 
burned.      Fourth,  wick-  or  oozing-furnaces,  where  the  liquid 


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52  HEAT  AND    HEAT-ENGINES, 

oil  is  made  to  rise  up  from  below  at  many  points  through  a 
layer  of  an  incombustible  substance  like  lime  or  asbestos  or 
pumice-stone,  or  even  sand.  The  oil  divides  itself  among 
the  interstices  and  burns  fiom  the  top  surface,  where  it  meets 
the  air  as  a  lamp-flame  from  a  wick.  The  difficulty  is  the 
certain  clogging  of  the  capillary  surfaces  by  the  heavy  resid- 
ual matters,  which  are  sticky  and  refuse  to  come  to  the  top 
and  burn 

46.  Oil-vapor  Burners. — The  most  widely  extended  and 
successful  system  for  generating  heat  from  oil-fuel  is  to  com- 
minute or  atomize  the  oil  by  a  current  of  air  or  steam  which 
blows  acrcSss  or  through  it  under  pressure  in  an  appliance  or 
apparatus  which  is  called  a  burner.  The  oil  is  drawn  into 
the  current  of  air  or  steam  by  induction  and  is  torn  into 
shreds  or  drops  by  the  high  velocity  through  a  small  opening, 
so  that  it  enters  as  a  mist  into  the  fire-box,  and  ignites  by 
flame  or  heat  already  there,  all  through  the  saturated  atmos- 
phere, forming  a  volume  of  flame  of  great  intensity  and  heat- 
ing effect.  It  is  rarely  or  never  wise  to  have  the  oil  flow  by 
gravity  to  the  burner,  since  the  flow  of  oil  should  positively 
cease  when  the  inducing  current  of  air  or  steam  is  shut  off, 
and  to  diminish  the  fire  danger. 

The  burner  is  usually  a  modification  of  the  injector  in 
principle.  Its  outlet  is  either  a  slit  or  a  nozzle.  In  the  slit 
sprinklers  the  orifice  is  divided  by  a  thin  partition,  the  oil 
<;oming  on  one  side  of  it  and  the  air  on  the  other.  When  the 
slit  is  horizontal,  as  has  been  usual,  the  oil  is  above  and  the 
air  or  steam  blows  through  the  film  of  oil.  Sometimes  the 
partition  has  grooves,  so  that  oil  passes  in  threads.  Slit 
:sprinklers  are  wasteful  of  oil  and  of  steam  as  compared  with 
the  other  types.  They  will  call  for  6.6  pounds  of  oil  per 
H.P.  per  hour,  and  will  use  from  6  to  8  per  cent  of  the 
steam  which  is  made  by  the  boiler  for  which  the  burner  sup- 
plies necessary  heat.     They  also  are  liable  to  become  clogged 


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FUELS.  53 

with  the  solid  matters  of  the  oil  residue,  and  to    become 
blown  out  by  their  own  operation. 

Nozzle  sprinklers  have  the  air  and  oil  concentric  in  a  con- 
verging tube — ^the  air  usually  in  the  middle.  The  air-  or 
steam-nozzle  is  usually  adjustable  within  the  oil-tube,  so  as  to 
vary  the  flow  of  oil,  and  to  permit  cleansing  of  the  oil-tube 
by  retracting  the  air-nozzle.  Such  burners  will  require  from 
4.4  to  5.5  pounds  of  oil  per  H.P.  per  hour,  and  will  consume 
from  4  to  6  per  cent  of  the  steam  which  the  burner  will  make. 
When  there  is  no  nozzle  adjustment  the  sprinkler  will  be 
called  a  pipe  burner  rather  than  a  nozzle  sprinkler.  Some 
forms  of  burner  aspirate  a  current  of  air  first  by  a  steam-jet, 
and  then  the  combined  air-  and  steam-current  aspirate  and 


OiL 


Fig.  7. 


atomize  the  oil.  The  jet  of  oil-vapor  should  impinge  upon 
fire-brick  or  similar  refractory  material,  which  becomes  incan- 
descent and  keeps  the  flaming  vapor  alight.  Metal  surfaces 
are  eroded  rapidly  from  the  intense  heat  when  the  flame  im- 
pinges upon  them.  The  fire  is  started  by  an  igniter  of  chips 
or  waste  soaked  with  kerosene;  but  after  becoming  well 
started  the  mass  of  fire-brick  will  start  the  flame  anew  after 
the  oil  has  been  shut  off  for  a  while.  There  are  several  de- 
signs of  oil-burner,  known  by  their  manufacturers'  names. 
(Figs.  7  and  8  illustrate  types.) 


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54 


HEAT  AND   HEAT-ENGINEti, 


With  respect  to  the  use  of  air  or  steam  for  the  inducing 
means  to  draw  up  and  atomize  the  oil,  it  may  be  said  on 
behalf  of  steam  that  it  requires  no  s^ir-compressing  plant  to 
bring  it  up  to  pressure  for  use  under  boilers,  and  there  is  not 
introduced  into  the  flame  a  mass  of  inert  nitrogen  which 
must  be  heated  at  the  expense  of  the  oil-fuel,  and  acts  to 
cool  it.    Steam  is  hot,  furthermore,  when  it  enters  the  flame, 


Fie.  8. 

and  may  be  superheated.  On  the  other  hand,  air  must  be 
introduced  for  combustion,  and  it  is  best  to  introduce  it  as 
the  spraying  and  subdividing  medium;  steam  dilutes  the 
burning  gas  if  it  is  not  dissociated;  and  if  it  is,  the  heat  of 
dissociation  is  lost  unless  the  temperature  is  high  enough  for 
recombination. 


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FUELS,  5S 

47.  Oil-gas  Systems. — The  third  group  of  methods  for 
getting  heat  from  oil  is  the  plan  of  making  the  oil  into  a  gas 
by  heating  it  in  a  proper  retort,  into  which  also  superheated, 
steam  is  introduced,  at  a  temperature  above  300°  F.  The 
Archer  process  is  one  of  the  best  known  of  its  class,  and  has 
the  steam  and  oil  enter  a  cylindrical  retort  or  thermogen  in 
such  a  way  as  to  secure  an  intimate  mixture  of  the  constit- 
uents. The  plant  at  the  outset  involves  more  than  the 
burner  or  vapor  plans,  and  the  retort  connections  are  liable 
to  clogging  from  the  residues  of  the  oil.  Sometimes,  how- 
ever, by  the  finer  subdivision  and  better  access  for  air  which 
gas-firing  permits,  the  gas  systems  burn  less  oil  for  a  given 
heating  effect  than  the  vapor-furnaces. 

A  form  of  oil-gas  is  much  used  wherein  the  gas  is  made 
by  forcing  air  under  pressure  through  a  liquid  hydrocarbon, 
such  as  gasoline.  The  carbureter  is  placed  between  the 
pressure-tank  and  the  burner,  and  the  air  on  its  way  to  the 
burner  picks  up  enough  carbon  to  form  an  illuminating-gas. 
This  method  has  been  considerably  applied  for  railway-car 
lighting.  When  so  used,  the  air  is  delivered  to  the  carbu- 
reter from  the  air-brake  tanks,  passing  through  a  spiral  coil 
of  fine  copper  pipe  in  the  chimney  of  the  lamp.  The  car- 
bureter contains  a  gasoline  of  about  88^  Baum^,  absorbed  in 
a  tightly  compressed  cotton  wicking. 

The  Pintsch  oil-gas  (Julius  Pintsch,  Berlin,  1871)  is  a 
true  or  fixed  gas  made  in  retorts  by  vaporization  of  crude 
petroleum.  From  70  to  85  cubic  feet  of  a  50-  to  60-candle- 
power  gas  results  from  distillation  of  one  gallon  of  oil.  For 
railroad  use  this  gas  is  compressed  in  tanks,  to  150  pounds 
pressure  or  more,  which  supply  the  smaller  gas-tanks  under 
the  cars.  Each  of  these  car-tanks  will  hold  enough  for  from 
two  to  six  days*  travel.  The  gas  is  rich  in  illuminating  prop- 
erties and  does  not  lose  so  much  of  its  illuminating  power  by 
compression  as  a  coal-gas.  A  small  deposit  of  hydrocarbon 
is  found  in  the  bottom  of  the  storage  tanks,  however. 


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56  HEAT  AND   HEAT-ENGINES. 

48.  Advantages  of  Oil-fuel. — Oil  or  liquid  fuel  offers- 
many  attractive  advantages  over  the  solid  fuels.  Many  of 
these  are  those  incidental  to  mechanical  firing,  to  which  oil 
lends  itself  easily,  but  besides  these  there  are  many  others  of 
its  own. 

Mechanical  handling  of  oil  by  pumps  or  aspirating  burners 
gives  the  following  advantages: 

1.  Economy  of  labor.  One  fireman  by  handling  the  nec- 
essary valves  can  manage  eight  to  ten  or  more  boilers  of  100 
horse-power  each.  With  hand-firing  of  coal,  one  man  can. 
never  manage  more  than  four  such  boilers. 

2.  No  ashes,  and  their  attendant  labor  and  possible  cost- 
Economy  and  convenience  in  oil-firing  result  from: 

3.  No  waste  of  fuel  in  ashes  and  cleaning  of  fires 

4.  No  waste  of  fuel  in  banking  fires  overnight. 

5.  No  opening  of  furnace-doors  for  firing  or  cleaning. 
This  is  easier  upon  the  brick-work  of  the  setting,  and  on  the^ 
metal  of  the  boiler,  by  diminishing  strains  of  sudden  contrac- 
tion. 

6.  No  injury  from  firing-tools  in  fire-boxes. 

7.  No  sparks  pass  out  from  a  chimney,  to  set  fire  to 
combustibles  outside. 

8.  Absence  of  dust  and  ashes  in  fire-room  and  adjoining 
engine-room. 

9.  Wide  range  of  controllability  of  fire,  not  only  within 
the  limits  of  ordinary  consumption,  but  beyond  these.  The 
fire  is  put  out  when  demand  for  heat  stops  ;  an  excessive 
demand  for  heat  can  be  met  by  unusually  great  supply  of  oil. 
With  solid  fuel,  a  charge  once  made  must  burn  itself  out. 
In  boilers,  safety-valve  waste  is  diminished. 

10.  The  greater  calorific  power  of  oil,  and  its  controlled 
combustion,  enable  more  energy  to  be  gotten  from  a  plant 
whose  capacity  has  been  calculated  upon  a  solid  fuel  basis. 

11.  Smokeless  combustion  is  more  easily  secured,  and 
there  is  diminished  loss  of  unburned  carbon. 


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FUELS.  IT 

12.  Lower  temperatures  of  fire-rooms,  and  lessened  phys- 
ical strain  upon  firemen. 

13.  Absence  of  sulphur  to  corrode  metal. 

14.  Fires  easily  started. 

15.  Economy  of  stowage  and  carriage  of  oil  as  compared' 
with  solid  fuel. 

16.  Economy  of  fuel-stations  for  navy  or  locomotive 
practice. 

17.  No  grates  are  required. 

Usual  relations  of  oil  to  coal  as  fuel  give  i  pound  of  oil 
to  if  pounds  of  coal;  or  i  gallon  of  oil  equals  6.5  to  6.7 
pounds  of  oil  and  will  compare  to  12  pounds  of  coal;  or  190 
gallons  of  oil  will  equal  a  long  ton  of  coal  of  2240  pounds. 

49.  Disadvantages  of  Oil-fuel. — There  are  objections  to 
oil  as  a  dependence  for  a  source  of  heat. 

1.  The  use  of  crude  oil  with  the  volatile  constituents  in  it 
is  opposed  by  the  health  ordinances  of  some  cities.  In  others 
the  fire  or  insurance  ordinances  permit  the  use  of  oil  only  if 
the  oil-tank  is  below  ground,  or  so  placed  that  it  cannot  flow 
out  of  its  reservoir  and  carry  flame  to  other  buildings  in  case 
of  conflagration. 

2.  The  vapor  from  crude  oil  is  ill-smelling  and  makes  an 
explosive  mixture  with  air.  It  vaporizes  even  at  lov/  temper- 
atures. 

3.  If  fuel-oil  must  be  used,  it  is  usually  more  costly  than 
coal  in  most  places.  The  problem  is  really  to  get  the  most 
heat-units  for  a  unit  of  value.  If  the  quotient  of  the  calorific 
power  of  oil  per  pound  divided  by  its  price  per  pound  at  any 
point  is  greater  than  the  same  quotient  for  solid  fuel,  the  oil 
is  the  cheaper. 

4.  The  total  oil-production  of  the  world  would  supply  but 
a  small  portion  of  the  demand  for  heat  as  a  source  of  energy. 
This  would  immediately  affect  the  price  of  oil,  if  any  large, 
number  of  consumers  were  to  decide  to  use  oil. 


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58  HEAT  AND   HEAT-ENGINES. 

5.  Most  o£  the  spray  burners  make  an  objectionrable  roar- 
ing noise. 

6.  The  surfaces  exposed  to  an  oil-flame  usually  become 
coated  with  a  deposit  of  residue  from  the  burning  oil. 

7.  Oil  creeps  past  valves  and  leaks  in  a  way  which  is  an- 
noying and  may  be  dangerous. 

8.  Explosion^  occur  from  the  flame  blowing  out,  and  ignit- 
ing again  with  dangerous  combinations  of  oil-vapor  and  air. 

9.  Auxiliary  apparatus  in  the  way  of  a  source  of  steam  or 
compressed  air  is  required  for  the  burners;  in  starting,  there 
must  be  a  supply  available  of  air  or  steam  from  a  boiler  or 
reservoir. 

50.  Gaseous  Fuels.  General. — It  is  one  of  the  most 
tenable  theories  of  the  combustion  of  solid  and  liquid  fuels, 
that  the  effect  of  the  igniting  heat  is  to  gasify  the  carbon  or 
hydrocabron  on  the  surface,  and  that  chemical  union  with 
oxygen  takes  place  when  both  are  gases,  the  carbon  gas  being 
in  a  nascent  state.  If  this  view  is  sound,  there  are  advan- 
tages connected  with  the  plan  of  making  gas  on  a  large  scale 
artificially,  or  in  using  natural  gas  as  a  fuel.  Gas-firing 
offers  the  same  advantages  as  a  principle  as  those  which  un- 
derlie the  use  of  oil  in  the  matter  of  mechanical  handling, 
control,  cleanliness,  and  convenience.  Gas-firing,  further, 
requires  less  excess  of  air  for  combustion — or  none;  and  when 
gas  can  be  used  as  a  source  of  heat  energy  direct  in  the  cyl- 
inder, the  advantages  are  introduced  which  follow  from  avoid- 
ing some  of  the  necessities  for  losses  which  are  introduced  in 
other  systems. 

Gas-fuel  may  be  natural  gas  or  a  manufactured  article. 
Manufactured  or  artificial  gas  may  be  producer-gas,  water- 
gas,  or  illuminating-gas. 

51.  Natural  Gas. — In  certain  parts  of  America,  notably 
in  Pennsylvania,  Ohio,  and  Indiana,  large  accumulations  of 
a  natural  fuel-gas  are  found  in  subterranean  cavities  or  strata, 
^'hich  can  be  reached  by  wells.     This  gas  is  either  a  stored 


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FUELS. 


59 


product  of  a  previous  distillation,  or  else  is  a  product  of  a 
process  still  in  operation.  It  is  usually  under  considerable 
pressure  at  the  wells,  so  that  it  can  be  piped  to  industrial 
centres  without  too  great  losses,  or  artificial  pressure  may  be 
secured  by  proper  gas-pumps. 

Various  districts  give  var>'ing  constitution  of  gas  and 
hence  varying  calorific  power  ;  around  Pittsburg,  Pa.,  i 
pound  of  coal  is  considered  to  be  the  equivalent  of  from  7J 
to  \2\  cubic  feet  of  gas.  The  following  tables  give  some 
analyses: 

VARIATION    IN    COMPOSITON    OF    NATURAL    GAS. 


Constituents. 


Marsh-g^s 57-85 

Hydrogen 

Ethylic  hydride 

defiant  gas 

Oxygen 

Carbonic  oxide 

Carbonic  acid 

Nitrogen 


9.64 
5.20 
0.80 
2.10 
1. 00 
0.00 
23-41 


75.16 
14.45 
4.80  I 
0.60  I 
1.20 
0.30  I 
0.30  < 
2.89  I 


72.18 

65.25  ' 

60.70 

20.02 

26.16  ! 

29.03 

3.60 

5.50 

7.92 

0.70 

0.80 

0.98 

1. 10 

0.80 

0.78 

1. 00 

0.80 

0.58 

0.80 

0.60  , 

0.00 

0.00 

0.00 

I 

0.00 

49.58 
35.92 
12.30 
0.60 
Q.80 
0.40 
0.40 
0.00 


Analyses  from  various  wells  in  Indiana  and  Ohio  indicate 
the  composition  to  be  as  follows: 

COMPOSITION    OF    NATURAL    GAS    FROM    OHIO    AND    INDIANA. 


Constituents. 


Hydrogen 

Marsh-gas 

defiant  gas 

Carbonic  oxide 

Carbonic  acid 

Oxygen 

Nitrogen   

Hydrogen  sulphide. 


Ohio. 

Indiana. 

Fostoria 

Findlay 

St. 
Mary's. 

Muncie. 

Ander- 
son. 

Koko. 
mo. 

1.89 

1.64 

1.94 

2.35 

1.86 

1.42 

92.84 

93.35 

93.85 

92.67 

93 'O7 

94.16 

0.20 

0.35 

0.20 

0.25 

0.47 

0.30 

0.55 

0.41 

0.44 

0.45 

0.73 

0.55 

0.20 

0.25 

0.23 

0.25 

0.26,     0.29' 

0.35 

0.39 

0.35 

0.35 

0.42      0.301 

3.82 

3.41       2.98,      3.53 

3.02      2.80, 

0.15 

0.20 

0.21 

0.15 

O.It 

0.18, 

Marion. 


1.20 
93.57 
0.15 
0.60 
0.30 
0.55 
3-42 
0.20 


The  Indiana  gas  weighs  0.045  pound  per  cubic  foot. 


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6o  HEAT  AND   HEAT-ENGINES. 

52.  Producer-gas. — Gas  made  by  distilling  bituminous  or 
anthracite  coal  in  a  closed  furnace,  using  part  of  its  own  heat 
of  combustion  to  effect  the  chemical  reactions,  is  often  called 
producer-gas,  from  the  name  given  to  the  gas-generator.  A 
thick  bed  of  fuel  rests  upon  properly  constructed  grates,  and 
air  or  steam  or  both  is  forced  from  below  the  grates  up 
through  the  bed  of  fuel.  The  first  combustion  is  to  carbonic 
acid  (CO,)  with  air  alone,  or  to  CO,  and  hydrogen  if  steam 
is  used  also.  This  carbonic  acid  gas,  meeting  the  layers  of 
carbon  above  where  no  free  oxygen  reaches,  is  decomposed 
by  the  carbon  into  two  units  of  carbonic  oxide  (CO),  which 
with  the  hydrogen  passes  up  through  the  bed  of  fuel  and  out- 
wards through  a  proper  pipe  to  the  place  where  it  may  meet 
the  required  oxygen  and  be  burned  at  the  point  desired. 
Early  producers  of  the  Siemens  type,  operating  with  open 
ash-pits  and  no  pressure  below  the  grates,  lost  much  of  their 
possible  efifectiveness  in  the  cooling  of  the  gases  after  leaving 
the  producer.  This  loss  is  estimated  at  30  per  cent.  To 
blow  with  air  alone  is  to  introduce  inert  nitrogen  which 
dilutes  the  gas  and  lowers  its  calorific  power.  On  account  of 
the  loss  of  heat  in  the  producer  itself  in  the  distilling  process, 
and  some  loss  in  the  dissociation  of  the  water,  which  is  not 
all  recovered,  producer-gas  usually  carries  only  87  per  cent  of 
the  calorific  energy  of  the  carbon.  Some  loss  in  unreduced 
CO,  must  be  allowed  for,  and  the  cost  of  making  the  steam 
used.  Eighty-two  per  cent  is  a  more  usual  figure  when 
anthracite  is  used  as  fuel  instead  of  bituminous  coal.  Much 
inferior  grades  of  fuel  can  be  used  in  the  producer  than  could 
be  used  direct,  however. 

If  an  analysis  of  85  per  cent  of  solid  carbon  be  assumed 
for  an  anthracite  stock,  with  5  per  cent  of  volatile  hydrocar- 
bons and  10  per  cent  of  ash,  and  the  further  assumption  be 
made  of  a  combustion  of  80  pounds  to  CO,  and  5  pounds  of 
CO,  the  following  calculated  statement  of  process,  products,, 
and  resulting  energy  may  be  agreed  to: 


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FUELS.  6l 


Process. 


^o  lbs.  C  burned  to CO 

5  lbs.  C  burned  to COt 

5  lbs.  vol.  HC  (distilled) 

I20  Ib^.  oxygen  are  required,  of  which  30 

lbs,  from  H«0  liberate H 

90  lbs.  from  air  are  associated  with. .  .N 


Products. 

Pounds. 

Cubic  Feet. 

Anal,  by  Vol. 

186.66 

2529.24 

33.4 

18.33 

157.64 

2.0 

5.00 

116.60 

1.6 

3.75 

712.50 

9.4 

301.05 

4064.17 

53.6 

514.79         7580.15 


Energy  in  the  above  gas  obtained  from  100  pounds  an- 
thracite : 

186.66  lbs.  CO 807,304  heat-units. 

5.00   ♦*     CH« 117.500 

3-75    '*     H 232,500  '• 


1.157,304 

Total  energy  in  gas  per  lb 2,248  '* 

*'          '•         "  100  lbs.  of  coal.  1,349,500         ** 
Efficiency  of  the  conversion 86  per  cent. 

If  the  gas-stock  be  a  bituminous  coal  with  55  per  cent  of 
fixed  carbon,  32  per  cent  of  volatile  matter,  and  13  per  cent 
of  ash,  and  the  calorific  power  of  the  hydrocarbons  be  taken 
at  20,000  heat-units  to  the  pound,  the  following  table  results 
under  the  same  assumptions: 

Process.  , 

Pounds.  Cubic  Feet.    Anal,  by  Vol. 

50  lbs.  C  burned  to CO  116.66  1580.7  27.8 

5  lbs.  C  burned  to CO«  18.33  I57«6  2.7 

32  lbs.  vol.  HC  (distilled) 32.00  746.2  13.2 

80  lbs.  O  are   required,  of  which  20  lbs., 

derived  from  H9O.  liberate H  2.5  475.0  8,3 

60  lbs.  O,  derived  from  air,  are  associated 

with N  200.70  2709.4  47.8 


Products. 


370.19  5668.9  99.8 

Energy  in  116.66  lbs.  CO 504,554  heat-units. 

**        •'   32.00  lbs.  Vol.  HC. . .       640,000         " 
*•     2.50  lbs.  H 155,000 

1,299,554 

Energy  in  coal i,437,5oo         *' 

Per  cent  of  energy  delivered  in  gas 90.0 

Jieat-units  in  i  lb.  of  gas 3484 


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62 


HEAT  AND   HEAT-ENGINES. 


Fig.  9  illustrates  the  old  type  of  Siemens  producer  with- 
out  artificial  blast,  and  Fig.  lo  the  more  modern  Taylor  pro- 
ducer with  forced  steam-blast  and  revolving  grates. 


Fig.  9. 

Ordinary  producer-gas  has  a  calorific  value  of  no  B.T.U. 
per  cubic  foot. 

53.  Water-gas. — A  great  deal  of  gas  for  illuminating  and 
power  purposes  is  now  made  by  the  process  of  intermittent 
and  alternate  blowing  of  air  and  steam  through  a  thick  bed 
of  fuel  in  a  cylindrical  producer  of  boiler-plate  lined  with 
refractory  material.  The  fuel  is  blown  by  air  from  below 
until  it  becomes  highly  incandescent;  the  producer  may  be 
open  at  the  top,  and  waste  the  lean  carbonic  oxide  which 
comes  off  from  the  top,  or  the  latter  can  be  caught  and  used. 
After  blowing  with  air  as  long  as  necessary,  the  air  is  shut  off, 
and  steam  is  similarly  blown  from  below,  with  the  producer 
closed  except  at  its  delivery  to  a  gas-holder.  The  steam  is 
dissociated  by  the  incandescent  carbon  into  hydrogen  and 
oxygen,  and  the  latter  unites  with  the  carbon  as  in  the  air- 
producer,  to  be  reduced  to  carbonic  oxide.  The  hydrogen 
passes  out  without  further  chemical  reaction.      This  process 


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FUELS. 


63 


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•64 


HEAT  AND   HEAT-ENGINES, 


was  introduced  in  1874  by  Mr.  T.  S.  C.  Lowe,  and  is  often 
known  generally  as  the  Lowe  process.  For  illuminating  pur- 
poses this  fuel  gas  is  more  highly  carburetted  by  sprays  of 
hydrocarbon  vapors  (such  as  naphtha  or  similar  petroleum 


Fio.  106. 
-products)  which  are  made  a  fixed  gas  by  later  heating  in  a 
superheater. 

Fig.  1 1  illustrates  what  is  called  in  England  the  Dowson 
gas-producer,  which  belongs  to  this  class.  Its  product  is 
sometimes  known  in  America  as  semi-water-gas.  Its  analysis 
runs  by  volume : 

Hydrogen,  H from   18.73     to 


26.55 


Marsh-gas,  CH, 

Olefiant  gas,        C,H, 
Carbonic  oxide,  CO  . 
Carbonic  acid,     CO,.. 
Oxygen,  O  .  . 

l^itrogen,  N.  .  . 


•3M.  . 

.31) 

I. II 

25.07    * 

18.20 

6.57  ' 

'     11.30 

.03    ' 

.47 

48.98    ' 

'   42.28 

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The  ash-pit  B  is  closed  and  air  and  steam  are  forced 
through  N  and  up  through  the  mass  of  anthracite  or  coke 
which  fills  the  producer-chamber.  The  feedmg  is  done 
through  the  hopper  A'  by  means  of  its  double  lid  and  air-lock 
action.  The  gas  passes  up  through  the  coke-scrubber  into 
the  holder  K. 


Pig.  11. 

A  French  form  of  water-gas  producer  is  known  as  Len- 
cauchez*.  Its  object  is  to  improve  on  the  Dowson  type  by 
saving  waste  heat,  and  render  it  available  for  coals  having 
some  tendency  to  fuse  together  from  the  presence  of  tarry 
matters  (Fig.   12).     The  hanging  bridge  E  forces  the  gases 


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66 


HEAT  AND   HEAT-ENGINES. 


above  the  middle  of  the  fuel-bed  to  pass  downwards  before 
escaping  to  the  flue  /%  and  so  out  to  the  holder  through  the 


Fig.  12. 

passage  /.  The  annular  chamber  H  is  a  steam-boiler,  whose 
water  cools  the  outflowing  gases,  and  whose  steam  entering 
the  chamber  G  meets  with  air  from  a  blower  through  the  pipe 


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FUELS.  67 

Z,  and  the  combined  air  and  steam  are  forced  through  the 
pipes  M  into  the  closed  ash-pit  and  so  up  through  the  fuel. 
The  descent  of  the  distilled  gas  through  the  hot  fuel  before 
passing  out  is  the  feature  which  is  expected  to  break  up  the 
tarry  elements  of  the  distillation.  Lencauchez'  gas  analysis 
shows : 

Hydrogen,  H 18.34 

Olefiant  gas,  CH, 1.25 

Hydrocarbons,  QH 1.55 

Carbonic  oxide,  CO 27.32 

Carbonic  acid,  CO, 3.60 

Sulphur  dioxide,  SO, 04. 

Hydrogen  disulphide,  H,S 06 

Nitrogen,  N 47-84 

Dowson  gas  has  a  calorific  value  averaging  150  B.T.U. 
per  cubic  foot,  while  the  true  water-gas  should  have  290. 

54.  Coal-gas  or  Illuminating-gas. — The  ordinary  gas 
used  in  cities  and  large  towns,  and  which  was  universal  pre- 
vious to  the  introduction  of  water-gas,  is  made  by  distilling 
bituminous  coal  in  retorts.  These  retorts  are  long  semi-cy- 
lindrical tubes  holding  each  from  160  to  300  pounds  of  caking 
bituminous  coal — often  enriched  by  some  cannel-coal — under 
and  around  which  the  heat  from  a  coke-fire  is  maintained. 
The  vapors  distilled  off  become  a  fixed  gas  by  being  passed 
through  that  part  of  the  distilling  apparatus  which  is  kept  at 
a  white  heat.  Other  features  of  the  process  involve  the 
methods  for  condensing  tarry  and  offensive  vapors  and  for 
cleansing,  which  are  aside  from  the  present  purpose.  The 
products  of  distillation  of  I(X)  pounds  of  ordinary  gas-coal  are 
usually: 

Coke 64     to     65  pounds 

Purified  gas 15      **      12        ** 

Ammonia  liquor 10      ''      12        *' 

Tar 6.5  *'        7.5    '* 

Loss  and  impurities 4-5  **        35    ** 

lOO.O  lOO.O 


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68  HEA  T  AND   HEA  T-ENGINES. 

The  composition  by  volume  usually  ranges: 

Hydrogen 38     to     48  per  cent 

Carbonic  oxide 2      **      14        ** 

Marsh-gas,  CH, 43      '*      31        ** 

{Ethylene  \ 

Propylene         >  7-5  **        4»S     *' 
Benzole  vapor ) 

Nitrogen i      **        3        ** 

The   following  analyses  are  taken  from  a   report  of  Dr. 
Gideon  E.  Moore  on  the  Granger  Water-gas,  1885  : 

ANALYSES    OF    WATER-GAS    AND    COAL-GAS    COMPARED. 


Composition  by  Volume. 

Composition  by  Weight. 

Water-g^as. 

CoaUgas. 
Heidel- 
berg. 

Water-gas. 

Coal-gas. 

Worcester 

Lake. 

Worcester 

Lake. 

Nitrogen 

2.64 
0.14 
0.06 
11.29 
0.00 

1.53 
28.26 
18.88 
37.20 

3-85 

0.30 

0.01 

12.80 

0.00 

2.63 

23.58 

20.95 

35.88 

2.15 
3.01 
0.65 

2-55 
1. 21 

1.33 

8.88 

34.02 

46.20 

0.04402 
0.00365 
O.OOII4 
0.18759 

0.o6l75j  0.04559 
0.00753    0.09992 

0.00018     ^   e\i e.f\€\ 

Carbonic  acid 

Oxvcen  ..•..•■ 

Ethylene 

0.20454 

0.05389 
0.03834 
0.07825 
0.18758 
0.41087 
0.06987 

Proovlene 

Benzole  vapor 

Carbonic  oxide 

Marsh-eras 

0.07077 
0.46934 
0.17928 
0.04421 

O.I 1 700 

0.37664 
O.I9133 
0.04103 

H  vdroflren 

100.00 

100.00 

100.00 

I.OOOOC 

I. 00000 

I. 00000 

Density:  Theory.. . . 
Practice  . . . 

0.5825 
0.5915 

0.6057 
0.6018 

0.4580 

B    T    U     from   i   cu 

650.1 
597.0 

688.7 
646.6 

642.0 
577.0 

ft.:  water-liquid.. 
**       vapor.. 



Flame-temp.,  Fahr... 

5311-2' 

5281. 1 

5202.9° 

Av.  candle-power. . . 

22.06 

26.31 

1 

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FUELS,  69 

CALORIFIC    EQUIVALENTS   OF   CONSTITUENTS   OF    ILLUMINATING-GAS. 

Heat-units  from  1  lb. 

Water>liquid.  Water- vapor. 

Ethylene 21,524.4  90,134.8 

Propylene 21,222.0  19,834.2 

Benzole  vapor 18,954.0  17,847.0 

Carbonic  oxide 4>395*6  4t395*6 

Marsh-gas 24,021.0  21,5^2.8 

Hydrogen 61,524.0  51,804.0 

55.  Acetylene-gas. — The  gas  C,H,  released  from  calcium 
carbide  by  addition  of  water  is  as  yet  of  no  significance  for 
large-scale  heating,  but  has  been  much  examined  for  use  in 
motor-carriages  and  elsewhere  where  gas-power  in  small  bulk 
is  the  prerequisite.  One  pound  of  calcium  carbide  with  a 
half-pound  of  water  will  liberate  5f  cubic  feet  of  gas.  It  has 
a  heat  capacity  of  18,260  B.T.U.  per  pound  or  1259  per 
cubic  foot,  at  14^  cubic  feet  to  the  pound.  It  requires  12^ 
volumes  of  air  to  burn  it,  which  is  usually  raised  to  14  or  15 
in  practice.  It  has  been  compressed  to  a  liquid  at  68^  F.  by 
a  pressure  of  600  pounds  per  square  inch. 

Acetylene  ignites  at  510°  F.  in  proper  mixtures  with  air, 

56.  Comparison  of  Gaseous  Fuels. — Of  the  four  sorts  of 
gas  used  as  a  source  of  heat,  water-gas  has  the  highest  theo- 
retical temperature  of  combustion — 4850°  F.  Producer-gas 
gives  3441°.  The  natural  gas  and  coal-gas  are  nearly  of  the 
same  value  as  the  water-gas.  The  following  tables  quoted 
from  Mr.  Emerson  McMillin  give  some  interesting  facts. 

Including  natural  gas  the  relative  volumes  and  weights  of 
gaseous  fuels  are: 

By  Weight.  By  Volume. 

Natural  gas 1000  looo 

Coal-gas 949  666 

Water-gas 292  292 

Producer-gas 76.5  13a 


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70 


HEAT  AND   HEAT-ENGINES, 
COMPOSITION    OF    GASES    BY    VOLUME. 


Hydrogen 

Marsh-gas 

Carbonic  oxide 
defiant  gas.. . . 
Carbonic  acid  . 

Nitrogen 

Oxygen  

Water-vapor. . . 
Sulphydric  acid 


Findlay,0., 

Natural 

Gas. 


2.18 
92.60 
0.50 
0.31 
0.26 
3.61 

0.34 
0.00 
0.20 


100.  cx> 


Coal-gas. 


46.00 
40.00 
6.00 
4.00 
0.50 
1.50 
0.50 
1.50 


Water-gas. 


45.00 
2.00 

45.00 
0.00 
4.00 
2.00 
0.50 
1.50 


Penna. 
Stccl-works 
Producer-gas. 


6.00 
3.00 

23.50- 
0.00 
1.50 

65.00 
0.00 
1. 00 


COMPOSITION    OF   GASES    BY    WEIGHT. 


Hydrogen 

Marsh-gas 

Carbonic  oxide. 
Olefiant  gas  . . . 
Carbonic  acid. . 

Nitrogen  

Oxygen 

Water-vapor.. . 
Sulphydric  acid 


Findlay.O., 

Natural 

Gas. 


0.268 
90.383 
0.857 
0.531 
0.700 
6.178 
0.666 
0.000 
0.417 


100.000 


Coal-gas. 


8.21 

57.20 

15.02 

10.01 

1.97 

3.75 

1.43 

2.41 


Water-gas. 


5-431 
1. 931 

76.041 
0.000 

10.622 
3.380 
0.965 
1.630 


100.600 


Penna. 

Steel-works 

Producer-gas. 


0.458 
1. 831 

25.095 
0.000 

2.517 

69.413 

0.000 

0.686 


TABX.E    OF    RELATIVE    EVAPORATION    OF    WATER    IN    A    STEAM-BOILER. 


Natural-gas. 

Coal-gas. 

Water-gas. 

Producer  gas 

Cubic  feet  gas. . . 

. ..    1000 

1000 

1000 

1000 

Pounds  of  water. 

. . .     893 

591 

262 

"5 

TABLE    OF    RELATIVE   COSTS    OF    GASES    PER    MILLION    B.T.U.    WHICH 
THEY   ARE   THEORETICALLY    ABLE    TO    PRODUCE. 

Cents  per 
Million  B.T.U. 

Coal*gas 734.976  units,  costing  20.00  cents 27.21 

Water-gas 322340     **  **       10.88     "     33.75 

Producer-gas....   117,000     **  **         2.58     **    22.05 


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FUELS. 


n 


£.  P.  Reichhelm  has  discussed  the  use  of  gaseous  fuel  for 
forge  fires,  for  drop-forging,  in  annealing-ovens,  and  fur- 
naces for  melting  brass  and  copper,  for  case-hardening,  muffle- 
furnaces,  and  kilns.  Under  ordinary  conditions,  in  such 
furnaces  he  estimates  that  the  loss  by  draft,  radiation,  and 
the  heating  of  space  not  occupied  by  work  is  with  coal  80 
per  cent,  with  petroleum  70  per  cent,  and  with  gas  above 
the  grade  of  producer-gas  25  per  cent.  He  gives  the  follow- 
ing table  of  comparative  cost  of  fuels,  as  used  in  these  fur- 
naces : 


Kind  of  Gas. 


Natural  gras. 

Coal-fira&.  90  candle>power 

Carbureted  water.gaa 

Gasolene  gas,  ao  cand  le-po wer 

Water-gas  from  coke 

"Water-gas  from  bituminous  coal 

Water-gas  and  producer-gas  mixed 

Producer-gas   

Naphtha-gas,  fuel  3^  gallons  per  looo  ft.. 


Number  of 
Heat-units 
in  1000  cu. 

ft.  used. 


1,000,000 
675,000 
646,000 
690,000 
3«3fOa> 
377.000 
185,000 
150.000 
3061365 


Number  of 
Heat-units 
in  Furnaces 

after 
deducting 
35$  Loss. 


730,000 
506,350 
484.500 
517.500 
234.750 
aba,75o 
"38,750 
119,500 
339.774 


Coal,  $4  per  ton,  per  1,000,000  heat-units  utilized 

Crude  petroleum,  3  cu.  per  gal.,  per  i,ooO|Ooo  heai-uniis. 


Average 
Cost  per 

zooo  It. 


$1.35 

z.oo 

.90 
.40 

'45 

.30 

•«5 
•IS 


Cost  of 

1,000,000 

Heat-uniu 

obtained 

in 

Furnaces. 


$3.46 
a.o6 

«-73 
X.70 
X.59 
««44 
«-33 
.65 


.73 
•73 


In  the  use  of  natural  gas  in  boiler-firing,  it  has  been  found 
that  one  man  can  attend  to  1500  horse-power  of  boilers,  while 
"with  coal  he  could  handle  only  200  horse-power;  hence  a 
Tatio  of  2  to  1 5  in  labor  cost  would  show  that  where  wages 
are  $2.50  per  day  and  the  boilers  require  4  pounds  of  coal 
per  horse-power  per  hour,  the  cost  of  firing  with  coal  will  be, 
per  ton  of  coal  per  12-hour  shift, 


2.5  X  2000 
12  X  200  X  4 


dollars  =  52  +  cents, 


ivhile  lor  gas  but  ^  of  this  will  be  required.  Hence  the  fol- 
lowing table  will  show  the  relative  costs  of  coal  and  gas 
{water)  with  and  without  difference  in  labor  cost: 


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HEAT  AND   HEAT-ENGINES. 


Price  of  Gas  per  1000  cubic  feet. 

Cost  of  Coal 

delivered  to 

Boiler-room 

per  Ton  of  2000  lbs. 

Not  including  Difference  in  Cost 
QtAttendance. 

Including  Difference  in  Cost  of 
Attendance. 

Carbureted. 

Uncarbureted. 

Carbureted. 

Uncarbureted. 

$6.00 
5.00 
4.00 
3.00 
2.00 
1. 00 

14.8  Cts. 

12.3    •• 

9.9    •• 

7.4  •• 
4.9    " 

2.5  " 

6.5  cts. 
5.4    •• 
4.4    " 
3.3    •• 
2.2    •• 
I.I     '* 

16.0  cts. 
13.6    - 

11. 1  •* 
8.6    •• 
6.2    " 
3-7    " 

7.1  Cts. 
6.0    *• 

4.9    *' 
3.8    •• 
2.7    " 
1.6    •* 

The  uncarbureted  gas,  exclusive  of  interest  on  capital, 
costs  from  lo  to  20  cents  per  1000  cubic  feet.  Hence  the 
advantages  in  the  use  of  gas  are  from  other  directions  than 
economy.  The  calorific  power  of  the  uncarbureted  gas  is 
about  54  per  cent  of  that  of  the  carbureted  gas  in  the  above 
table. 

The  heating  value  of  New  York  City  illuminating-gas,  as 
used  in  gas-engines  and  for  general  heating,  has  been 
reported  by  Mr.  E.  G.  Love,  per  cubic  foot  at  60°  F.  and 
barometer  at  30  inches: 

715,  692,  725,  732,  691,  738,  735,  703,  734,  730,  731,  727, 
giving  an  average  of  J2i, 

Probably  710  heat-units  would  be  more  nearly  represent- 
ative of  average  good  quality.  The  coal-gas  of  London,  with 
l6  to  17  candle-power,  has  a  calorific  power  of  668  units  per 
foot  and  costs^from  60  to  70  cents  per  thousand  cubic  feet. 
It  ignites  at  temperatures  of  750**  to  800°  F.  with  proper 
mixtures  of  air. 

57.  Powdered  Fuel. — Among  the  many  experiments 
which  have  been  tried  to  utilize  waste  coal  in  dust  or  culm 
from  mine  or  breaker  refuse  is  to  be  mentioned  the  plan  of 
reducing  the  coal  to  powder,  and  blowing  it  into  the  furnace 
in  the  state  of  fine  division.     The  pulverizers  may  be  of  any 


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FUELS.  73 

type;  the  fuel-dust  is  injected  by  means  of  an  injector  such 
as  is  used  for  oil-vapor  systems,  using  air  as  the  conveying 
medium.  The  furnace  has  to  be  lined  with  fire-brick  which 
must  be  first  brought  to  a  high  temperature  by  an  open  fire. 
Then  the  powder  is  blown  in,  and  once  ignited  burns  regularly 
and  with  good  economy  and  without  smoke,  maintaining  an 
intense  heat. 

58.  Calorific  Power  of  a  Hydrocarbon.-^It  has  been 
already  said  that  the  calorific  power  of  a  compound  was  the 
sum  of  the  calorific  power  of  its  components  (§  22).  Thus 
for  olefiant  gas,  C,H^,  made  up  of 

C,  +  H^  =  24  +  4  =  28  parts  by  weight, 

^^  =  \  will  be  hydrogen,  and  |f  =  ^  will  be  carbon.  If  then 
\  of  the  calorific  power  of  hydrogen  be  added  to  •  of  the 
calorific  power  of  carbon,  their  sum  will  be  the  calorific 
power  of  the  compound.  With  analyzed  hydrocarbons  the 
percentages  of  each  constituent  will  be  used  instead  of  the 
fraction  above. 

The  accepted  formula  for  computing  the  calorific  power 
from  an  analysis  is  due  to  the  physicist  Dulong  and  is  known 
by  his  name.     It  is: 

Calorif.  power  of  i  lb.  inB.T.U.  =  14S00C  +  62500^!!  —  -^j. 

In  this  C,  H,  and  O  are  the  percentages  respectively  of  car- 
bon, hydrogen,  and  oxygen,  divided  by  100  to  reduce  them 
to  actual  fractions  of  one  pound.  This  is  often  transformed 
by  the  expedient  of  factoring  the  constants  -denoting  the 
respective  calorific  powers  of  carbon  and  hydrogen  so  as  to 
read: 

Calorif.  power  =  14500   C  +  4.3i^H  —  -g-j j> 

62500 

smce =  4.31. 

14500       ^  ^ 


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74  ^JSA  T  AND   HEA  T-ENGINES. 

For  an  analyzed  gas,  when  the  weight  of  a  cubic  foot  is 
known  and  the  proportion  of  each  combustible  in  such  cubic 
foot,  the  calorific  power  is  found  by  multiplying  each  weight 
as  a  fraction  of  the  whole  by  the  calorific  power  of  a  whole 
unit  of  that  combustible  and  adding  these  products  together. 
The  calculated  calorific  powers  in  the  following  tables  (§  60) 
were  calculated  in  this  way. 

59.  Evaporative  Power  of  a  Fuel.  Efficiency.  Heat- 
balance. — When  a  fuel  is  used  for  making  steam  to  be  used 
as  a  medium  in  an  engine-cylinder,  the  weight  of  water  at 
212°  F.  which  that  fuel  will  make  into  steam  at  atmospheric 
pressure  becomes  of  interest,  and  is  a  standard  unit  of  com- 
parison between  fuels.  Experiment  has  shown  that  to 
•change  the  state  of  water  at  212°  into  steam  at  212^  requires 
an  absorption  of  966  British  thermal  units  per  pound  of 
water  so  evaporated.  Hence  if  the  calorific  power  of  the 
fuel  be  divided  by  966,  the  quotient  will  be  the  maximum 
evaporative  capacity  of  that  fuel.  For  pure  carbon  the  cal- 
culation is 

14500 
E  =  — ^^  =  15  pounds  of  water  from  and  at  212®. 

This  figure,  of  course,  is  never  reached  in  actual  firing  of 
boilers.  Eighty  per  cent  of  the  total  heat  can  be  obtained  in 
special  conditions;  70  to  75  in  regular  practice  with  good 
anthracite  coal.  What  are  the  reasons  why  the  theoretical 
efficiency  is  not  attained? 

1.  The  loss  in  raising  the  air  and  the  resulting  products  of 
combustion  from  the  temperature  of  the  fire-room  to  that  of 
the  flues  and  chimney-stack.  This  loss  will  be  diminished 
by  preheating  the  air  by  some  waste  heat,  and  by  diminishing 
the  weight  of  diluent  air  in  excess  of  that  needed  for  combus- 
tion. 

2.  The  loss  in  evaporating  any  water  in  the  coal,  and  in 


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FUELS.  75 

the  air  itself.     This  moisture  has  to  be  raised  to  212°  and 
made  into  steam  at  atmospheric  pressure. 

3.  The  heat  lost  in  heating  up  the  earthy  matter  or  ash 
in  the  coal  from  the  temperature  of  the  fire-room  to  that  of 
the  fire.  Obviously,  therefore,  the  less  the  percentage  of 
such  ash  the  more  effective  the  fuel. 

4.  The  heat  absorbed  in  distilling  off  from  the  fuel  the 
volatile  matter  or  hydrocarbons,  if  any,  and  raising  them  and 
the  solid  carbon  of  the  fresh-fuel  charge  to  the  point  at  which 
they  will  burn.  This  often  makes  the  softer  bituminous 
coals  show  to  a  disadvantage  in  competition  with  hard  coal 
containing  less  volatile  matter. 

5.  The  loss  of  unburned  carbon  dropping  down  with  the 
ash  and  removed  with  it. 

6.  Radiation  losses  from  the  furnace  outwardly  to  the  air. 
In  brick-set  furnaces  the  mass  of  brick  absorbs  heat  in  start- 
ing, which  it  returns  in  part  at  the  latter  part  of  a  run;  but 
the  continuous  transfer  after  stationary  conditions  are 
reached  is  never  regained.  These  are  largely  unavoidable. 
Preventable  losses  will  arise  from : 

7.  Unnecessarily  high  stack  temperature,  due  either  to 
excessive  firing  or  to  inability  of  an  inadequate  absorbing  sur- 
face in  the  boiler  to  take  care  of  heat  supplied  to  it. 

8.  Incomplete  combustion,  with  loss  of  available  carbon 
up  the  chimney-stack  as  gas  or  as  smoke. 

9.  Excess  of  diluting  air  either  below  the  grate  or  above 
It,  or  behind  the  bridge-wall. 

10.  Loss  of  solid  carbon  as  sparks  or  cinders  with  a 
strong  draft. 

Many  of  these  are  interrelated  to  each  other,  and  will 
furthermore  be  affected  by  size  of  the  fuel  selected  for  use. 
Their  diminution  by  mechanical  stoking  and  forced  draft  con- 
ditions will  be  discussed  in  subsequent  chapters. 

A  comparison  of  water  evaporated  by  different  qualities 
of   fuel  has  been  made  by  Mr.  Geo.   H.   Barrus,   in   which 


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HEAT  AND   HEAT-ENGINES. 


broken  anthracite  is  assumed  to  have  a  capacity  of  1 1  pounds 
of  water  if  free  from  ash.  The  figure  given  in  the  table  for 
this  fuel  is  that  corresponding  to  1 1  per  cent  of  ash. 


Kind  of  Coal. 


Cumberland 

Anthracite,  broken 

Anthracite,  chestnut 

Two  parts  pea  and  dust  and  one  part  Cumberland 

Two  parts  pea  and  dust  and  one  part  culm 

Anthracite,  pea 

Nova  Scotia  culm 


Water 

Relative 

Evaporated 

Efficiency 

from  and  at  9 19** 

in  Per  Cent, 

by  One  Pound 

Cumberland 

of  Dry  Coal. 

=  100. 

11.04 

ICO 

9-79 

89 

9.40 

85 

9-38 

85 

9.01 

82 

8.86 

80 

8.42 

76 

An  interesting  computation  of  the  results  and  require- 
ments with  a  combustion  of  100  pounds  of  anthracite  is  given 
in  the  following  table,  where  it  is  assumed  that  the  coal  and 
air  have  a  temperature  of  60°  and  that  the  chimney-gases  are 
at  500°.  Hot  ashes  are  withdrawn  at  450°,  and  2  per  cent  of 
carbon  goes  out  with  them.  Under  the  assumed  conditions 
2 1  per  cent  is  lost,  for  which  ash  and  moisture  in  coal  and 
air  are  responsible  for  over  5  per  cent. 

HEAT-LOSSES    INCIDENT    TO    THE    COMBUSTION    OF    lOO    POUNDS 
ANTHRACITE    COAL. 


Heat-lossea. 


By  water  =  [(919-60)  X  wl.]  -+-  9C'.-7X wt.  -f  [sp.  heat  X  (500-912)  X  wt.] 

By  carbonic  acid  =  wt.  X  sp.  hea:  X  (500  —  60) 

By  nitrogen  =  wt.  X  sp.  hea    X  (500  —  60) 

By  free  oxygen  =  wt.  X  sp.  beat  X  (500  -  60) 

By  ash  =  wt.  X  sp.  heal  X  (450  -  60) 

By  carbon  in  ash  =  wt.  X  sp.  heat  X  (450  -  60)  +  wt.  X  14650 

By  carbonic  oxide  =  wt.  X  sp.  heal  X  (500  -  60)  -j-  wi.  X  44«> 

Total  heat  lost  exclusive  of  loss  by  radiation 

Theoretically  possible  evaporation  in  pounds  of  water  from  and  &t  a  1.1° 

per  pound  of  combustible  utilized 

Theoretically  possible  evaporation  in  pounds  of  water  from  and  at  212° 

per  pound  of  fuel  utilized 


Number 

of 
B.  T.  U. 


37019.5 
97994.2 
158452.8 
91973.6 
1105.7 
29488.3 


276027.1 


Per  cent 

of  Total 

Heat  of 

Fuel. 


9.83 

S-I3 
12.07 
1.67 
0.08 
2.94 


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FUELS. 


77 


Kntering 
furaace. 


loolbs. 
of  coal. 


X9a9.83  lbs. 
of  air. 


f  Water 

Ash 

Carbon  ... 
Hydrogen  . 
Oxygen.... 
Nitrogen  .. 


Pounds, 
a.oo— 

XI. I 


8a.oo-< 

a.oo 

1.60 

0.90 


Oxygen  for  COj.    813.33 

Oxygen  for  H,0.       14.40 

Oxygen  for  CO. .  oo.ooa^ 

Oxygen  free 887. 73=^=:- 

Nitrogea 1474. 37-- 

Water 9.50 — 


t 


Wasts  Products  in  Chimnbt. 


I 

111 

I — -Steam... 

I  I: 

-V-'-^O, 893-33 


Pounds. 
29.50 


Nitrogen.  1475.37 
■CO 00.00 


r-=Oxygen..    827.73 


Per  Cent 

by  Wi. 

1.46 

14. 48 

73.83 

00.00 

II    24 


I 
— ^ 


Wastk  Products  in  A.-^h-i-it. 


Pounds. 


(Ash 

I  Carbon  . 


Per  Cent 
by  Wl. 

50  15. lb 

00  14.81 


Total  Heat  or  Fubu 

Weight  of  C  X  i4»65o  =  82  X  14.650  =  x.aoi.joo  B.  T.  U. 

Weight  of  H  -  (^^'^^  ^)  X  6a.ioo  =  a  -  (^)  X  62.100  =  11 1.780 

1.3x3,080         •• 

Hbat  Gbnbkatco. 
3oX  14,650  =s x,i73,ooo  B.  T.  U. 

8 -(~)x  62,100  « 111,780         ** 

x,883,78o         ** 

This  method  is  interesting  as  presenting  for  the  purpose  in 
hand,  the  practice  of  striking  a  heat-balance  in  any  test  of  a 
heat  appliance.  It  will  be  noted  that  the  heat-engine  or 
boiler  will  be  charged  with  the  total  quantity  of  heat  energy 


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78 


HEAT  AND   HEAT-ENGINES. 


delivered  to  it  from  all  sources  during  a  test,  and  credited 
with  the  units  of  heat  delivered  from  it  in  all  directions  as 
observed  in  the  test  or  assumed  from  experience  with  like 
apparatus.     The  form  of  balance-sheet  would  be  as  follows: 

HEAT-BALANCE. 
Dr.  Cr. 

To  heat  By  heat 

from  coal,  in  dry  steam, 

from  air,  in  moisture  and  water  mechanically  suspended  in 

(rom  feed-water.  steam, 

in  dry  flue-gases, 

in  moisture  in  coal,  )    at    temper-^ 

in  water  resulting  from  combustion,    V     ature  of 

in  vapor  in  air,  )   flue-gases. 

lost  through  incomplete  combustion  to  CO, 

in  ashes, 

lost  by  radiation  and  otherwise  unaccounted  for. 

Of  two  appliances  for  utilizing  heat  energy,  that  is  the 
more  effective  which  most  completely  renders  the  available 
heat  into  useful  work  or  product.  Examples  of  the  distribu- 
tion of  the  available  heat  as  reported  by  various  authorities 
are  given  in  the  following  table: 


,                  DISPOSITION    OF    HE. 

\T    IN 

STEA 

M-BOILERS. 

Auihoriiy. 

Disposition  of  Heat. 

Bunt^. 

Scheurer 

and 
Meunier. 

Donkin 

and 

Kennedy. 

A 

B 

C 

D 

E 

2 

Waste  in   flue-gases,  including  evaporation 
of  moisture  in  coal  and  heating  vapor  in 
air  when  these  losses  are  not  separately 
g^  ven 

18.6 
3.5 

5-5 
».5 

■^:; 

9.4 
0.1 

22.5 
o.x 

6.5 
0.0 

5. 04 

0  18 

Evaporatinfjf  moisture  in  coal 

Heatinff  vapor  in  air 

Imperfect  combustion 

8.0 

7.6 

58> 

6.0 



ia.7 
0.1 

0.0 
0.2 

II. 0 
66.2 

0.0 
0.0 

15.0 

785 

1-44 

Clinker  and  ash 

Radiation  and  beat  not  otherwise  accounted 
for ». 

23  5 
61.0 

V, 

4.00- 

87.79- 

Healing  and  evaporation  of  water.. 

60.  Data  Concerning  Fuels. — In  the  following  tables 
gathered  from  various  sources  are  grouped  summaries  of  the 
data  which  have  been  discussed  in  the  foregoing  paragraphs. 
The  results  are  from  experiment  and  analysis. 


Digitized  by  VjOOQ IC ' 


FUELS. 


79 


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«o 


HEAT  AND   HEAT-ENGINES. 


TABLE    OF   AMERICAN    COALS. 


COAL. 
Name  or  Locality. 


Arkansas. 

Coal  Hill,  Johnson  Co 

Coal  Hill,  Johnson  Co 

Huntinf^ton  Co 

Huntindfton  Co 

Huntington  Co 

Lignite 

Jenny  Lind,  Sebastian  Co. 
Spadra,  Johnson  Co 


Colorado. 

Lignite 

Lignite 

Lignite,  slaclc 

Lignite,  slack.  North  Colorado.. 
Rouse  Mine 


Illinois. 

Big  Muddy,  Jackson  Co 

Big  Muddy,  Jackson  Co.  ... 

Big  Muddy,  Jackson  Co 

Big  Muddy,  Jackson  Co 

Bureau  Co 

Colchester 

Colchester  Slack 

-Collinsville,  Madison  Co.... 

Dumferline  Slack 

Duquoin  Jupiter,  Perry  Co 
Ellsworth,  Macoupin  Co.... 

<^illespie,  Macoupin  Co 

-Girard,  Macoupin  Co 

Girard,  Macoupin  Co 

Heitz  Bluff,  St.  Clair  Co.... 

Johnson's,  St.  Clair  Co 

Loose's,  Sangamon  Co 

Mercer  Co  

MontaukCo 

Mt.  Olive,  Macoupin  Co.... 

Oakland,  St.  Clair  Co 

Reinecke,  St.  Clair  Co 

Riverton,  Sangamon  Co.... 

St.  Clair 

St.  Clair 

St.  Clair 

Si.  Bernard 

St.  John,  Perry  Co 

St.  John,  Perry  Co 

Sireator,  LaSaile  Co 

Trenton,  Clinton 

Trenton,  Clinton 

Vulcan  nut,  St.  Clair  Co 

Vulcan  nut,  St.  Clair  Co. . . . 


Indiana. 


Block... 
Block... 
(  aking. 
CaiincT  . 


Constituents  in  Per  Cent  of 
Total  Weight. 


14. So 
18.88 
3-»3 


7-30 
6.12 
5.85 
6.35 


11. 60 
5.30 
9.30 
9.64 

11.30 
9.26 

12. 61 
9.70 
8.90 
8.95 
5.50 

10.71 


10.38 
8.30 
7.56 

11.06 
7.80 

10.35 

IX. 15 

14.36 

9 
13.60 

12. 01 

13-34 
9-95 
7-44 

10.30 


»4-93 
14.60 
18.95 
18. < 
18.: 


17.64 
13.27 


32.00 
3^ '74 
37  32 


38.28 
30-95 
3».84 
31-50 


25.02 

25-45 
45.89 
28.86 

30-3« 
42.23 

30.58 
34-39 
.3«-»S 
37.81 
40.14 
37.62 


36.68 
34-40 
39 -81 
37-94 
30.69 

33- »o 
34- »9 
30.86 

28.35 
34.46 
II  32 
30.39 

3»04 

30.86 
37.91 


74.06 
74.91 

71. 5» 
73.15 
7«'74 


73.48 
78.63 


43.86 
40.08 
30.00 


53-87 
53-74 
55-7* 
55 -'5 


44-76 
38.  »5 
3  J -57 
39-48 
49.91 
43.17 
45  •27 
45.76 
43.89 
48.34 
40.53 
45  07 


9  66 
8.79 
8.34 
6.65 
8.10 


8.63 
6.63 


«o.34 


X0.46 

9.19 

6.59 
6.90 


3-04 
3.04 
0.78 
0.75 
0.65 


46.10 
43-" 
42.49 
43.98 
39.68 
41.7^ 
44-94 
48.39 
45.77 
43.54 
48  78 
51.96 
52.03 
45-og 
48.99 


63.10 


18.63 
31.10 
»3.34 
33.03 

8.48' 

6.35, 
"•54 
10.15 
15.96 

5.00 
»3.83 

6.60 


6.84 
14.18 
10.14 
8.02 
91.83 
14.86 
9.73 
6.39 
16.08 
1C.40 
3-89 
4.3» 
6.98 
T6.61 
ia.8o 


Fuel  Value  per  Lb. 
of  Coai. 


0.76 
0.61 


0.98 
1.32 
9.93 
9. OS 


9315 
13^64 
14430 


13560 
13865 
8500 


19567 
13025 


1.20 

5*34 

0.91 
2.62 
x-45 
3-49 
8.10 
3.27 
4. So 
a -39 


3.53 
4.42 

4.03 

3-27 

9.63 

6.9= 

4.27 

1.38 

3. 06 
1.83 
9.38 
0.92 
1.04 
1.32 
0.71 


0.98 


1 1 733 

"479 
13133 
13659 
11763 


Il8l3| 

11756 
1 1907 

»2537 


IT466 

11521. 
IT781 


9848 
9035 

10147 
9401 

107 10 

9739 
V954 
10269 1 
10332' 


14. 10 
12.33 
13.17 

13.  32 

13.97 
9-54 
14.40 
14.90 


'siio 


1 1730 
11406 


Z4090 

13588 
14146 

13097 


9261 

10394 

10647 

10080 

976; 
983I 
11403 
X0584 

"245 
9450 
10696 


11.87 
"-93 
13.19 
13.00 
»3-48 
10.19' 
9-35 
10.50 

11.08 
13.60 
10  09 
10.30 
10.63 
10.69 
13.10 
11.90 
13.58 
i3->o 

13. 90 
10.76 
13. 10 
11.80 

9  58 
10  65 

1I.03 
10.44 
10.10 
10.18 
11.80 
10.96 
XI. 63 
9.78 

IX. 00 


14-50 

14  38 
14.64 
13.56 


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FUELS, 


8i 


TABLE  OF  AMERICAN  COALS. 


ConstituenU  in  Per  Cent  of 
ToUl  Weight. 

Fuel  Value  per  Lb. 
of  Coal. 

COAL. 

Name  or  LocaUty. 

1 

1 

1 

.c 

< 

9 

% 

9 

§1.- 
|i5.£S 

Indian  Tbrkitory. 
A  loka . . ,  .• 

6.66 
«.59 

X0.85 

.,  „ 

1 

6.60'     3.73 

1 1088 
"789 

870a 

11.47 

•f^hnctaw  Nation  .                .    

ai.ll'    6fi-fie 

8  a«!     1-18     

'3-33 
9.0Z 

Iowa. 
Good  Cheer 

30.32 

31.38 

37.45 

7-32 

14391 

Kentucky. 
■Cakinf  

14.89 
16.76 

Caonei.***            ........        

I5198    

<:annel    



13360 
9326 

9890 

13. 84 

Lig'aite 

9.65 

Missouri. 
Bcvier  Mines 

X0.24 

Maryland. 
CuAberland                 .... 

12226 

12.65 



13500   

13  98 
ia.17 

14.20 

Nbw  Mexico. 

Coal 

Ohio. 
Briar  Hill   Mahonioir  Co 

a. 35 
9.47 

35-53 

50.34 

64.25 
53 -IS 

XZ.88 
1.45 

0.61 
o.c6 

13714 

11756 

Hocking  Valley  

8.35    ^c.88 

3.72.     o.ai 

I34I4    

'3.90 

Pennsylvania. 
Anthracite     * 

14199 

>3S35 
14221 

14.70 

Anthracite  

1 

78".  41 
81.3a 

I3-«9|    

10.06      0.67 

14.01 

Anthracite 

1 

14.72 

Anthracite,  pea 

Anthrarit<*.  buckwheat .-rr*  .r-. r-- 

a. 04!     6.36 
3.88      3. 84 

xa3oo     .... 

12?00    

I3»'4.^ 

11168 

12.73 

X2    63 

-Caonel.  • 

. . 

13. Co 

Connellsville             

54-94 
61.87 
58.93 
58.'6 
05.88 

61.63 

43.53 
49.27 

13.84 

Pittsburgh  (av.) 

Pittsburirh  ^cokinir^ .... 

X.80    35.34 
i.43|   30. ?2 
1.96,  34.06 

2.0a|    12.11 

7.92I      1.97' 

6.481       Z.ic'     \A.A.\^ 

I3«04 

12936 
12600 
12981 

13167 

9450 
"403 

13-46 
14.90 

6.88 
S.So 

4.75 

13. 02 
II. 41 

13. 39 

Youfifhioirhenv        .     .• 

0.88I 

»3.03 

Rey  noldsville 

Tennessee. 

ClenMary,  Scott  Co 

Texas. 

Ft.  Worth 

Ft,  Worth 

Lignite 

West  Virginia. 

X.30 

3.15 

14.4a 

4.60 

27.1a 

3t.47 

30  Qy 
34.7a 

0.94 

1.47 
1.56 

T4200 

»3-44 

"3-63 

9-73 
11.80 
13.41 

14.70 

New  River  

TJew  River                 • 

0.76 

18.19 
18.65 

75-89 
79.26 

4.68 

I.IT 

0.30 

0.2- 

I34'» 

•    -•    1 

13.87 

New  River 

1 

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82 


HEA  T  AND    HE  A  T-ENGINES. 


COMPOSITION   OF   COALS,   PER   CENTS. 


Description  of  Coal. 


Anthracites: 

French  

Welsh 

Rhode  Island 

Pennsylvanian 

Semi-biti'minous  : 

Maryland  

Welsh 

ElTUMINOUS: 

Pennsylvanian 

Indiana  

Illinois 

Virffinian 

Alabama 

Kentucky  

Cape  Breton     

Vancou verb's  Island.... 

Lancashire  i^as-coal . . . . 

Boghead  cancel 

LiCNiTKs : 

Californian  brown  coal 

Australian  brown  coal.. 
Pbtrolbums : 

Pennsylvanian,  crude.. 

Caucasian,  light 

'*  heavy 

Petroleum  refuse 


^ 

1 

t 

n 

>^ 

U 

K 

909 

«.47 

01.7 

3.78 

85.0 

371 

78.6 

2.50 

80.0 

5.ro 

18.3 

4.70 

75-5 

4-93 

f9.7 

5.10 

61.4 

4.87 

57-0 

4.96 

53.2 

4.81 

49.1 

4.95 

67  2 

4.26 

66.9 

5-33 

80.1 

5- 50 

63.1 

8.90 

49-7 

3.78 

73-2 

4.7» 

84.9 

13-70 

86.3 

13. 60 

86.6 

12.30 

87.x 

XI. 70 

153 
I  30 

a-39 
X.70 

a. 70 
0.60 

12. 35 
19.17 

35-43 
26.44 

32 -37 
4X'3 
ao.  16 
8.76 
8.10 
7.00 

30.19 
12.35 


I.XO 

1.20 


x.oo 
1.00 
x.oo 
0.80 

I.  TO 

1.40 

i.xa 

«-«3 
X.41 
X  .70 
X.62 

1.70 
1.07 

1.02 
I.  to 
o.ao 

1. 00 

I. XI 


0.80 
0.72 
0.90 
0.40 

x.ao 


x.io 
1.30 
i.ao 
1.50 
T.30 
1.40 

I. 31 
2.20 

X.50 
1. 00 

i'53 
0.63 


•s 

< 


4.30 

x.50 

7.00 

14. 80 

8.30 
3.ao 

5.00 
3- 50 
570 
8.40 
6.70 
7.20 
6.IO 

15-80 
2.70 

19.80 

13.80 
8.00 


\l 


»-35 
«-37 
1.48 
1-45 

».33 


1.32 
1.25 
1. 31 
x.32 
X.30 
X.28 

1-33 
1.28 


1.32 

1.27 

0.886 
0.884 
0.938 
0.938 


TABLE  SHOWING  THE  COMPOSITION  AND  CALORIFIC  POWER  OF 
VARIOUS  COMBUSTIBLES — THE  QUANTITY  OF  OXYGEN  AND  AIR 
NECESSARY  FOR  COMBUSTION-^AND  THE  VOLUME  OF  THE 
PRODUCTS    OF    COMBUSTION    OF    I    LB.    OF    COMBUSTIBLE. 


Name  of  Combustible. 


Carbon 

Anthracite  coal  

Qttuminous  coal 

Lignite 

Peat 

Peat,  0.20  water 

Coke 

Peat-charcoal 

Dry  wood 

Wood,  0.20  water 

Wocid-charcoal 

Hydrogen 

C.-irbonic  oxide    

Illuminating-gas 

Gas  Irom  blast-furnace  . 


Composition. 


0.90 
0.85 
o  70 
0.55 
0.39 
0.85 
0.82 
0.48 
0.40 
o.So 


0.43 
0.63 


0.03 
0.05 
COS 
0.05 
0.04 
0.05 

0.06 
0.05 


0.21 
0.0a 


0.03 
0.06 
0.20 
0.30 
0.50 


0.U5 
0.25 
0.04 

0.57 
0.17 
0.93 


0.04 
0.06 
0.05 
o.  10 
0.07 
o  10 
o.x8 
o.ox 
0.01 
0.07 


<<  f«  s 


14400,  2.C6 

13500J  2.64 

14400  2.66 
XI 700 

QOOO 

7200 
13(''00 

9000 

7.^00 

5400 
10800 
62000 


1630. 


2.26 
1.86 
1.49 
2.26 
2.18 
>.75 
1.40 
1.86 
8.00 
o  57 
2.64 
0.23 


5  V 


■  /.  a  I  -r 


,>'^^ 


:SS 


11.29 
II. ai 

11.29 
9.69 
7.90 
6.32 
9.69 
9.25 
7.43 
5-94 
7.90 

33-97 
2.4? 

1  t  32 

o  99' 


I37-<^| 
138. ol 
139  61 

120. 2| 

97-9, 
78.3 

120.2 

X14.5I 
91.01 
73- 5  I 
97-9 

420.61 
2  •.9| 

136  3' 

X2.2| 


»37-6 
136.2 
140.1 
116.3 
102. 1 
8T.5 
it6  9 
112.7 
8q.2 
7. .8 

CO.  J 

475.4 

35.6 

176.7 

30.S 


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FUELS. 
COMPARATIVE    COMPOSITION   OF   GAS. 


83 


CO.. 
H... 
CH|. 

CO9. 
N... 


0 

Vapor 

Pounds  in  1000  cubic  feet. . . . 
Heat  units  in  1000  cubic  feet  . 


Natural 
Gaa. 


0.50 
2.18 
92.6 
0.31 
0.26 
3.61 
0.34 


3^45 -6 
1,100,000 


Coal, 
gas. 


6.0 
46.0 
40.0 

4.0 

0.5 

1-5 

0.5 

1.5 

32.0 

735,000 


Water- 
gas. 


Producer-gas. 


45.0 

45.0 

2.0 


4.0 
2.0 
0.5 
1.5 
45.6 
322,000 


Antbra. 

27.0 

12.0 

1.2 


2.5 

57.0 

0.3 


65.6 
137.455 


Bitu. 
27.0 
12.0 

2-5 

0.4 

2.5 

56.2 

0.3 


65-9 
156.917 


NATURAL    GAS    IN    OHIO,    INDIANA,    AND    PENNSYLVANIA. 


Description. 


Hydrogen 

Marsh-gas 

Olefiant  gas 

Carbon  monoxide  . . 
Carbon  dioxide. . . . . 

Oxygen 

Nitrogen 

Hydrogen  sulphide 


Ohio. 


Indiana. 


Fos- 
toria. 


Findlay 


1.89 

92.84 

.20 

.55 
.20 

.35 
3.82 

•15 


St. 
Mary's. 


Muncie 


I.64I 
93.35 
.35 
.41 
.25 
•39 

3.41 
.20 


1.94 

93.85 

.20 

.44 
.23 
.35 
2.98 
.21 


2.35 
92.67 
.25 
.45 
.25 
•35 

3.53 
.15 


Ander- 

Koko- 

son. 

mo. 

1.86 

1.42 

93.07 

94.16 

.47 

.30 

.73 

.55 

.26 

.29 

.42 

.30 

3.02 

2.80 

.15 

.18 

Mar- 
ion. 


Penn. 


Pitls- 
burgti. 


1.20 

93-57 

.15 

.60 
.30 
.55 
3.42 
.20 


22. 

67. 
I. 

o. 

0.6. 

0.8 
3.0. 


Approximately  30,000  cubic  feet  of  gas  have  the  heating  power  of  one- 
ton  of  coal. 

PRODUCER-GAS  FROM  ONE  TON  OF  COAL. 


Analysis  by  Vol. 

Per 
Cent. 

Cubic  Feet. 

Lbs. 

Equal  to— 

Co 

25.3 
9.2 

3.1 
0.8 

3.4 

5?.2 

33,213  84 

12,077.76 

4,069.68 

1,050.24 

4.463-52 

76,404.96 

2451.20 

63.56 

174.66 

77-78 

519.02 

5659-63 

1050.51  lbs.  C  4-  1400.7  lbs.  0. 

H 

63.56    **     H. 

CHi 

174.66    '*     CH4. 

C,H4 

77.78    "     CaH*. 

CO 

141.54    **     C  + 377.44 lbs.  0. 
7350.17    "     Air. 

N  (by  difference) 

lOO.O 

131,280.00 

8945.85 

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84 


HE  A  T  AND  HEA  T-ENGINES. 


RELATIVE  CALORIFIC   VALUES. 

By  Weight.        Bjr  Volome. 

Natural  gas i,ooo  i,cxx) 

Coal-gas 949  666 

Water-gas 292  292 

Producer-gas 76.5  130 

The  following  table  gives  the  accepted  power  capacity  of 
various  sources  of  heat  energy  in  their  relation  to  motors 
using  these  combustibles  for  power  in  gas  or  other  engines. 


Material. 


sp. 


Hydrogen 

Carbon 

Crude  petroleum,  W.  Va, 
Light  petroleum.  Pa.,  sp 

Benzine  CgH* 

Gasoline 

Illuminating-gas,  38  c.  p.. . . 

"      19    •*   .... 

••      15    ••  .... 

Water-gas,  American 

Producer-gas,  English 

Water  producer-gas 

Ethylene-olefiant  gas  CtH*.. 

Gasoline  vapor 

Acetylene,  CjHa 

Natural  Gas,  Leechburg.  Pa 

**      Pittsburg,  Pa.. 

Marsh-gas,  methane,  CHi*- 


gr.  .873- 
.841 


Heat-units        Heat-units  per 
per  Pound.         Cubic  Foui. 


61560 
14540 
18324 
1 840 1 
1844S 


21430 
IIOOO 

21492 


23594 


293.5 


950 
800 
620 

185 

150 

104 

1677 

690 
868 
584 
495 
105 1 


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CHAPTER  VI. 
TEMPERATURES  OF  COMBUSTION.     PYROMETERS. 

6i.  Introductory. — It  will  have  been  noticed  that  the 
calorific  power  of  a  fuel,  or  the  total  heat  liberated  from  it 
upon  combustion,  is  a  quantity  which  is  independent  of  the 
time  required  for  that  combustion.  It  is  equally  a  fact  of 
common  observation  that  when  a  fuel  is  forced  to  burn 
rapidly  the  fire  is  hotter,  or  the  flame  has  a  higher  temper- 
ature, than  when  the  fuel  is  burned  more  gently,  and  the 
combustion  process  is  extended  over  a  longer  time.  In  other 
words,  the  temperature  of  the  fire  is  not  independent  of  the 
time  taken  for  combustion,  but  varies  inversely  as  such  time, 
while  the  calorific  power  is  independent  of  time.  This  makes 
it  a  vital  matter  that  the  engineer  should  be  able  to  control 
the  rapidity  of  the  combustion  of  the  fuel,  and  this  is  most 
easily  done  by  controlling  the  weight  and  velocity  of  the 
supply  of  air. 

The  higher  temperature  in  the  fire  under  rapid  or  forced 
combustion  is  due  not  only  to  the  fact  that  under  the  assump- 
tion of  a  constant  condition  of  intensity  more  fuel  units  will 
be  supplied  by  the  fireman  or  the  firing  machinery  per  unit 
of  time  when  the  combustion  is  more  rapid.  It  is  also  true 
that  the  more  intense  the  chemical  activity,  the  higher  the 
heat  which  accompanies  such  activity;  and  besides,  the  trans- 
fer of  heat  from  the  fire  to  absorbing  bodies  whereby  its  tem- 
perature is  lowered  will  be  greater  the  longer  any  ^[iven 
weight  of  fuel  is  permitted  to  occupy  the  grate  or  combustion 
area.     This  -would  imply  that  where  transfer  is  a  principal 

85 


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S6  HEAT  AND   HEAT-ENGINES. 

feature  of  a  combustion — as  in  a  boiler — there  may  be  an 
economical  maximum  rate  of  combustion  which  it  would  not 
be  desirable  to  exceed.  And  finally,  when  rapid  chemical 
combination  with  air  is  secured,  as  with  oil-  or  gas-firing,  and 
proper  provision  is  made  for  admitting  air  and  compelling 
chemical  action  by  attention  to  details,  a  less  excess  (or 
none)  of  free  oxygen  is  required  in  the  products  of  com- 
bustion, and  the  cooling  and  diluting  effect  of  the  air  and  its 
inert  nitrogen  is  diminished.  Two  questions  are  then  sug- 
gested: I.  What  is  the  probable  temperature  of  a  fire  and 
how  may  it  be  observed?  2.  By  what  means  shall  the  rate 
of  combustion  be  secured  and  controlled? 

62.  Temperature  of  the  Fire. — It  will  appear  to  be  an 
obvious  deduction  from  Chapter  III  (§§  ii  to  14)  that  when 
one  body  conveys  or  transfers  heat  to  another  substance 
which  absorbs  it  entirely  in  raising  its  temperature,  the  quan- 
tity of  heat  in  heat-units  so  transferred  will  be  represented  by 
the  product  of  the  weight  (w)  by  its  specific  heat  {c)  by  the 
change  in  temperature  indicated  by  the  difference  between 
its  final  temperature  and  its  initial  temperature  (/,  —  /,)  if  the 
body  in  question  was  hotter  after  the  transfer  than  it  was 
before.  This  holds  true  also  for  the  body  or  substance 
which  has  cooled,  since  the  one  has  lost  heat  to  the  same 
extent  as  the  other  has  gained  it.  In  symbols,  if  Q  repre- 
sents the  quantity  of  heat  in  units  transferred  from  one  body 
to  the  other, 

(2  =  ztr  X  ^  X  (^  -  o 

for  the  body  which  has  become  warmed,  and 

(2'  =  «/'x  ^'  X  (^- O 

for  the  body  which  has  cooled,  having  a  different  weight  and 
different  specific  heat.  But  Q  =  Q .  It  has  therefore  been 
a  convention  to  assume  that  the  temperature  of  the  fire  was 
the  same  as  that  of  the  flaming  products  of  the  combustion 


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TEMPERATURES   OF  COMBUSTION,     PYROMETERS.       8/ 

at  the  instant  when  combustion  was  complete;  and  that  all 
the  heat  liberated  from  the  fuel  was  used  to  raise  the  prod- 
ucts of  combustion  to  this  fire  temperature.  All  that  is 
unknown  then  in  the  above  formula  is  the  final  high  temper- 
ature of  the  products  of  combustion,  when  the  total  heat 
transferred,  the  weight  of  the  products  of  combustion  (§§  24 
to  28)  are  known,  and  their  specific  heat.  This  theory  is 
sound  and  applicable  for  the  conditions  which  prevail  in  a 
determination  with  a  coal-calorimeter  (§  23),  but  the  consid- 
erations advanced  in  the  preceding  paragraph  throw  some 
doubt  upon  its  reliability  as  applied  to  practice.  The  assump- 
tion is  further  implied  that  specific  heats  are  constant  at  all 
temperatures.  The  specific  heats  under  constant  pressure  of 
the  constituents  of  the  fire  are: 

For  carbonic  acid  gas 0.2 17 

*'    steam  or  water- vapor 0.480 

**    nitrogen 0.244 

*'    air 0.238 

**    ashes  (probably) 0.200 

The  data  for  the  computation  of  a  hypothetical  fire-tem- 
perature for  two  combustibles,  such  as  pure  carbon  and 
olefiant  gas,  will  be: 

Carbon,  Olefiant  Gas, 

C  C.H, 

(i)  Calorific  power 14.500  21,300 

{2)  Pounds  weight  of  products  of  combustion 13.00  1^.43 

(3)  Mean  specific  heat 0.237  0.257 

(4)  Specific  heat  and  weight 3.08  4.22 

Value  for  (/a  — /i),  or(i)-s-(4) 4580*  5050* 

This  assumes  no  dilution  of  the  products  by  air.  The  use 
of  diluting  air  will  act  to  lower  the  hypothetical  temperature 
by  increasing  the  weight  to  be  heated.  The  specific  heat  of 
course  approaches  more  nearly  to  that  of  air  the  greater  the 
proportion  of  air  in  the  products  of  combustion. 

Recent  investigations  with  the  pyrometer  show  that  tem- 


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88 


HEAT  AND   HEAT  ENGINES. 


peratures  hitherto  have  been  often  overestimated,  and  that 
the  high  values  obtained  by  the  above  method  are  not 
reached  in  practice.  A  generally  accepted  series  of  data  is 
given  in  the  table  below,  constructed  by  M.  Pouillct.  Its 
use  of  course  must  be  subject  to  the  peculiarities  of  the 
individual  and  the  degree  of  general  illumination  prevalent. 


Heat. 

Deg.  C. 

Dcg.  1'. 

977 
1292 
1472 
1652 
1832 
20:1 

Heat. 

Deg.  C. 

De«.  F. 

Incioicnt  red  ••••••■.. 

535 
700 
800 
900 
1000 
1 100 

Clear  oranire 

1200 
1300 
1400 
1500 

to 
1600 

2192 
2372 
2552 
2732 

to 
2912 

Dull  red. ....    .    

White  heat 

Incipient  cheery 

Cherrv-red  >..>•  ...••• 

Bright  white  heat 

Dazzling  white  heat.  -J 

Clear  cherry-red 

Deep  orange 

The  melting  or  heating  of  metals  with  fuel  implies  that 
the  heat  of  the  fire  should  not  be  less  than  that  demanded  by 
the  metal.  Recent  determinations  by  Prof.  Roberts-Austen. 
give  melting-temperatures  as  follows: 

Copper 1929°  to  1996°  F. 

Cast-iron ,  white 2075 

'*  gray 2228 

Steel,  hard 2570 

"      mild 2687 

Wrought  iron 2732  to  2912 

Platinum 3227 

The  melting-temperature  of  steel  at  the  end  of  its  conver- 
sion in  the  open-hearth  steel  process  is  among  the  highest 
usually  met  in  industry,  and  is  about  2732°  F.  Even  this, 
however,  is  only  attained  by  preheating  both  gas  and  air  used 
in  the  process.  The  heat  in  a  furnace  for  baking  hard  porce- 
lain may  rise  to  2500°  F.  Furthermore,  it  is  a  question 
somewhat  of  quantity  of  heat  rather  than  its  intensity.  The 
platinum  value  is  that  for  material  which  is  only  fusible 
before  the  oxyhydrogen  blowpipe.  All  these  data  tend  to 
throw   a   certain   doubt  upon    the    validity  of  the    accepted. 


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TEMPERATURES  OF  COMBUSTION.     PYROMETERS.       89 

method  of  working  out  flame  or  fire  temperatures,  and  leave 
the  field  open  for  practical  determinations  by  pyrometer. 

Hoadley  gives  the  temperature  in  a  boiler-fire  as  ranging 
from  2493**  F.  to  2793°  F.  in  its  heart,  and  1340"*  to  1600**  F. 
at  the  bridge- wall.  In  a  marine  boiler,  Durston  records 
1644^  in  the  combustion-chamber.  Clark  gives  1705*'  for  a 
combustion  rate  of  20  pounds  per  square  foot  grate,  rising  to 
2icx>**  at  a  120-pound  rate. 

63.  Pyrometers.  General. — The  usual  appliances  for 
measuring  temperature  (§§  13  to  15)  are  not  suitable  for  higli 
heats,  with  the  possible  exception  of  the  air-thermometer. 
Mercury-thermometers  with  nitrogen  gas  in  the  tube  above 
the  mercury  can  be  used  up  to  800**  F. ;  the  ordinary  con- 
struction being  open  to  the  objection  that  the  rate  of  expan- 
sion of  mercury  increases  with  the  rise  of  temperature,  so 
that  a  mercury-thermometer  which  agreed  with  an  air-ther- 
mometer at  212*  would  read  low  at  temperatures  below  this 
point,  and  high  at  temperatures  above  it. 

The  name  pyrometer  is  given  to  an  appliance  for  measur- 
ing or  observing  high  temperatures.  There  are  several  prin- 
ciples which  have  been  applied  in  such  instruments. 

1.  Melting-points  of  various  metals  or  alloys.  This  is 
approximate  only,  since  the  melting-p6int  varies  with  chem- 
ical purity  of  the  metals  in  question,  and  undergoes  change 
with  time,  with  frequency  of  melting,  and  deterioration  by 
heat. 

2.  Expansion  of  metals  by  heat.  These  may  be  single 
bars,  or  compound  bars  of  two  or  more  metals  whose  rate  of 
expansion  is  not  the  same.  Copper  and  iron  are  two  usual 
metals  to  use  (as  in  Brown's  pyrometer  and  Bulkley's);  the 
bar  flexes,  and  the  amount  of  flexure  indicates  the  heat  on  a 
convenient  dial.  To  this  class  belongs  the  use  of  clay  bars, 
which  contract  under  heat,  as  in  the  Wedgwood  pyrometer 
formerly  used  by  potters  for  their  ovens.  Clay,  however,  is 
not  uniform  nor  permanent,  and  in  the  case  of  the  metal  bars 


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90  HEAT  AND    HEAT-ENGINES. 

a  permanent  change  occurs  by  and  by  in  the  molecular  struc- 
ture consequent  upon  the  prolonged  heating,  which  prevents 
accuracy. 

3.  Changes  in  volume  and  action  of  a  permanent  gas  such 
as  air,  either  using  its  expansion,  as  in  the  air-thermometer 
and  nitrogen-thermometer,  and  in  the  Wiborgh  pyrometer,  or 
depending  on  the  changes  in  rate  of  flow  with  temperature, 
as  in  the  Uehling-Steinbart  pyrometer. 

4.  Methods  based  upon  the  specific  heat  of  solids,  raised 
to  the  fire-temperature  and  cooled  in  water. 

5.  Time  required  to  heat  a  weighed  quantity  of  water 
enclosed  in  a  vessel,  as  in  the  water-pyrometer. 

6.  Changes  in  the  electric  resistance  of  a  refractory  con- 
ductor such  as  platinum  exposed  to  heat,  as  in  the  Siemens 
pyrometer. 

7.  Measurement  of  the  strength  of  a  thermo-electric  cur- 
rent produced  by  heating  the  junction  of  two  metals,  as  in 
the  Le  Chatelier  pyrometer. 

8.  Optical  effects  in  deflection  of  light  rays  from  incan- 
descent solids,  as  in  Mesur6  and  Nouel's  pyrometric  tele- 
scope. 

64.  Metal-ball  Pyrometer. — The  metal-ball  pyrometer  is 
one  of  the  easiest  to*  arrange  for.  A  ball  or  other  mass  of 
metal  of  known  weight  and  specific  heat  is  put  into  the  place 
whose  heat  is  desired,  and  left  there  until  it  gains  the  same 
temperature  as  the  medium  around  it.  It  is  then  withdrawn 
and  dropped  into  a  known  weight  of  water  of  observed  tem- 
perature, and  the  rise  of  temperature  is  observed  which  it 
causes  in  the  water.  The  principles  of  transfer  demand  that 
if  W\s  the  weight  of  water  with  a  specific  heat  of  unity  and 
an  initial  temperature  of  f  F.,  while  w  is  the  weight  of  the 
ball,  c  its  specific  heat,  T  the  final  temperature  of  the  water, 
then  the  unknown  temperature  x  of  the  ball  \Yill  be  given 
/rom  the  equality 

^X  I  X  (r-/)  =  ?t/X  if  X  (^-  T)\ 


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TEMPERATURES   OF  COMBUSTION.     PYROMETERS,       9 1 

whence 

WC 

For  greater  accuracy,  corrections  must  be  made  for  variations 
of  specific  heat,  for  the  capacity  of  the  cooling  vessel  itself 
for  heat,  for  losses  in  transit  from  fire  to  cooling  vessel,  etc. 
The  ball  may  be  platinum,  iron,  or  other  metal,  or  fire-clay 
or  fire-brick. 

65.  Wiborgh  Air-pyrometer. — This  form  of  pyrometer 
involves  the  use  of  a  porcelain  globe  or  cylinder  connected 
through  a  capillary  tube  with  the  exterior  air.  The  air  in 
the  globe  is  heated  by  the  temperature  to  be  measured,  with 
the  tube  open.  Then  a  known  volume  of  air  of  known  tem- 
perature is  forced  into  the  globe  with  its  outlet  closed,  and 
the  resulting  pressure  observed  by  a  delicate  pressure  record- 
ing-device. Then,  since  the  initial  volume  and  pressure  are 
known  before  the  addition  of  the  cooler  air,  and  the  final 
pressure  is  observed  when  the  volume  and  temperature  of  the 
added  air  are  known,  the  only  unknown  factor  is  the  original 
temperature,  which  is  the  quantity  desired. 

This  form  of  apparatus  is  useful  for  temperatures  between 
0°  and  2400^  F.,  such  as  occur  at  metallurgical  and  similar 
furnaces. 

66.  Uehling-Steinbart  Pyrometer. — The  Uehling  py- 
rometer depends  on  a  principle  of  the  flow  of  a  permanent 
gas,  such  as  air  through  a  minute  aperture,  which  makes 
the  weight  which  flows  in  a  given  time  a  function  of  the 
density  of  the  air,  which  varies  directly  as  the  absolute  tem- 
perature. This  is  applied  by  having  a  closed  tube  or  cham- 
ber fitted  with  minute  inlet  and  outlet  orifices  and  causing 
air  to  flow  in  through  one  and  out  through  the  other,  by 
means  of  proper  aspirating  appliances,  while  the  tension  in 
the  chamber  is  carefully  measured  by  a  sensitive  manometer. 
The  air  to  enter  is  made  to  have  the  desired  temperature  by 
locating  the  inlet  aperture  in  the  end  of  a  platinum  tube  in 


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92  HE  A  T  AND    HE  A  T  ENGINES. 

the  bulb  of  a  porcelain  tube  over  which  the  hot  gases  pass^ 
or  which  is  inserted  in  the  chamber  or  place  whose  tempera- 
ture is  to  be  ascertained.  The  outlet  aperture  is  kept  at  a 
lower  but  constant  temperature,  and  is  operated  at  a  constant 
suction  effort  by  surrounding  it  with  boiling  water  in  a 
proper  coupling  and  aspirating  by  means  of  a  water-column 
kept  at  a  constant  height. 

67.  Le  Chatelier  Thermo-electric  Pyrometer.  Siemens 
Pyrometer. — The  principle  of  the  thermo-electric  pile  is  used 
in  this  apparatus.  Two  wires,  one  of  platinum  and  the 
other  of  platinum  with  10  per  cent  of  rhodium,  are  made  into 
the  usual  thermo-electric  couple  of  the  physical  lab.  ratory, 
^nd  are  presented  to  the  heat  to  be  measured.  Tlie  action 
of  heat  creates  a  current  of  electricity  in  the  couple,  whose 
intensity  is  measured  by  a  galvanometer.  The  instrument 
should  be  calibrated  experimentally  by  heating  the  junction 
of  the  pile  to  temperatures  which  are  known  as  observed  by 
the  air-thermometer,  and  plot  the  curve  of  deflections  from 
these  data.  The  error  of  a  Le  Chatelier  pyrometer  is  usu- 
ally less  than  50°,  up  to  its  limit  of  use.  The  Siemens 
pyrometer  depends  upon  the  principle  that  the  conductivity 
of  platinum  wire  is  diminished  by  heat,  and  measurably  to  a 
degree  proportional  to  that  temperature  if  the  wire  is  thor- 
oughly homogeneous.  If,  therefore,  an  electric  current  is 
divided,  and  by  a  Wheatstone  bridge  or  other  controllable 
resistance  the  two  branches  are  made  to  have  equal  resistance 
at  the  same  known  temperature,  it  becomes  easy,  by  raising 
one  branch  of  the  wire  to  known  temperatures  and  equating 
the  varying  resistance,  to  make  a  calibration  wherebv 
unknown  temperatures  may  be  determined,  either  by  the 
galvanometer-reading  directly,  or  by  the  resistance  necessary 
to  introduce  to  keep  its  reading  constant.  An  uncertainty 
is  introduced,  however,  by  the  difficulty  of  avoiding  a  molec- 
ular change  in  the  conductor  which  is  exposed  to  heat,  of 
whose  extent  and  effect  there  is  alwys  some  uncertainty. 


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TEMPERATURES  OF  COMBUSTION.     PYROMETERS,       93 

68.  Mesurd  and  Noel's    Pyrometric  Telescope. — For 

observing  temperature  of  incandescent  or  glowing  bodies  by 
the  color  of  the  rays  of  light  which  they  emit,  an  appliance 
can  be  easily  constructed  which  shall  serve  as  a  pyrometer, 
basing  it  on  the  principle  that  a  plate  of  quartz  cut  at  right 
angles  to  the  crystalline  axis  rotates  the  plane  of  pola^'ization 
of  polarized  light  to  a  degree  nearly  inversely  proportional  to 
the  square  of  the  wave-length  of  such  light.  If,  then,  two 
Nicols  prisms  be  placed  in  a  tube  and  a  ray  of  monocliro 
matic  light  be  passed  through  the  first  prism  or  polarizer, 
and  watched  through  the  second  or  analyzer,  with  the  plate 
of  quartz  between  them,  a  part  of  the  light  which  passed  the 
first  and  in  the  absence  of  the  quartz  was  extinguished  will 
be  made  visible  when  the  quartz  is  present.  To  extinguish 
it  the  analyzer  must  be  rotated,  and  rotated  further  as  the 
light  from  the  hot  body  gathers  the  shorter  waves  of  orange 
and  yellow  and  emits  them  all  as  it  passes  to  the  dazzling 
glow  of  white  light.  The  degree  to  which  the  analyzer 
must  be  turned  is  a  measure  of  the  temperature  of  the  radi- 
ating body. 

Like  the  foregoing  instruments,  this  should  be  calibrated 
experimentally,  and  has  the  great  advantages  of  cheapness, 
convenience,  and  portability  to  offset  the  absence  of  e»act 
definition  of  temperature,  and  the  difficulty  in  applying  it  to 
widely  varying  materials. 

69.  Some  Standard  Temperatures. — For  use  in  stand- 
ardization of  other  appliances,  or  for  direct  use  in  pyrometry, 
certain  accepted  temperatures  gathered  from  various  sources 
are  here  presented  in  tabular  form. 


T>cg.  F. 

Deg.C 

Deg.  F. 

Deg.C 

212 

100 

Water  boils. 

1733 

945 

Silver  melts. 

618 

326 

Lead  melts. 

1859 

1015 

Potassium      sulphate 

676 

358 

Mercury  boils. 

melts. 

779 

415 

Zinc  melts. 

1913 

1045 

Gold  melts. 

838 

448 

Sulphuj  boils. 

1929 

1054 

Copper  melts. 

"57 

625 

Aluminum  melts. 

2732 

1500 

Palladium  mel'a. 

1229 

665 

Selenium  boils. 

3227 

1775 

Platinum  melts. 

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94 


HE  A  T  AND   HEA  T-ENGINES. 


BOILING-POINTS   AT    ATMOSPHERIC    PRESSURE. 
14.7  lbs.  per  square  inch. 


Ether,  sulphuric loo'  F. 

Carbon  bisulphide 118 

Ammonia 140 

Chloroform 140 

Bromine 145 

Wood-spirit 150 

Alcohol 173 

Benzine 176 

Water 212 


Average  sea-water 213.2*  F. 

Saturated  brine 226 

Nitric  acid 248 

Oil  of  turpentine 315 

Phosphorus 554 

Sulphur 570 

Sulphuric  acid 590 

Linseed  oil 597 

Mercury 676 


The  boiling-points  of  liquids  increase  as  the  pressure  increases. 


MELTING-POINTS    OF   VARIOUS   SUBSTANCES. 

The  following  figures,  are  given  by  Clark  (on  the  authority 
of  Pouillet,  Claudel,  and  Wilson),  except  those  marked*, 
which  are  given  by  Prof.  Roberts-Austen  in  his  description  of 
the  Le  Chatelier  pyrometer.     These  latter  are  probably  the 


most  reliable  figures. 

Sulphurous  acid —  148*  F. 

Carbonic  acid —  108 

Mercury —  39 

Bromine +  9.5 

Turpentine 14 

Hyponitric  acid 16 

Ice 32 

Nitro-glycerine 45 

Tallow 92 

Phosphorus 112 

Acetic  acid 113 

Stearine 109  10  120 

Spermaceti 120 

Margaric  acid 131  to  T40 

Potassium 136  to  144 

Wax 142  to  154 

Stearic  acid 158 

Sodium 194  to  208 

Alloy,  3  lead,  2  tin,  5  bismuth  199 

Iodine 225 

Sulphur 239 

Alloy,  i^  tin,  i  lead 334 


Alloy,  I  tin,  i  lead.     370  to     466*  F. 

Tin 442  to     446 

Cadmium 442 

Bismuth 50410     507 

Lead 608  to     618* 

Zinc 680  to     779* 

Antimony 81010  1150 

Aluminum ii57* 

Magnesium 1200 

Calcium Full  red  heat. 

Bronze 1692 

Silver 1733*  to  1873 

Potassium  sulphate 1859* 

Gold 1913*  to  2282 

Copper 1929*  to  1996 

Cast  iron,  white. .    1922    to  2075* 
"  gray  2012  to  2786  2228* 

Steel 2372  to  2532 

"    hard....   2570*;  mild,  2687* 

Wrought  iron 2732  to  2912 

Palladium 2732* 

Platinum 3227* 


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CHAPTER  VII. 
RATE  OF  COMBUSTION.     DRAFT. 

75-  Introductory. — It  has  been  previously  observed  that 
the  calorific  power  of  a  fuel  is  a  reasonably  fixed  quantity 
and  is  independent  of  the  time  taken  to  burn  it  (§§  22,  23, 
58,  and  59).  On  the  other  hand  the  temperature  of  the 
fire  depends  on  the  number  of  pounds  of  fuel  burned 
therein  per  hour  (§§  61  and  62),  and  the  permitted  dilution 
with  excess  of  air  (§  30).  It  becomes  of  interest  then  to  ex- 
amine how  many  units  of  weight  of  a  fuel,  with  a  given  heat- 
ing effect,  are  usually  burned  per  unit  of  grate-surface  in  a 
given  time. 

76.  The  Rate  of  Combustion. — The  rate  of  combustion 
with  English  units  is  usually  expressed  by  giving  the  number 
of  pounds  of  fuel  burned  per  square  foot  of  grate-surface  per 
hour.  The  table  on  page  96  gives  a  summary  of  practice 
and  opinion  upon  this  subject  as  respects  steam-boilers. 

An  interesting  comparison  of  tests  recently  made  shows 
a  tendency  to  regard  13  pounds  per  hour  per  square  foot  as 
representing  prevalent  American  practice  for  stationary  boil- 
ers on  land.  The  use  of  higher  pressures  will  be  likely  to 
increase  this  rate.  The  number  of  pounds  of  fuel  which  can 
be  burned  will  be  determined  absolutely  by  the  weight  of 
oxygen  or  volume  of  air  which  can  be  supplied  to  it  in  a  unit 
of  time.  It  becomes  a  question  of  moment,  therefore,  to  de- 
cide on  the  method  of  supplying  the  necessary  air  for  com- 
bustion (§§  24  to  27),  and  to  provide  a  method  to  remove  the 

95 


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96 


HEAT  AND   /fEAT-ENGlNES. 
TABLE    OF    RATES   OF   COMBUSTION. 


Type  of  Boiler. 


Land  types . . . 

«4  <l 

Marine  types. 


Cornish 

Flue 

Factory 

Marine 

Locomotive. . . 
Torpedo-boat . 


Average. 


Pounds  of  Coal  per  Hour  per 
Square  Foot  of  Grate. 


Anthracite. 


6-12 


7-i6 


Bituminous. 


12-27 
65-80 
12-27 
18-20 
20-30 

4-6 

10 
12-16 
16-14 
40-100 
60-125 


12-1S 
60 


Draft. 


Chimney 

Forced 

Chimney 

Forced 
Chimney 


Forced 


Chimney 
Forced 


Authority. 


Whitham 

Seaton 

Shock 
44 

Seaton 
Rankine 


products  of  combustion  (§§  28  and  29)  which  are  not  sup- 
porters of  such  combustion,  but  tend  to  extinguish  it  if  aot 
removed. 

77.  Draft  for  Combustion.  General. — There  are  two 
generic  ways  of  bringing  air  to  a  motive-power  fire:  it  may 
be  done  by  a  mechanical  apparatus,  such  as  a  fan  or  a  steam- 
jet;  or  it  may  be  done  by  means  of  the  greater  weight  of 
cold  air  per  cubic  foot  as  compared  with  warm  air,  in  a  verti- 
cal column  of  such  warm  air  enclosed  within  the  walls  of  what 
is  called  a  chimney.  The  first  plan  is  known  as  mechanical 
or  forced  draft;  the  second  is  called  natural  draft  or  chimney- 
draft.  The  term  natural  draft  is  unfortunate,  because  the 
chimney  is  a  simple  machine,  and  both  methods  are  mechan- 
ical, or  equally  dependent  on  a  natural  law.  The  term 
forced  draft,  on  the  other  hand,  should  be  restricted  to  cases 
in  which  the  velocity  of  the  air-current  is  made  greater  than 
it  is  possible  to  make  it  with  a  chimney  of  any  ordinary  or 
practical  height.  A  mechanical  apph'ance  must  be  used  in 
this  case  because  the  velocity  is  caused  by  a  higher  pressure 


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RATE   OF  COMBUSTION,     DRAFT,  gj 

of  the  air  where  it  enters  the  fire  than  can  be  secured  by- 
natural  processes.  The  two  alternatives  are  therefore  natural 
or  forced  draft,  having  respect  to  the  differences  in  pressure 
and  velocity  usual  on  the  one  hand ;  and  the  other  division 
would  be  into  chimney-draft  or  mechanical  draft  according  as 
the  current  is  produced  by  chimneys  or  by  fans. 

78.  Chimney-draft.  General. — It  has  long  been  a  matter 
of  common  observation  that  heated  air  is  lighter  than  the 
same  bulk  of  cold  air.  In  any  volume  of  air  either  in  en- 
closed spaces  or  in  the  open,  the  greater  weight  of  the  colder 
air  will  tend  to  draw  it  into  the  parts  nearer  to  the  earth,  and 
in  so  doing  it  will  displace  the  lighter  warmer  air  and  send 
it  upward.  If  either  the  warmer  or  the  cooler  air  or  both 
are  confined  in  tubes  or  ducts  or  flues,  the  movement  of  dis- 
placement becomes  a  definite  flow  through  the  flue  or  tube, 
and  the  action  of  gravity  on  the  denser  air  becomes  a  means 
of  moving  the  necessary  weight  or  volume  of  air  through  the 
fuel  to  be  burned.  The  chimney  is  the  tube  containing  the 
lighter  gas,  at  the  bottom  of  which  is  the  fire  or  source  of 
heat.  The  column  of  cooler  and  heavier  air  outside  of  the 
-chimney  is  the*motor  energy  which  sets  the  warm  column  in 
motion  against  the  resistances  of  friction  and  the  obstruction 
at  the  fire  itself.  The  volume  which  the  chimney  will  pass 
through  its  area  will  vary  with  its  cross-section  and  with  the 
velocity  of  flow  through  this  cross-section.  The  velocity  of 
flow  will  be  fixed  by  the  difference  in  weight  of  the  hot 
column  and  of  the  cold  column  of  equal  height.  This  differ- 
ence is  fixed  by  the  temperature  outside  the  chimney  and 
within  it,  which  determines  the  density  or  weight  per  cubic 
foot  of  each  column. 

While  it  would  appear,  however,  that  the  velocity  in- 
creases with  temperature,  it  must  not  be  overlooked  that  the 
weight  is  decreasing  with  the  higher  temperature,  and  that 
weight  of  oxygen  is  really  the  important  thing  to  be  pre- 
sented to  the  fire.     There  is  therefore  a  certain  temperature 


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98 


HEA  T  AND   HEA  T-ENGINES. 


of  chimney-gas  at  which  the  greatest  weight  of  oxygen  wilF 
be  passed  through  the  fire.  Below  this  the  velocity  is  not 
high  enough,  and  above  this  the  weight  per  cubic  foot  is  de- 
creasing faster  than  the  velocity  is  increasing.  It  is  moreover 
of  advantage  not  to  have  too  high  a  chimney  temperature 
made  necessary  to  cause  proper  draft,  because  each  unit  of 
heat  passing  off  in  the  chimney  unnecessarily  (§  59)  is  a 
waste  which  should  have  been  utilized,  and  that  heat  should 
have  been  transferred  to  the  motor  fluid  in  the  form  of  heat 
energy  instead  of  being  wasted  to  create  draft. 

79.  Theory  of  Chimney-draft  by  P6clet.— The  most 
widely  accepted  theory  of  the  action  of  the  chimney  was  first 
elaborated  by  P^clet,  and  developed  and  quoted  by  Rankine 


>^% 


I 


I 


"n. 


i      i 


-h 


fi 


^ 


Fig.  18. 


and  other  writers.  His  discussion  can  be  made  most  easily 
to  be  understood  by  the  conception  of  the  chimney  as  ar> 
inverted  siphon,  with  the  fire-grate  at  the  bend  at  the  bot- 
tom.   In  Fig.  13  the  hatched  section  represents  the  chimney^ 


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RATE   OF  COMBUSTION.     DRAFT.  99 

and  the  dotted  lines  the  siphon  leg  of  cold  external  air.  A 
diaphragm  A-B  in  the  bend  of  the  siphon  will  have  unequal 
pressures  on  its  two  sides  if  the  legs  are  of  equal  length  and 
equal  cross-section,  because  if  D^,  denotes  the  density  of  the 
external  air  and  its  weight  per  cubic  foot,  and  Z>^  denote  the 
density  of  the  warmer  lighter  chimney-air,  then  HD^  acts  on 
one  side,  and  the  less  HD^  on  the  other.  To  equalize  the 
pressures  an  extra  effort  must  be  exerted  on  the  lighter  leg 
to  balance  the  heavier,  so  that  an  extra  length  of  column  of 
hot  air  of  unknown  height. A,  and  having  a  density  Z?„  must 
exert  a  pressure  /  =  hDc  to  effect  this  balance.     Or,  since 

we  can  write 

as  the  pressure  exerted  on  the  diaphragm  or  on  a  film  of  air 
at  the  base  of  the  siphon  and  which  causes  the  flow  when 
there  is  no  balancing  pressure  at  the  top  of  the  chimney. 
But  since  /  =  hD^  the  height  of  the  column  of  hot  gas 
will  be 

A-        ^^       , 

and  the  question  of  the  values  of  these  two  densities  is  a 
question  for  observation  or  calculation.  At  32°  F.,  D^  for 
air  is  .0807,  and  by  reducing  D  to  32°  F.  the  value  for  h 
can  be  found  in  feet,  or  more  conveniently  the  expression  can 
be  transformed  to  read  in  absolute  temperatures  instead  of 
densities  by  the  relation  that  the  densities  will  be  inversely 
as  the  temperatures,  so  that 

D,  -  t; 

But  the  chimney-gas  is  a  mixture,  and  not  a  constant  or 
permanent  gas.     An  accepted  value  for  its  ordinary  density 


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lOO 


HE  A  T  AND   HE  A  T- ENGINES, 


at  32°  F.  is  .08424,  which   is  derived   from  an  averaging  of 
many  analyses  and  experiments  which  give  for  such  gases: 

Carbonic  acid  10  per  cent,  weighing  at  32** 12344 

Nitrogen  79        '*  **         *•    *' 07860 

Oxygen  11        **  *'         •*     ** 08926 

Multiplying  the  per  cent  of  each  by  its  weight,  we  have: 

Weight  of  CO, 01234 

*'  N 06209 

*'  O 00981 


Total 0842  4 

If  the  composition  of  the  gases  differs  from  the  above 
assumption  as  determined  by  analysis  or  otherwise,  additional 
data  are  given  in  the  following  table: 


Hydrogen 

Oxygen 

Nitrogen 

Carbon  dioxide. . . 
Carbon  monoxide. 

Water 

Air 

Ash 


Specific 
Volumes. 


178.881 
11.2070 
12.7561 

8.10324 
12.81 


12.3900 


Specific  Heat 
in  Gaseous 
Condition. 


Density 

or  Weight  of 

OncCubicFool. 


3.4oyo 

0.2175 
0.2433 
o.2i6q 

0.2450 
0.4805 
0.2375 
0.2 


0.00559 
0.08928 
0.07837 

o. 12341 
0.07806 


0.08071 


Substituting,  then,  for  D  in  the  formula  for  height  the 
expression 

T 
A  =  .08424-^, 

the  expression  for  that  height  becomes 

[.o8o7j^-.98424yJ 


h^H- 


.08424 


7; 


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RATE  OF  COMBUSTION.    DRAFT.  lOI 

which  becomes  by  performing  the  operations 


A=//(.96y^-i). 


The  velocity  in  feet  per  second  caused  by  a  height  h  in 
feet  will  be  denoted  by  z;  =  ^2^/1;  the  volume  Fper  second 
if  the  cross-section  be  denoted  by  A  square  feet  will  be  Av, 
and  becomes 


for  the  temperature  of  32^  F.  If  it  be  required  to  bum  W 
pounds  of  coal  per  second,  and  KfV  cubic  feet  of  gas  at 
32**  F.  be  the  result,  we  shall  have  an  equation  for  IF,  since 


JF  = 


V^-^^^Ti^) 


AT 


as  the  theoretical  pounds  of  coal  which  will  be  burned  by  a 
chimney  of  height  If  and  area  A  when  the  resistances  to  flow 
of  air  and  gas  are  disregarded. 

80.  Discussion  of  P6clet's  Theory  of  Chimney-draft.— 

P^clet  developed  a  later  theory  in  which  the  dynamic  energy 
for  the  flow  of  air  to  the  furnace  was  a  head  in  feet  expressed 
in  terms  involving  the  cold  gas  or  external  air.  He  also 
developed  an  expression  for  the  velocity  of  flow,  starting 
from  the  general  expression  for  the  relation  between  the  head 
in  a  pipe  and  the  flow  which  it  produces  in  the  case  of  a 
liquid.     A  form  for  this  is 

A=|:(i+Ar+J5r,+-0). 


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I02  HEAT  AND   HEAT-ENGINES 

which  in  Peclct's  form  appears  as 

2g\      ^        ^  ml 


In  this  equation  //  is  the  head ;  g  is  the  acceleration  due  to  grav- 
ity; /is  the  friction  against  sides  of  pipe  or  duct  or  flue;  K 
and  K^  or  G^  which  combines  them,  are  coefficients  to  express 
the  resistances  offered  by  bends,  elbows,  valves,  and  fittings 
in  hydraulic  work  and  by  the  grates,  tubes,  and  damper  in 
boiler-furnace  work;  /  is  the  length  of  the  pipe  or  gas- 
passage;  and  m  is  the  ratio  of  area  of  cross-section  to  the  pe- 
rimeter, called  the  hydraulic  mean  depth.  For  square  or 
round  flues  m  will  be  one  fourth  of  the  side  or  diameter, 

Since  -7  =  —   for  a  square    flue,    and    =  —  ==:—    for   a 

4*       4  ^  2nr       2        4 

round  one.     P^clet's  value  for  G  he   puts  at    12    for  cases 

where  20  to  24  pounds  of  coal  are  burned  per  hour,  and  for 

/  his  value  is  0.012  for  surfaces  covered  with  soot.      Hence 

his  formula  becomes 


^  =  ^(■3  +  ^0. 


2g\ 

whence  the  expression  for  volume  per  second  with  a  height  H 
would  appear 


V'^Av'^A      '  ■^' 


/  2gH[ 


967;-  7; 


/   ^ -^A_ 

\/  ,   0.012/ 

V  '3  +  --— 


The  uncertainty  as  to  coefficients;  the  fact  that  it  is  not 
true  that  v  =  Vigh  for  a  flow  of  a  gas  which  undergoes  any 
notable  change  in  pressure  or  temperature,  and  the  chimney 
problem  introduces  both;  the  fact  that  the  chimney  temper- 
ature Tc  is  not  constant  from  top  to  bottom;  and  the  neces- 
sity for  the  assumptions  of  area  and  temperature  and  velocity 


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RATE   OF  COMBUSTION.     DRAFT.  IO3 

tefore  a  height  can  be  worked  out,  have  thrown  designers 
upon  the  data  of  experience  rather  than  upon  the  foregoing 
•calculations. 

The  P^clet  formula,  however,  possesses  this  interest. 
Since  the  velocity  of  the  gas  in  the  chimney  increases  as  the 
square  root  of  the  height  of  the  dynamic  column,  and  there- 
fore with  V.g6T^  —  Ta  when  the  external-air  temperature  is 
fixed,  and  since  the  density  is  inversely  proportional  to  the 
temperature  in  the  chimney,  the  weight  discharged  will  be 
proportional  to 


which  becomes  a  maximum  when 

or  the  greatest  weight  will  be  discharged  when  the  absolute 
temperature  within  the  stack  is  ff  of  the  absolute  temper- 
ature of  the  external  air.  That  is,  if  the  external  air  be  at 
'62''  F.,  or  an  absolute  temperature  522°,  the  temperature 
within  the  chimney  for  a  greatest  weight  of  gas  flowing 
should  be  522  X  f|  ^^  1087°  absolute,  or  626''  F.  This  ex- 
plains  the  usual  preference  for  temperatures  around  600°  F. 
in  ordinary  boiler-stacks.  This  is  about  the  temperature  of 
melting  lead.  On  the  other  hand,  for  many  metallurgical 
purposes  a  higher  temperature  in  the  stack  is  a  necessity,  and 
a  greater  velocity  than  is  usual  in  steam-boiler  practice. 
When  this  maximum  temperature  prevails  h  =  //;  or  the 
extra  column  of  hot  gas  has  a  height  equal  to  that  of  the 
original  chimney,  and  the  density  of  that  gas  is  one  half  of 
that  of  the  external  air.  The  formula  also  indicates  that 
chimneys  draw  best  with  cold  air  outside  and  at  high  baro- 
metric pressures. 


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I04  HEAT  AND   HEAT-ENGINES. 

8i.  Some  Accepted  Chimney  Formulae  and  Data. — Mr. 

Wm.  Kent  in  1884  proposed  a  formula  based  on  successful 
practice  and  on  the  idea  that  the  effective  area  of  a  chimney 
was  less  than  its  gross  area  by  a  dead-space  of  two  inches 
radially  from  each  wall  of  a  square  chimney  or  all  around  a 
round  one.  This  idea,  if  A  be  the  gross  area  expressed  in 
square  feet,  and  E  the  effective  area,  will  make : 
For  square  chimneys 

E=ziy  -^  -^D  =  ^  -  i  1^. 
For  round  chimneys 

E  =  nil}'  -  -^B)  =  ^  -  o.S92^A. 
This  is  so  nearly  the  same  for  both  that  it  can  be  written 
£=zA-  0.6VZ 

Since  the  power  of  a  chiifiney  varies  both  as  the  square 
root  of  its  height  at  best  temperature  conditions  and  as  its 
effective  area,  it  can  be  written  that 

H.P.  =  EiOix  C 

in  which  C  is  a  constant  to  be  determined  from  successful 
practice.  A  boiler  horse-power  is  assumed  to  be  equivalent 
to  an  evaporation  of  30  pounds  of  water  per  hour  (§  10 1). 
Assuming  5  pounds  of  coal  per  horse-power  per  hour  to  take 
account  of  poor  conditions,  and  observing  the  number  of 
pounds  of  coal  which  a  successful  chimney  will  take  care  of, 
an  acceptable  value  for  C  is  found  to  be  3^.     Hence 

H.P.  =  3.33^^/'  =  3.33(^  -  .6VA)VA, 
which  can  be  written  also 

E  = 7f~> 

when  the  quantities  of  the  second  member  are  the  known  data. 
A  series  of  observations  by  Morin  &  Tresca  from  French 


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RATE  OF  COMBUSTION.    DRAFT. 


105 


«S   30    35    40    45    50 

55 

60 

«5 

.5   9-5   >o-5   "-6   ".4   »3.» 

«3-8 

M.5 

•5.« 

58   76    «4    93    99    105 

111 

116 

121 

75    80    85    90    95 

100 

105 

110 

16.4   16.9   17.4   18.0   18.5 

19.0 

19.5 

ao.o 

«3>    »35    »39    »44    m8 

«S» 

156 

160 

practice  have  resulted  in  the  following  table,  which  is  a  very 
safe  guide.  The  grate  is  eight  times  the  chimney  cross- 
section. 

HetKhis  in  ft.  of  chimney m 

Lbs.  per  hour  per  sq.  ft.  gyrate....    7.5 
"     "      *'      **     **    "  chimney.     60 

Heights  in  ft.  of  chimney 70 

Lbs.  per  hour  per  sq.  ft.  grate ....     15.8 
••     "      "       "    "    **   chimney.      ia6 

A  simple  formula  by  Thurston  agreeing  quite  closely  with 
the  above  table  is 

Rate  of  combustion  =  2V h--  i, 

in  which  h  is  the  height  in  feet. 

Other  designers  have  aimed  to  deduce  formulae  from  prac- 
tice which  should  take  account  of  the  prevalent  resistances  in 
grates  and  fires  with  different  grades  of  fuel,  introducing  the 
results  of  tests  into  formulae  as  coefficients.  But  successful 
practice  of  others  will  remain  the  preferred  guide.  Sectional- 
boiler  practice  using  water-tubes  has  deduced  the  following 
diagram  (Fig.  14)  to  represent  the  dra/t  in  inches  of  water 
DIAGRAN  OF  DRAFT  AND  CAPAOTY  OF  CHIMNEY. 


Pig.  14. 

(§  83)  corresponding  to  any  number  of  pounds  of  air  deliv- 
ered when  the  chimney  is  100  feet  high  and  the  external  air 
is  at  60°,  as  well  as  the  maximum  rendition-point  between 
500**  and  600°. 

Chimneys  over  150  feet  in  height  are  rarely  justified;  but 


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I06  HEAT  AND    HEAT-ENGINES. 

:2  50  fact  of  height  may  be  compulsory  in  towns  to  carry  off 
gaseous  or  noxious  products  without  possibility  of  nuisance. 
The  following  table  represents  conservative  data: 

Pounds  of  coal  consumed  per  hour Up  to  icx>     500      1000     2000     3000     4000     5000 

Height  in  feet 60      xcx>       xao        140        160       xSo       aoo 

Several  smaller  chimneys  are  often  used  instead  of  one 
large  one,  where  location  does  not  compel  great  height,  with 
considerable  economy. 

Fine  anthracite  coal  needs  a  higher  stack  than  good 
bituminous  coal,  both  on  account  of  the  grate  resistance  and 
the  lower  temperature  of  the  gases,  and  wood  requires  less 
than  either  of  the  other  two. 

Tallest  chimneys  of  record  are: 

Townsend's  Chemical  Works,  Glasgow 468  feet 

Hallsbruckner  Hiitte,  Saxony 460  ** 

Metropolitan  Street  Railway  Co.,  New  York.  ..  353  " 

Omaha  &  Grant  Smelting  Co,,  Denver 352  ** 

Clark  Thread  Co.,  Newark,  N.  J 335  ** 

Amoskeag  Mills,  Manchester,  N.  H 250  " 

Narragansctt  E.  L.  Co.,  Providence 238  '* 

Maryland  Steel  Co.,  Sparrows  Pt.,  Md 225  *' 

Passaic  Print  Works,  Passaic,  N.  J 200     '* 

Edison  Electric  Light  Co.,  Brooklyn  (two).  ...  150  ** 

82.  Cross-section  of  Chimney. — The  weight  of  chimney- 
gas  moving  per  second  through  the  fire  is  conditioned  both 
upon  velocity  and  cross-section,  which  for  a  fixed  quantity  of 
gas  can  vary  inversely  as  each  other.  Too  large  a  cross- 
section  causes  the  chimney  to  draw  badly  because  the  lower 
velocity  of  the  gases  permits  eddies  from  back-draft ;  the  gases 
are  cooled  by  contact  with  the  material  of  the  chimney,  and 
the  chimney  is  unnecessarily  costly  to  build.  Hence  a  sort 
of  empiric  standard  makes  the  cross-section  of  the  chimney 
to  be  one  eighth  of  the  area  of  the  grates  burning  coal  for 
it.  This  can  be  shown  to  be  ample  for  any  usual  assump- 
tions or  normal  velocity;  for,  if  an  area  of  one  square  foot  be 


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JiATE   OF  COMBUSTION.     DRAFT.  I07 


-taken,  and  a  temperature  for  maximum  output  z/,  =  ^2gHy 
and  if  H  be  taken  at  64  feet  of  height  for  illustration. 

v^  =  64  cubic  feet  per  second 

=  64  X  3600  =  296,000  cubic  feet  per  hour. 

Suppose  20  pounds  of  coal  burned  per  hour  per  square 
foot  of  grate,  and  300  cubic  feet  of  air  per  pound  of  coal; 
then  20  X  300  =  6000  cubic  feet  of  air  at  62°  will  be  required 
per  square  foot  of  grate.  At  626**  F.  in  the  chimney  this  air 
will  have  twice  its  volume  at  62°,  since 

r,  =  F,p  =  30<>W; 

whence 

Vf  =  12,000  cubic  feet, 

which,  if  multiplied  by  the  assumed  relation  of  chimney 
I  :  grate  8  =  96,ooo,is  only  about  -^gViftrV  or  one  third  of  what 
the  chimney  of  only  64  feet  high  will  take  care  of  per  foot  of 
area  of  cross-section. 

The  friction  becomes  greater  if  the  chimney  be  too  small, 
and  plants  are  usually  enlarged  after  some  years  of  use. 
Hence,  although  this  one-eighth  value  is  large,  it  is  usually 
best  not  to  pass  much  below  it  in  small  plants.  Possible 
excess  of  area  is  corrected  by  partly  closing  the  damper  in 
the  flue  to  the  stack. 

An  ingenious  designer  has  proposed  to  use  the  dead  area 
of  the  Kent  formula,  or  the  back-draft  area  in  the  above 
discussion,  as  a  passage  to  bring  preheated  air  down  the  stack 
so  as  to  introduce  it  below  the  fire  and  avoid  the  consump- 
tion of  fuel  required  to  raise  this  air  to  fire-temperature. 

83.  Draft-gauges. — It  is  usual  to  observe  the  pressure 
prevailing  at  the  base  of  the  stack  after  the  resistances  caused 
by  the  fire,  grate,  damper,  and  flues  have  been  encountered, 
and  to  call   this  pressure  that  which  causes  the  flow  in  the 


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I08  HEAT  AND   HEAT-ENGINES. 

siphon.  In  the  foregoing  discussion  it  was  given  in  feet  of 
head  of  hot  gas  (A)^  but  can  be  transformed  into  pounds  per 
square  foot  by  multiplying  iji)  by  the  weight  of  a  cubic  foot 
of  the  gas  (Z/^),  or 

as  shown  in  §  79.  The  velocity  is  then  worked  out  from  the 
pressure  by  finding  the  value  for  h  in  feet  when  /  and  D^  are 
observed,  and  by  calling  v  =    V2gh. 

The  most  usual  form  of  draft-gauge  is  a  U  tube  or  in- 
verted siphon  of  water,  of  which  one  leg  is  connected  to  the 
chimney-base  by  a  convenient  pipe-connection,  and  the  other 
is  open  to  the  atmosphere  (Fig.  15).  This  gauge  gives  a 
reading  in  inches  of  water,  and  the  relation  between  the  two 
units  is  found  as  follows:  since  I  cubic  foot  of  water  exerts  a 
pressure  per  square  foot  of  62.5  pounds,  hence  I  inch  exerts 

62.5  ,  ,  ,      I 

=  5.2    pounds  per  square  foot,    and  —  =  0.192.       If 

then  D^  and  Dg  are  densities  as  before,  and  we  have  values 

T  T 

D"  =  .o8o7y     and     D,  =  .084-^. 

Then,  if  the  force  of  the  draft  be  denoted  by/i 

/=  .I92//(A- A); 
or,  when  the  values  are  substituted, 

A  similar  calculation  under  the  condition  of  maximum 
quantity  of  draft,  with  60°  F.  outside  and  600°  in  the  chim- 
ney,  gives 

/(in  inches  of  water)  =  .0073//". 

The  U  tube  or  siphon-gauge  is  not  sensitive  to  very  slight 
differences  of  pressure,  and  many  improvements  have  been 


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RATE   OF  COMBUSTION,     DRAFT 


109 


suggested,  such  as  using  fluids  of  different  specific  gravities  in 
the  two  tubes  (Fig.  16);  using  a  large  surface  to  receive  the 
light  pressure,  while  reading  the  change  of  pressure  by  a  hook- 


Fig.  15. 


Fig.  16. 


gauge  (Fig.  17);  the  use  of  the  gas-holder  principle,  and 
many  other  arrangenients.  Five  to  seven  inches  of  water  is 
as  high  a  reading  as  is  secured  with  the  intense  forced  draft 
of  locomotives  or  torpedo-boat  practice;   two  inches  is  more 


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no 


HEAT  AND   HEAT-ENGINES. 


usual  when  the  air  is  forced  into  the  ash-pits  from  below  the 
grates;  a  fraction  of  an  inch  (from  -j^^  to  -^-^  is  all  which  can 


F"o":«T- 


^'' 


Li 

600' 


¥ 


1    Q 


Fig.  17. 


Pig.  18. 


be   usually  counted   on   with  ordinary  chimneys,  as   by  the 
following  illustrative  example: 

What  would  the  water-gauge   G  (Fig.  i8)  read   when  D^ 
for  outer  air  =  .0764,  and  A  J^  the  chimney  =  .0413  ? 

D,-  t: 


and 


or 


.-.     Z?. 

at; 

A 
A 

/ 

= 

h{D, 

-A) 

= 

3-51 

lbs.  per  square  foot, 

Py 

= 

3-51 

X  loox 

.192 

= 

.67  inch  of  water, 

3-! 

,1X1  = 
A  = 

A  X  62.5. 
.056  foot 
.67  inch. 

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RATE   OF  COMBUSTION,     DRAFT, 


III 


84.  Flue-gas  Analysis. — It  has  long  been  appreciated 
that  much  valuable  information  can  be  derived  from  an  analy- 
sis of  the  flue-gases  in  the  chimney,  at  any  rate  so  far  as  the 
presence  of  uncombined  oxygen,  carbon  monoxide,  and  car- 
bonic acid  are  concerned.  An  excess  of  oxygen  means  a  loss 
by  dilution  and  a  lowered  fire-temperature;  any  quantity  of 
carbonic  oxide  mean»a  waste  of  carbon  unconsumed  because 
there  is  available  heat  in  it  which  has  not  been  liberated  by 
combustion. 

The  remainder  of  the  flue-gases  is  commonly  assumed  to 
be  nitrogen,  but  it  includes  unburned  hydrocarbon,  if  there 
be  any,  and  steam  or  vapor  of  water.  The  Orsat  apparatus 
is  the  most  used  in  analyzing  flue-gases  and  is  illustrated 
in   Fig.    19.       P"\  P\  and  P'  are  pipettes  containing,  re* 


Fig.  19. 


spectively,  solution  of  caustic  potash  to  absorb  carbon  dioxide, 
pyrogallic  acid  and  caustic  potash  to  absorb  oxygen,  and  cu- 
prous chloride  in  hydrochloric  acid  to  absorb  carbon  monoxide. 
At  ^  is  a   cock  to  control  the  admission  of  gas  to  thft 


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112  HEAT  AND   HEAT-ENGINES, 

apparatus;  at  ^  is  a  graduated  burette  for  measuring  the 
volumes  of  gas;  and  at  ^  is  a  pressure-bottle  connected 
with  ^  by  a  rubber  tube  to  control  the  gases  to  be  analyzed. 
The  pressure-bottle  is  commonly  filled  with  water,  but  glycer- 
ine or  some  other  fluid  may  be  used  when,  in  addition  to  the 
gases  named,  a  determination  of  the  moisture  or  steam  in  the 
flue-gases  is  made. 

The  several  pipettes  P' ^  P" ^  and  P"*  are  filled  to  the  marks 
gy  f,  and  e  with  the  proper  reagents,  by  aid  of  the  pressure- 
bottle  A,  With  a  three-way  cock  to  open  to  the  atmos- 
phere, the  pressure-bottle  A  is  raised  till  the  burette  B  is 
filled  with  water  to  the  mark  m\  communication  is  then 
made  with  the  flue,  and  by  lowering  the  pressure-bottle  the 
burette  is  filled  with  the  gas  to  be  analyzed,  and  two  minutes 
are  allowed  for  the  burette  to  drain.  The  pressure-bottle  is 
now  raised  till  the  water  in  the  burette  reaches  the  zero 
mark  and  the  clamp  c  is  closed.  The  valve  in  the  pipe  to  the 
flue  is  now  opened  momentarily  to  the  atmosphere  to  relieve 
the  pressure  in  the  burette.  Now  open  the  clamp  c  and  bring 
the  level  of  the  water  in  the  pressure-bottle  to  the  level  of  the 
water  in  the  burette,  and  take  a  reading  of  the  volume  of  the 
gas  to  be  analyzed;  all  readings  of  volume  are  to  be  taken  in 
a  similar  way.  Open  the  cock  ^  and  force  the  gas  into  the 
pipette  P'^^  by  raising  the  pressure-bottle,  so  that  the  water 
in  the  burette  comes  to  the  mark  m.  Allow  three  minutes 
for  absorption  of  carbon  dioxide  by  the  caustic  potash  inP'", 
and  finally  bring  the  reagent  to  the  mark  a  again.  In  this 
list  operation,  brought  about  by  lowering  the  pressure-bottle, 
care  should  be  taken  not  to  suck  the  caustic  reagent  into  the 
stop -cock.  The  gas  is  again  measured  in  the  burette,  and  the 
diminution  of  volume  is  recorded  as  the  volume  of  carbon 
dioxide  in  the  given  volume  of  gas.  In  like  manner  the  gas 
is  passed  into  the  pipette  P"y  where  the  oxygen  is  absorbed 
by  the  pyrogallic  acid  and  caustic  potash;  but  as  the  absorp- 
tion is  less  rapid  than  was  the  case  with  the  carbon  monoxide. 


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RATE  OF  COMBUSTION.    DRAFT.  113 

more  time  must  be  allowed,  and  it  is  advisable  to  pass  the 
gas  back  and  forth,  in  and  out  of  the  pipette,  several  times. 
The  loss  of  volume  is  recorded  as  the  volume  of  oxygen. 
Finally,  the  gas  is  passed  into  the  pipette  P'^  where  the  car- 
bon monoxide  is  absorbed  by  cuprous  chloride  in  hydrochloric 
acid. 

The  solutions  used  in  the  Orsat  apparatus  are: 

P"'.  Caustic  potash,  I  part;  water,  2  parts. 

P".  Pyrog^lic  acid,  I  gram  to  25  cc.  of  caustic  potash. 

P' .  Saturated  solution  of  cuprous  chloride  in  hydrochloric 
acid  having  a  specific  gravity  of  1. 10. 

These  reagents  will  absorb  per  cubic  centimeter: 

P"' .  Caustic  potash  absorbs  40  cc.  of  CO,; 

P" .  Pyrogallate  of  potash  absorbs  22  **     **  Oxygen; 
P* .   Cuprous  chloride  absorbs  6  **     **  CO. 

Improvements  in  the  Orsat  apparatus  and  its  manipula- 
tion have  been  made  by  Hempel,  Carpenter,  Hale,  and 
others,  and  the  student  is  referred  to  HempePs  treatise  for 
further  detail. 

85.  Stability  and  Structure  of  Chimneys. — ^The  chimney 
and  a  proper  foundation  for  it  belong  rather  to  structural 
engineering  than  to  a  treatise  upon  heat,  and  it  would  divert 
from  present  purposes  to  discuss  these  questions  at  length. 
Wind-pressure  is  not  likely  to  reach  55  pounds  per  square 
foot  of  flat  surface;  and  the  chimney  may  be  viewed  as  a 
cantilever  loaded  uniformly  with  this  load.  In  brick  struc- 
tures this  must  never  produce  tension  on  the  windward  side, 
when  compounded  with  the  resistant  weight  of  the  bricks, 
which  will  range  from  100  to  130  pounds  per  cubic  foot;  nor 
on  the  compression  side  must  the  stress  exceed  8  tons  to  the 
square  foot,  which  the  brick  should  be  able  easily  to  with- 
stand. That  is,  if  h  be  the  height  in  feet,  d  the  average 
breadth,  and  b  the  breadth  at  the  base,  there  must  be  equi- 
librium between   W^  the  weight  of  the  chimney  in  pounds. 


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114  HEAT  AND   HEAl^-ENGJNES.  * 

and  the  quantity  C—r*     In  the  latter,  the  coefficient  C  is  a 

factor  for  wind-pressure  p^r  square  foot  pf  area.  It  is  56  for 
a  square  chimney,  35  for  an  octagonal,  and.  28  for  a  round 
chimney.  A  brick  chimney  so  proportioned  will  withstand 
any  gale  likely  to  be  experienced.  It  will  appear,  however, 
that  a  chimney  from  these  causes  and  the  concentration  of 
weight  on  a  small  area  is  a  structure  particularly  liable  to 
unequal  settling  of  its  foundations.  The  latter,  therefore, 
should  receive  most  careful  attention  from  a  competent  de- 
signer of  foundations,  and  should  be  laid  by  experienced  per- 
sons. Natural  and  undisturbed  soil  will  carry  one  ton  per 
square  foot;  loam,  compact  sand,  or  hard-pan  can  carry  two 
tons  per  square  foot.  Where  natural  foundations  cannot  be 
had,  piling  and  other  artificial  methods  are  to  be  resorted  to. 

With  respect  to  their  structure,  chimneys  may  be  grouped 
into — 

(i)  Brick. 

(2)  Steel  or  iron  shell,  brick-lined. 

(3)  Skeleton  iron  and  brick. 

Brick  chimneys  are  rouod,  square,  octagon,  or  star- 
shaped.  Circular  section  seems  best,  as  lighter,  stronger, 
and  more  shapely.  English  rule  is,  base  equals  one  tenth  of 
height ;  the  batter  or  taper  in  American  practice  is  from  one 
sixteenth  to  one  quarter  inch  to  the  foot  on  each  side.  One 
in  thirty-six  is  the  English  standard. 

The  upper  25  feet  is  one  brick  thick  (8''  or  9'');  thickness 
increases  by  one  half  brick  per  25  feet.  If  the  diameter  ex- 
ceeds 60  inches,  begin  at  top  with  one  and  a  half  bricks. 

An  inner  lining  or  core,  detached  from  the  wall  proper 
and  running  either  nearly  to  top  or  over  50  or  60  feet  up,  pre- 
vents expansion  from  cracking  the  walls.  It  need  not  be  fire- 
brick all  the  way  up,  or  even  further  than  one  half.  The  core 
is  made  of  tangent-laid  brick,  with  an  occasional  header  to 
guide  the  core  by  the  wall. 


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Another  practice  is  to  make  a  100- foot  chimney  in  three 
sections:  first,  20  feet  high,  16  inches  thick;  second,  30  feet 
high,  12  inches  thick;  third,  50  feet  high,  8  inches  thick. 
Core  in  three  sections  of  12,  8,  and  4  inches  thick,  respectively. 

The  top  of  a  chimney  is  exposed  to  weather  and  frost  and 
snow,  melting  and  freezing.  There  should  be  a  cast-iron  cap, 
or  a  stone,  to  protect  the  top  edge  of  the  brick.  Large 
moulded  terra-cotta  or  fire-clay  blocks  are  also  used,  clamped 
and  dowelled  together. 

Cylindrical  steel  chimneys  of  riveted  plate  steel,  secured 
by  a  flare  in  the  lower  10  to  25  feet  to  a  cast-iron  base-plate, 
which  again  is  anchored  by  heavy  foundation-bolts  to  a  ma- 
sonry foundation,  require  no  guy  or  stay  ropes  and  are  35  to 
50  per  cent  cheaper  than  a  brick  stack.  They  take  less  room, 
are  strong  and  safe,  and  no  air  leaks  in  to  cool  the  gas. 
They  are  brick-lined  part  way  or  all  the  way  up.  They 
must  be  kept  painted. 

Stacks  when  not  anchored  to  foundations  by  bolts,  and 
all  light  and  unlined  stacks,  require  to  be  stayed  by  guys  of 
wire  rope.  They  are  attached  opposite  the  centre  of  effort 
of  the  winds,  at  two  thirds  of  the  height ;  are  usually  four  in 
number,  the  first  being  led  in  the  direction  of  the  most 
violent  wind,  and  each  guy  of  a  cross-section  in  square  inches 
one  thousandth  of  the  exposed  area  in  feet. 

Skeleton  chimneys  have  been  put  up  by  iron-works,  but 
have  no  advantage  over  steel  cylinders,  and  for  many  reasons 
are  not  as  good.  Brick  is  built  in  between  uprights  of  rolled 
iron,  which  are  banded  by  flat  rings  on  the  outside. 

Access  should  be  permitted  to  the  chimney  at  its  base 
through  a  proper  door  either  in  the  flue  or  in  the  foundation 
of  the  chimney,  and  it  is  best  that  a  ladder  on  the  outside  of 
the  chimney  should  give  access  to  its  top.  In  a  square  chim- 
ney this  ladder  can  be  made  by  bars  let  into  two  walls  at  a 
corner.  Figs.  20,  21,  and  22  show  chimney  constructions 
and  the   proportions   which    have  been  found  satisfactory, 


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RATE  OF  COMBUSTION.    DRAFT.  II7 

according  to  which  the  thickness  may  be  reduced  as  the 
chimney  attains  height. 

86.  Artificial  or  Mechanical  or  Forced  Draft. — It  has 
been  already  pointed  out  (§  72)  that  a  movement  of  the  air 
for  combustion  might  be  mechanically  produced  by  a  proper 
appliance  for  this  purpose. 

A  calculation  of  efficiencies  shows  that  for  heights  of 
chimneys  such  as  are  ordinarily  used  the  mechanical  methods 
of  securing  draft  are  the  more  efficient,  so  that  it  becomes  a 
question  of  consideration  whether  the  necessary  air  for  com- 
bustion shall  be  furnished  by  a  costly  chimney  or  group  of 
them,  or  by  a  continuously  running  machine  of  some  different 
type.  Artificial  draft  can  be  secured  by  two  general  meth- 
ods. The  first  type  is  that  made  familiar  in  locomotive  prac- 
tice, in  which  a  rapid  motion  is  given  to  the  air  to  draw  it 
out  of  the  smoke-box  so  that  the  reduction  of  pressure  within 
the  latter  shall  cause  a  flow  through  the  grates,  fire,  and 
tubes  to  equalize  this  rarefaction.  This  is  called  the  in- 
duced-draft system,  and  as  applied  when  fans  are  used,  as  in 
steamship  practice,  is  illustrated  in  Fig.  25. 

The  other  plan  is  to  cause  a  pressure  of  air  in  the  ash-pit 
below  the  grate-bars  so  that  the  air  will  flow  up  through  the 
fire,  the  setting,  and  flues  by  the  excess  of  pressure  which 
prevails  in  the  ash-pit.  This  is  called  the  forced-draft  sys- 
tem, and  is  becoming  more  usual  in  high-speed  marine  prac- 
tice. The  mdvement  of  the  air  can  be  produced  either  by 
means  of  a  steam-jet  inducing  a  current  of  air  to  flow,  or  fans 
or  blowers  either  of  the  centrifugal  or  positive  type  may  be 
used.  If  the  first  or  aspirating  principle  is  used,  the  products 
of  combustion  must  pass  over  the  aspirating  appliance. 
These  gases  are  hot  and  possibly  corrosive.  The  heat  makes 
lubrication  difficult,  and  almost  excludes  the  use  of  apparatus 
where  lubrication  must  be  provided  unless  all  bearing-surfaces 
can  be  without  the  flues  which  carry  the  gas.  Protection 
against  corrosion  can  be  secured  if  proper  trouble  is  taken, 


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HEA  T  AND  HE  A  T-ENGINES. 


but  where  this  is  not  guarded  against  the  apparatus  deterio- 
rates rapidly.  The  forcing  system  has  the  fresh  cool  air  pass 
through  the  forcing  appliance,  and  has  furthermore  the  ad- 
vantage of  maintaining  a  higher  tension  within  the  setting 


Fio.  25. 

than'  prevails  outside  of  it,  so  that  there  is  little  or  no  ten- 
dency for  cool  air  to  leak  through  cracks  or  porous  brick-work 
into  the  gas-currents.  This  is  a  difficulty  present  where  the 
draft  is  done  by  aspiration.  On  the  other  hand,  the  pressure 
system  makes  a  hot  and  gassy  fire-room  if  there  are  places 
where  gas  can  escape  through  cracks,  doors,  or  elsewhere 
from  within  the  setting  into  the  room.     Fig.  26  shows  Mr. 


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119 


Jno.  C.  Kafer's  closed  ash-pit  system,  similar  to  that  on  the 
U.  S,  S,  Swatara  and  Kearsarge.  Since  combustion  is  more 
efficient  the  denser  the  air  used  to  effect  it,  the  pressure 


Fig.  26. 

system  offers  an  advantage  from  this  point  of  view,  as  cona- 
pared  with  natural  draft  or  the  aspiration  system. 

87.  Advantages  of  Artificial  Draft. — It  is  to  be  said  in 
favor  of  natural  or  chimney  draft  that,  when  the  chimney  is 
once  built  and  paid  for,  the  draft-machine  costs  nothing  to 
run  except  the  heat  which  is  used  for  this  purpose,  and  it 
undergoes  little  or  no  deterioration  with  use.  Furthermore, 
in  cities  the  necessities  imposed  upon  the  power  plant  to 
carry  the  products  of  combustion  high  enough  up  to  create 
no  nuisance  in  its  neighborhood  compel  a  height  and  cost  of 
chimney  which   makes  the   consideration  of   artificial  draft 


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I20  HEAT  AND  HEAT-ENGINES. 

unnecessary,  since  the  high  chimney  must  be  there  in  any  case. 
Again,  where  the  plant  is  so  large  that  the  cost  of  the  draft- 
machine  becomes  considerable,  or,  what  is  the  same  thing, 
the  cost  of  the  expensive  chimney  becomes  distributed  over 
a  large  number  of  horse-power  units,  the  advantages  of  arti- 
ficial draft  are  not  so  apparent. 

Artificial  draft,  on  the  other  hand,  offers  the  following 
advantages : 

(i)  The  rapidity  of  combustion  in  the  fire-box  is  not  lim- 
ited by  atmospheric  conditions.  With  a  demand  for  high 
steam -pressure  and  great  capacity  in  a  limited  space  the 
forced  draft  is  a  necessity,  as  in  war-ship  practice. 

(2)  It  is  possible  to  increase  the  evaporative  capacity  of  a 
given  plant  without  other  change  than  the  velocity  of  the 
draft-machine.  This  increase  may  be  either  permanent  or 
to  meet  sudden  demands  for  steam,  such  as  occur  in  street- 
railway  practice  at  busy  hours.  With  natural  draft  the  chim- 
ney must  be  designed  to  meet  the  maximum  requirement, 
and  will  be  partly  shut  off  at  other  times. 

(3)  It  is  possible  to  burn  inferior,  cheaper,  and  smaller 
sizes  of  fuel  with  artificial  draft,  because  a  high  pressure  can 
be  maintained  which  will  force  the  necessary  air  through  a 
compact  body  of  fuel. 

(4)  The  draft  arrangements  are  more  portable  than  chim- 
neys can  be. 

(5)  The  plant  is  more  flexible  for  changes  in  qualit}'^  or 
size  of  fuel,  and  the  desirable  thickness  of  fuel-bed  on  the 
grates.  Grate-bars  can  be  altered  more  easily  if  this  should 
be  desirable. 

(6)  Where  high  stacks  are  not  made  necessary  the  cost 
which  they  entail  is  avoided,  or  is  obviated  by  a  less  cost  of 
the  draft-machine.  The  troublesome  settling  of  massive 
stacks  is  avoided  when  foundations  are  diflScult  or  defective. 

(7)  Leakage  of  air  into  the  setting  does  not  occur  with 
forced  draft  on  the  pressure  system. 


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RATE  OF  COMBUSTION.     DRAFT  121 

88.  Disadvantages  of  Artificial  Draft. — ^The  objections 
to  be  raised  against  the  artificial  draft  are: 

(i)  The  running  cost  of  the  machine.  While  it  takes  less 
coal  than  the  chimney  to  do  a  given  work,  the  fuel  is  not  the 
only  expense  where  an  engine  must  be  run,  consuming  oil  and 
other  supplies,  calling  for  repairs  and  supervision,  and  the 
expense  of  the  latter  may  be  considerable. 

(2)  The  artificial-draft  machine  occupies  space  which  can 
often  be  ill  spared. 

(3)  Running  machinery,  and  particularly  that  at  high 
speed  such  as  most  draft  appliances  demand,  is  rarely  silent, 
is  often  noisy,  and  is  liable  to  breakdowns  which  compel  it  to 
stop. 

It  will  be  seen  that  chimney-draft  is  not  liable  to  these 
disadvantages. 

The  machine  for  causing  the  draft  may  be  a  centrifugal 
fan  driven  either  by  its  own  directly  coupled  engine  or  by  a 
detached  engine,  or  a  revolving  shaft,  or  by  means  of  an 
electrical  motor.  The  positive  blowers  will  be  driven  by 
belts,  or  their  own  direct-coupled  engine  or  motor,  whether 
used  for  pressure  or  suction  methods,  and  the  steam-jet, 
which  is  the  third  appliance,  requires  no  moving  machinery 
when  used  in  either  system.  It  will  be  seen  that  each  of 
these  offers  some  advantages  and  disadvantages  of  its  own. 
The  fan  method,  if  driven  by  belting,  increases  the  running 
cost;  and  if  electric  current  must  be  generated,  the  cost  of 
its  transformation  must  be  considered.  The  steam-jet  plan 
occupies  very  little  space  and  is  cheap  to  buy  in  the  first 
instance.  It  is,  however,  wasteful  of  steam  as  compared  with 
the  other  systems,  and  is  in  most  cases  too  noisy.  If  used 
as  a  forcing  system,  the  steam  passes  through  the  fire  and  is 
objectionable.  If  used  as  a  suction  system,  the  steam  goes 
out  with  the  products  of  combustion  and  does  no  harm. 

The  methods  which  have  been  used  in  marine  practice  to 
secure  the  necessary  forced  draft  are  either  the  closed  ash- 


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HEAT  AND   HEAT-ENGINES. 


pit  system,  the  closed  fire-room  system,  or  the  induced-draft 
system.     The  combination  of  closed  ash-pit  system  with  the 


Pig.  28. 

induced-draft  system  enables  preheating  of  the  air  to  be  easily 
done  before  it  enters  the  ash-pit.  Figs.  27,  28,  and  29  show 
typical  stationary  arrangements. 


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123 


89.  Smoke-prevention. — The  preceding  discussion  on  the 
liberation  of  heat  from  a  fuel  for  motive-power  purposes 
would  not  be  complete  without  a  reference  to  the  loss  of 
energy  which  occurs  when  combustible  carbon  passes  out 
with  the  products  of  combustion,  and  without  having  under- 
gone complete  oxidation  at  the  desired  point.  When  this 
carbon  goes  off  as  carbon  monoxide,  the  loss  is  that  made 


Fig.  29. 

manifest  in  §  24.  When  incandescent  solid  carbon  fails  to 
meet  oxygen  under  favorable  conditions  for  its  union  with  it, 
the  extinction  of  the  glowing  particles  forms  them  into  lamp- 
black or  soot,  which  particles  color  the  products  of  combus- 
tion, and  cause  them  to  darken  the  air  and  to  defile  the  sur- 
faces which  they  touch,  A  smoke,  in  its  exact  sense,  is  a 
•current  of  products  of  combustion  from  a  fire,  in  which  the 
otherwise  colorless  gases  carry  finely  divided  particles  of  black 
carbon.  This  carbon  resulting  from  incandescence  which  has 
ceased  is  practically  incombustible  at  ordinary  heats.  It 
could  have  been  burned,  however,  if  the  union  with  oxygen 
had  taken  place  while  the  carbon  was  in  the  nascent  or  favor- 


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124  HEAT  AND   HEAT-ENGINES. 

able  state  of  its  first  incandescence,  and  the  effort  of  the 
designer  and  manager  of  the  combustion  must  be  directed  to 
keep  up  the  gases  to  the  temperature  of  the  ignition  of  the 
carbon,  and  with  a  full  supply  of  oxygen  at  sufficient  temper- 
ature to  satisfy  the  carbon.  Pure  hydrogen  combustions  are 
normally  smokeless,  because  of  the  absence  of  solid  matter 
in  the  flame.  Such  flames  are  usually  non-luminous  for  the 
same  reason. 

The  various  methods  for  smoke-prevention  have  been 
grouped  under  the  following  heads: 

(i)  The  supply  of  excess  of  air  by  steam-jets,  inducing- 
currents  which  they  warm,  and  supplying  excess  of  warm  air 
above  the  fire  and  behind  the  bridge-wall.  The  diflSculty 
with  these  has  been  that,  after  distillation  of  the  gas  is  com- 
pleted, after  a  charge  of  fresh  fuel  is  thrown  on  the  fire,  this 
excess  of  air  is  not  needed,  and  the  products  of  combustion 
are  cooled  by  the  diluting  oxygen.  Attempts  have  been 
made  to  correct  this  by  graduating  the  supply  of  fresh  air  by 
chronometric  or  other  appliances,  so  that  the  excess  should 
be  cut  off  after  such  an  interval  as  is  usually  needed  for  the 
first  distillation  of  gas. 

(2)  By  the  coking  methods  of  firing.  By  these  plans  a 
large  dead-plate  was  used,  so  that  the  gases  should  be  distilled 
off  from  the  fresh  fuel  before  its  combustion  was  really  begun 
on  the  grate-surface  proper,  and  when  the  coking  was  com- 
plete only  fixed  carbon  remained  to  burn  on  the  grate-surface 
proper  when  pushed  back.  The  gas  distilled  from  the  fuel 
on  the  dead-plate  passed  over  the  hot  fire,  and  was  so 
warmed  that  it  was  ready  to  combine  and  burn.  Alternate 
firing  of  the  two  sides  of  the  furnace,  or  the  use  of  two  fur- 
naces delivering  into  a  common  combustion-chamber  which 
were  fired  alternately,  belong  to  this  same  class. 

(3)  The  methods  belonging  to  the  principles  of  mechan- 
ical stoking  are  smoke-preventing  methods  in  that  each  part 
of  the  fire  always  remains  in  the  same  condition,  and  the  fresh 


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RATE  OF  COMBUSTION,     DRAFT,  12$ 

coal  which  distils  off  gas  is  received  in  the  coolest  part  of  the 
grate,  and  passes  to  the  hotter  sections  only  after  the  volatile 
matter  has  been  distilled  off  and  burned  in  passing  over  those 
hottest  portions. 

(4)  Gas-  and  oil-firing  are  smoke-preventing  methods, 
since  when  properly  done  the  combustion  ought  to  be  com- 
plete, and  no  carbon  should  pass  out  of  the  setting  except  in 
the  form  of  carbonic  acid.  It  is  to  this  group  that  those  set- 
tings belong  in  which  the  actual  combustion  of  the  fuel  con- 
taining volatile  matter  is  done  in  a  separate  furnace  and 
away  from  contact  with  the  boiler.  This  makes  a  relatively 
smokeless  and  efficient  apparatus,  and  will  answer  with  coals 
which  cannot  be  economically  burned  in  any  other  way. 

(5)  The  down-draft  furnac^appears  to  be  one  of  the  most 
successful  appliances  for  smoke-prevention  with  smoky  coals. 
As  satisfactorily  applied  it  involves  the  use  of  two  sets  of 
grate-bars,  one  over  the  other,  so  arranged  that  the  draft 
passes  downwards  through  the  upper  and  lower  sets  of  bars, 
or  else  passes  downwards  through  the  upper  and  upwards 
through  the  lower.  Each  set  has  its  own  fuel,  but  the  inten- 
tion is  that  the  gases  shall  be  distilled  off  from  the  fresh  fuel 
on  the  upper  grate,  and  shall  be  drawn  downwards  to  mix 
with  the  hot  products  escaping  from  the  lower  where  the  solid 
carbon  is  burning.  By  this  the  temperature  of  ignition  is 
maintained  for  the  distilled  gas,  so  that  it  shall  burn  with  the 
abundant  supply  of  warm  air  admitted  for  this  purpose. 
Figs.  30  and  3 1  show  boiler-settings  of  this  type. 

(6)  The  use  of  fire-brick  or  similar  refractory  material  for 
the  furnace  or  in  the  combustion-chamber  (Fig.  32).  This 
becomes  hot  by  the  impact  of  flame  and  gas,  and  keeps  the 
temperature  of  the  gas  up  to  ignition.  It  imparts  some  of 
its  heat  to  the  boiler  by  radiation  after  it  is  once  brought  up 
to  full  heat. 

(7)  Preheating  of  the  air-supply  by  hollow  walls  or  flue- 


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iij|iHi|ii[lilii||i|;iy|ji'lTi..* 


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X27 


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RATE   OF   COMBUSTION,     DRAFT  I2g 

boxes  which  the  hot  gases  surround  while  the  fresh  air  flows 
within  them. 

The  objections  to  most  of  the  smoke-prevention  devices 
have  been  that  the  introduction  of  such  appliances  diminishes 
either  the  economy  or  the  capacity  of  the  plant  as  compared 
with  what  it  was  when  the  chimneys  were  allowed  to  smoke. 
The  excess  of  air  diluting  products  of  combustion  explains  a 
loss  of  economy  and  capacity,  and  the  superior  efficiency  of 
the  yellow  flame,  as  compared  with  the  colorless  flame  of 
perfect  combustion,  is  also  responsible  in  part  for  this  result. 
The  losses  seem  to  be  about  12  per  cent  of  power  or  from  7 
to  13  per  cent  of  economy. 

The  term  smoke-consumption  or  smoke-burning  is  an 
improper  one.  Lamp-black  once  made  is  incombustible  and 
cannot  be  burned.  The  products  of  combustion  are  often 
colored  brown  by  the  presence  of  tarry  or  similar  combus- 
tible matters,  and  these  will  ignite  if  the  temperature  be 
made  hot  enough.  It  is  possible  to  prevent  appearance  of 
smoke  by  catching  it  in  water  through  which  the  products  of 
combustion  pass,  and  in  which  the  carbon  is  thrown  down. 

90.  Mechanical  Stoking. — Modern  successful  combustion 
is  also  much  indebted  to  improvement  in  the  grate-bar  of  the 
furnace  for  the  securing  of  smokelessness.  While  the  shak- 
ing-grate has  made  the  fireman's  work  more  easy,  it  is  to  the 
step-grate  and  the  travelling-grate  that  smokeless  combustion 
is  more  largely  due. 

In  the  step  grate  the  bars  are  flat  surfaces  or  treads 
arranged  so  that  the  upper  one  slightly  overlaps  the  one 
below  it,  while  leaving  open  for  the  passage  of  air  the  space 
which  corresponds  to  the  riser  in  stairway  construction.  It 
will  be  seen  that  this  construction  permits  abundance  of 
access  of  air  with  little  or  no  possibility  of  coal  dropping 
through  the  grate-surface;  or  the  principle  of  a  forced  draft 
can  be  applied  (Fig.  33).  When  the  bars  are  laid  across  the 
furnace,  as  is  usual,  the  slice-bar  of  the  fireman  can  cleanse 


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130  HEAT  AND   HEAT-ENGINES. 

each  bar  separately  by  working  through  the  vertical  opening 
between  the  bars,  or  the  method  of  firing  may  be  used 
whereby  the  coal  is  fed  first  on  the  upper  bar,  and  from  that 
IS  gradually  pushed  down  the  steps  from  bar  to  bar  until  at 
the  bottom  it  will  be  pushed  off  with  all  available  combusti- 
ble   matter    utilized,    and    only    refuse   and    ash    remaining 

(Fig.  33). 

It  is  very  easy  to  convert  such  a  step-grate  into  a  shak- 
ing- or  dumping-grate  by  arranging  each  bar  so  as  to  permit 
a  motion  to  tip  its  burden  down  the  steps.  This  can  be  done 
cither  by  hand  or  mechanically. 

The  principle  of  successful  passage  of  fuel  from  bar  to  bar 
suggested  in  the  previous  paragraph  leads  to  a  construction 
of  grate  which  is  known  as  the  travelling-grate.  The  bars, 
instead  of  being  continuous  and  solid,  are  made  up  of  a  series 
of  short  bars  which  are  pinned  together  so  as  to  form  a  flat 
chain  with  the  links  edgewise.  These  chains,  made  endless^ 
mounted  upon  proper  carrying-rollers  at  the  front  of  the 
furnace  and  at  the  rear,  and  having  the  width  of  the  furnace- 
area,  can  be  driven  by  machinery  attached  to  the  rollers  so 
as  to  draw  the  chain  from  the  front  of  the  furnace  to  the 
back,  carrying  on  its  surface  the  fuel  to  be  burned.  The 
speed  of  driving  should  be  so  proportioned  that  the  fresh  fuel 
charged  at  the  front  upon  the  travelling  bed  of  the  grate 
should  be  completely  burned  during  the  period  of  its  transit 
tion  to  the  back,  so  that  when  a  given  chain  of  links  reaches 
the  rear  roller  and  is  dropped  over,  there  is  carried  with  it 
and  dropped  only  the  incombustible  matter  in  that  given 
amount  of  coal.  Such  a  grate  is  practically  self-cleansing 
and  leads  at  once  to  the  use  of  an  automatic  appliance  for 
feeding  the  fuel  to  it  to  make  it  complete.  Fig.  34  shows 
a  typical  travelling-grate,  and  the  plan  shown  in  Fig.  33 
can  be  made  automatic. 

If  the  self-cleansing  mechanical  grate  can  be  combined 
with  automatic  or  mechanical  feeding  of  the  fresh  fuel  which 


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RATE  OF  COMBUSTION.    DRAFT. 


131 


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132 


HEAT  AND   HEAT-ENGINES. 


is  to  be  burned  upon  it,  it  will  be  apparent  that  not  only  has 
the  supply  of  fuel  as  a  source  of  heat  energy  become  contin- 
uous and  uniform,  but  the  combustion  of  the  fuel  is  made 
regular  and  continuous  because  the  fire  is  at  all  times  in  the 
same  condition.  Furthermore  the  labor  of  the  fireman  has 
changed  from  a  hard  muscular  exertion  of  hand-firing  to  the 
skilled  supervision  of  machinery  of  sufficient  power  to  do  the 
required  work.     In  the  mechanical  stokers  which  have  been 


MCeHANJSM  or  OQXE^B  CHAIN  GflATE  VTOKEHh 


Fig.  84. 

approved  the  coal  is  fed  upon  the  travelling  or  mechanical 
moving  grate  from  a  hopper,  either  through  an  opening  or 
between  rails  which  carry  ribs  lengthwise  so  as  to  form  pock- 
ets to  receive  the  fuel.  Thus  the  speed  of  these  pockets 
measures  the  quantity  of  fuel  delivered.  The  travelling-grate 
or  the  measuring-rollers  can  have  their  speed  regulated  by 
simple  mechanical  means  connected  with  the  steam-pressure; 
and  if  the  air  for  combustion  is  supplied  by  mechanical  means, 
the  volume  of  that  air  can  be  regulated  by  the  rise  and  fall 
of  the  pressure  of  steam  by  causing  the  latter  to  vary  the 
speed  of  the  engine  which  drives  the  fan  or  controls  the  valve 
which  supplies  the  steam-jet.      Figs.  33  and  35   show  types 


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RATE  OF  COMBUSTION.     DRAFT 


133 


in  which  the  motion  of  the  step-bar  itself  causes  the  fuel  to 
be  carried  down  the  steps  to  be  delivered  as  ash  at  the  bot- 
tom. It  will  be  seen  that  the  form  of  grate  shown  in  Fig. 
36  can  also  be  very  easily  and  properly  fitted  to  the  principle 


«dLRicxif  \iJtt,  qsn  n^.ihir* 


Fig.  85. 


of  automatic  stoking.  The  supply  of  fuel  to  the  hoppers  at 
the  boiler-fronts  will  be  done  by  the  principle  of  mechanical 
conveyors  with  elevators  if  the  supply  of  coal  in  pockets  can- 
not conveniently  be  made  overhead.  If  the  coal-vault  can 
be  over  the  boiler-room,  the  coal  may  descend  by  gravity 


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134  HEAT  AND  HEAT-ENGINES. 

through    proper   spouts    into    the    furnace-hopper   without 
handh'ng. 

This  principle  of  mechanical  handling  of  fuel,  combined 
with  mechanical  handling  of  ashes  and  with  the  principle  of 
automatic  control  of  the  machinery  of  stoking  as  the  steam- 
pressure  may  vary,  gives  to  a  modern  power  plant  where  the 
principle  is  applied  all  advantages  derivable  from  doing  away 
with  human  labor  and  replacing  it  with  intelh'gent  control  of 


I  IV 


#  ^ 


Fig.  86. 

inanimate  force.  It  has  not  been  proved  that  the  advan- 
tages from  uniformity  and  continuous  action  always  represent 
a  surplus  sufficient  to  pay  for  the  increased  cost  of  the  installa- 
tion, but  the  saving  of  labor  expense  usually  leaves  a  margin, 
in  a  plant  of  any  considerable  size,  which  is  abundant  to 
offset  such  cost. 

Mechanical  stoking  has  not  achieved  its  best  success  with 
the  hard  varieties  of  anthracite  coal  with  which  the  fireman's 
labor  is  the  least.  Again,  with  certain  varieties  of  bituminous 
coal  which  cake  and  melt  it  has  been  found  that  their  working 


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SATE  OF  COMBUSTION.    DRAFT, 


135 


''•'irf 


I 


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136 


HEAT  AND  HEAT-ENGINES. 


is  not  satisfactory  in  every  case.  Fig,  37  shows  a  form  of 
stoker  in  which  the  feeding  of  fresh  fuel  is  done  from  the 
bottom,  so  that  the  products  of  the  first  distillation  are  forced 
to  pass  up  through  the  bed  of  incandescent  fuel  from  which 
the  gases  have  been  removed.  This  brings  them  up  to  the 
point  of  ignition,  and  the  slope  of  the  sides  of  the  bed  of 
fuel  is  covered  with  coal  in  the  condition  of  fixed  carbon, 
which  when  completely  burned  falls  off  as  clinker  or  ash  at  the 
sides  of  the  grate,  or  is  removed  by  slicing.  Forced  draft 
on  the  closed  ash-pit  or  closed  fire-room  system  can  often  be 
applied  to  this  stoker  with  advantage  (Fig.  38), 


Fig.  88. 

It  has  recently  been  suggested  that  a  standard  color 
scheme  should  be  accepted  by  engineers  and  inspectors  in 
dealing  with  the  smoke  problem.  The  Ringelmann  scale  is 
exhibited  in  Fig.  39,  which  proposes  four  standards.  The 
smoke  is  to  be  observed  against  a  clear  sky,  and  its  color 


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X^  TE  OF  COMBUSTION.    DRAFT. 


137 


r 

Ao. 

1. 

" 

* 

" 

" 

"    " 

" 

' 

" 

" 

"    " 

" 

" 

" 

"   ' 

"    " 

"    " 

" 

" 

" 

" 

" 

" 

" 

*    " 

" 

" 

"    " 

. 

■ 

" 

" 

" 

" 

"    " 

I 

■ 

" 

" 

\  3 

^ 

. 

.    , 

No.  2. 


No.  3. 


No.  4. 


THE 


RINGELMANN  SCALE  FOR  GRADING  THE  DEN^T^J^^F  @^^q{^ 
Fig     Li>.  O 


138  HEAT  AND   HEAT-ENGINES. 

compared  with  th^  effect  upon  the  eye  of  an  8-inch  square 
black-and-white  grating  of  the  scale  standard  held  at  50  feet 
distance  from  the  eye.  No.  i  would  be  pure  white  paper, 
and  No.  6  in  the  series  would  be  entirely  black;  hence  each 
intermediate  proportion  corresponds  to  a  20  per  cent  range. 


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CHAPTER  VIII, 
TRANSFER  OF  HEAT.    HEATING  SURFACE. 

91.  Introductory. — In  the  four  chapters  which  have  pre- 
ceded (Chapters  IV  to  VII)  it  has  been  the  object  to  show 
how  the  energy  stored  in  the  fuel  could  be  liberated  there- 
from at  the  will  of  the  engineer  for  motive  power  or  indus- 
trial uses.  The  next  step  must  be  to  examine  how  this  liber- 
ated energy  in  the  form  of  heat-units  per  pound  of  combus- 
tible can  be  made  available  for  the  doing  of  mechanical  work. 
Two  steps  or  stages  are  involved  in  this  transformation :  the 
first  is  the  transfer  of  the  heat  to  a  medium  convenient  to 
carry  the  energy  from  the  fire  to  the  motor  cylinder  or  organ 
of  the  machine;  the  second  is  the  effect  produced  upon  that 
medium  by  such  increase  of  its  previous  heat  energy,  and  a 
discussion  of  the  availability  and  convenience  of  various 
media. 

Certain  necessary  investigations  are  at  once  suggested : 

1.  How  is  heat  transferred  from  one  body  to  another. 

2.  What  are  the  best  media,  or  those  which  give  most 
efficient  transformations  of  the  heat  energy  of  the  fire  into 
motor  energy. 

It  is  also  apparent  that  from  this  point  onward  the  prop- 
erties of  the  medium  used  as  a  heat-carrier  from  the  fire  to 
the  cylinder  are  likely  to  require  to  be  taken  into  consider- 
ation either  expressly  or  by  implication,  and  that  a  sort  of 
general  division  along  this  line  seems  to  be  required.  This 
scheme   of   differentiation   would  separate  heat-motors  into 

139 


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I40  HEAT  AND   HEAT-ENGINES. 

two  great  classes.  The  first  class  would  include  those  in 
which  the  liberation  of  heat  occurs  directly  in  or  around  the 
motor-cylinder;  the  second  class  would  be  those  in  which 
the  liberation  of  heat  occurs  in  or  at  a  second  apparatus  from 
which  the  energy  passes  to  the  motor-cylinder  through 
pipes  or  passages  by  which  generated  pressure  is  supplied  to 
the  cylinder.  The  first  class  would  include  the  gas-engines, 
the  hot-air  engines,  the  oil-engines,  the  explosive-vapor 
engines,  the  gunpowder-engines.  The  second  class  contains 
the  steam-engines,  the  ammonia  or  volatile-vapor  engines, 
the  compressed-air  engines,  and  other  types  in  which  a  boiler 
or  generator  and  a  reservoir  of  pressure  are  necessary  features 
in  addition  to  or  outside  of  the  engine  proper.  The  signifi- 
cance of  this  division  will  appear  more  manifest  in  later  chap- 
ters and  after  detailed  discussion. 

Speaking  more  roughly  and  with  less  regard  to  exactness 
of  detail,  heat-motors  may  be  classified  into  those  using  the 
permanent  gases,  which,  like  air,  do  not  change  their  state 
under  changes  of  heat-condition,  which  form  one  class;  and 
those  using  water  or  other  liquids  which  will  form  gases  or 
vapors  under  increase  of  heat  energy,  which  motors  form  the 
second  class.  This  does  not  quite  coincide  with  the  funda- 
mental idea  of  the  previous  division,  and  yet  does  not  disa- 
gree with  it  and  has  some  conveniences.  The  subject  of 
transfer  of  heat,  however,  may  be  discussed  with  both  classes 
in  view. 

92.  Transfer  of  Heat.  General. — In  every  heat-engine 
operating  by  pressure  caused  by  heat,  that  pressure  must  be 
contained  in  or  resisted  by  a  closed  vessel^ — usually  metallic 
— and  in  most  cases  the  heat  is  outside  of  this  vessel  and 
must  be  transferred  to  the  motor  medium  within  it.  Hence 
the  heat  must  be  first  transferred  to  the  metal  enveloping  the 
medium,  and  secondly  must  pass  from  the  metal  to  the  me- 
dium, and  thirdly  must  distribute  itself  through  the  medium 
if  the  latter  has  any  extended  volume.     In  oil-  or  gas-engines. 


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TRANSFER  OF  HEAT.  I4I 

-where  combustion  takes  place  directly  in  the  working  cylin- 
der, only  the  two  latter  steps  occur.  The  combined  process 
of  giving  out  heat  by  the  fire,  and  its  absorption  by  the 
medium,  is  called  the  transfer  of  heat.  Refrigeration  as  a 
process  is  also  a  transfer  of  heat,  but  in  the  opposite  direc- 
tion, since  the  object  is  to  diminish  the  heat  energy  of  the 
body  acted  on,  and  not  to  increase  it  as  in  heating.  In  more 
exact  language,  the  object  of  a  process  of  transfer  of  heat  is 
to  increase  the  heat  energy  of  the  cooler  body,  and  to  equal- 
ize the  intensity  of  heat-motion  of  their  respective  molecules. 
If  the  hotter  body  receives  no  increment  of  heat  during  the 
transfer  process,  it  is  refrigerated  by  the  transfer.  Ordi- 
narily, of  course,  the  heat  condition  of  the  hot  body  is  kept 
as  near  uniform  as  possible,  and  heat  energy  passes  con- 
stantly out  to  the  absorbent  body. 

It  will  be  at  once  apparent  that  the  rate  of  transfer  should 
be  faster  the  further  apart  the  heat  condition  of  the  two 
bodies,  and  that  when  their  heat  condition  is  nearly  equal- 
zied  the  transfer  per  unit  of  time  will  be  correspondingly 
diminished,  and  will  become  zero  when  both  are  in  the  same 
state  of  heat  energy. 

Experience  and  observation  show  that  heat  can  be  trans- 
ferred by  four  processes : 

(i)  By  radiation. 

(2)  By  contact. 

(3)  By  conduction  in  solids. 

(4)  By  convection  in  fluids. 

In  radiation  the  two  bodies  are  separated  by  a  space.  In 
contact  they  touch  each  other  but  are  not  one.  In  con- 
duction the  heat-motion  is  at  first  more  active  in  one  part  of 
a  solid  body  than  in  another,  and  that  heat-moLion  is  trans- 
mitted neither  by  radiation  nor  by  contact  with  another  body. 
In  convection  the  cooler  denser  particles  of  a  mobile  fluid 
displace  the  hotter  lighter  particles, — which   seems   like   a 


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142  HEAT  AND  HEAT-ENGINES. 

transfer  of  heat,  but  is  rather  a  mechanical  displacement  of 
particles  until  all  are  equally  heated. 

The  principles  of  transfer  by  each  method  will  be  dis- 
cussed hereafter, 

..  When  two  bodies  are  equalizing  their  heat  conditions  by 
a  transfer  of  heat  from  one  to  the  other,  as  when  a  metal 
mass  at  one  temperature  is  immersed  in  a  fluid  at  another, 
the  action  may  be  expressed  by  an  equation  which  shall 
express  the  gain  or  loss  of  heat  in  heat-units.  It  takes  the 
following  form : 

t/  =  w  X  ^  X  (/,  -  0  =  «''  X  ^'  X  (^  -  /). 

In  this  U  is  the  desired  units  of  heat  transferred;  ixr 
and  w'  are  the  respective  weights  in  pounds;  c  and  c'  are 
the  respective  specific  heats;  t^  and  /,  their  respective  ini- 
tial temperatures,  and  /  their  common  final  temperature. 
One  body  will  have  gained  what  the  other  has  lost,  and  the 
value  of  U  can  be  calculated  from  either.  The  application 
of  this  expression,  however,  must  be  restricted  to  the  cases 
for  which  it  is  true. 

93.  Transfer  of  Heat  by  Radiation. — When  a  body  is 
radiating  heat,  its  condition  is  one  in  which  lines  of  heat 
energy  emanate  from  the  body  in  every  direction  into  space. 
Bodies  which  are  in  the  path  of  these  heat-lines  receive  the 
impact  of  the  heat-waves,  and  their  heat  condition  increases 
in  intensity  until  their  own  tendency  to  transfer  heat  to  other 
bodies  precludes  their  rising  any  higher  in  the  heat  scale. 
Heat  behaves  like  light  in  a  transfer  by  radiation  so  far  as 
the  radiating  body  is  concerned.  Unlike  light,  however, 
the  effect  of  heat  on  the  absorbing  body  is  cumulative,  up 
to  the  point  where  the  absorbent  begins  itself  to  transfer. 

Heat  from  radiation  appears  to  vary  inversely  as  the 
square  of  the  distance,  because  a  body  at  a  distance  2  from  a 
centre  of  heat-motion  receives  only  one  quarter  as  many 
heat-impulses  in  a  given  time  upon  a  given  area  as  that  same 


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TJfANSFEU  OF  H^4T. 


143 


area  would  receive  at  a  distance  unity;  or  the  area  at  2  to 
receive  as  many  heat-impulses  as  are  intercepted  at  i  must 
have  twice  the  height  and  twice  the  breadth  needed  at  i 
(Fig.  40).  If  the  rays  also  grew  less  intense  by  distance, 
the  effect  of  distance  would  be  to  make  the  effect  of  heat 


Fig.  40. 


vary  as  the  fourth  power  of  the  distance  when  absorbing 
areas  were  the  same.  This  same  area  effect  explains  why 
radiation  is  less  effective  in  heating  inclined  surfaces  than 
when  the  heat-impulses  are  normal.  The  projected  area  is 
the  effective  one  only. 

Radiation  has  been  studied  by  physicists  with  heated 
solids  having  a  radiating  area.  Dulong  and  Petit*s  formula 
is,  for  metric  units, 

Q  =  daf^  -  1). 

Cj  IS  a  constant  depending  on  the  surface  of  the  radiating 
body,  large  for  dark  color  and  rough  surface  and  least  for 
smooth  and  polished  surfaces  light  in  color,  a  is  the  number 
1.0077,  a  constant  according  to  Dulong  and  Petit,  variable 
according  to  De  la  Provostaye  and  Desains.  Q  is  the 
quantity  of  heat  in  calories  emitted  from  a  unit  of  surface  in 


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144  HEAT  AND   HEAT-ENGINES. 

a  unit  of  time.     /^  is  the  excess  of  the  temperature  of  the 
radiant  body  over  the  absorbent  in  centigrade  degrees. 
The  radiation  formula  is  also  written 

Q  =  Caf{a*^  -  I), 

in  which  /  is  the  temperature  of  the  absorbent  body. 
Experimental  formulae  by  Hopkins  give: 

For  glass,  Q  =  9.s66^z'(^z'»  —  i). 

For  sandstone,  Q  =  %.ma\a*^  —  i). 

For  polished  limestone, 

Q  =  9.  io6a\a^^  —  i). 

In  this,  Q  is  the  quantity  of  heat  radiated  per  minute 
from  one  square  foot  of  surface  in  units  to  raise  a  kilogram  of 
water  1°  C. 

Better  ideas  about  radiation  are  derived  from  tables  of 
comparison.  This  table  is  by  Leslie,  the  experiments  being 
made  at  180°  F. : 


Lampblack 100 

Paper 98 

Resin 96 

Sealing-wax 95 

Crown  glass 90 

India  ink 88 

Ice 85 

Red  lead 80 


Mica 80 

Graphite 75 

Tarnished  lead 45 

Mercu  ry 20 

Polished  lead 19 

Polished  iron 15 

Tin-plate 12 

Gold  and  silver 13 


Darkness  and  roughness  of  surface  increase  radiation, 
while  smoothness  and  polish  diminish  it. 

Magnus*  experiments  at  270**  F.  give  relations  for  radiat- 
ing effect: 

Blackened  silver 100      I   Rock  salt 13 

Glass 64      I  Polished  silver 9.7 

Fluor-spar 45.5 

The  conditions  in  a  boiler  or  a  heat-engine  furnace  are  very 
different   from   those  of  the   foregoing,    and   the  only   data 


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TRANSFER   OF  HEAT.  MS 

usually  referred  to  are  from  P^clet,  who,  having  found  the 
total  heat  of  combustion,  says  that  from  a  fire  of  coal,  coke, 
-or  charcoal  it  is  50  per  cent,  from  peat-charcoal  48  per  cent, 
and  from  wood  and  peat  about  25  to  29  per  cent.  Flame 
heats  by  radiation  from  the  incandescent  particles  in  it. 
Gases  without  such  incandescent  material  seem  to  produce  no 
effect  by  radiation  however  high  their  temperature. 

Radiant  heat  does  not  warm  air  or  other  gases  directly. 
Open  fires  warm  only  the  objects  and  persons  in  a  room, 
which  in  turn  warm  the  air  by  contact. 

94.  Transfer  of  Heat  by  Contact. — By  far  the  most  im- 
portant in  transfer  of  heat  in  the  heating  of  buildings,  and  in 
the  heating  and  cooling  of  air  in  engines,  is  the  interchange 
when  the  two  bodies  are  in  contact,  as  when  the  hot  prod- 
ucts of  combustion  pass  over  the  metal  of  the  boiler  and  give 
up  their  heat  to  it.  Transfer  by  contact  is  also  of  primary 
importance  in  refrigeration. 

For  contact    of  solids  with  fluids   the  P^clet  formula  is 

the  notation  as  before.  Balfour  Stewart  gives  as  Hopkins's 
formulae: 


For  air,  0  =  0.0372  (^)    C*^; 

For  CO. ,  0  =  o.03?9(^)  'V'^- 


when  p  is  the  pressure  of  the  gas  in  millimeters,  and  Q  is  the 
quantity  of  heat  emitted  from  one  square  foot  as  in  §  93. 

These  data  also  are  not  of  great  significance  for  design  of 
generators,  while  more  practical  than  the  radiation  results; 
but  the  hot  gases  do  not  heat  the  motor  fluid  directly,  but 
heat  the  metal  of  the  enveloping  reservoir,  which  conducts 
-the  heat  to  the  motor-fluid. 


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146 


HEA  T  AND   HEA  T-ENGINES. 


It  is  interesting  to  note,  however,  that  in  these  two 
formulae  for  radiation  and  contact  the  difference  in  temper- 
ature enters  in  one  as  an  exponent,  and  in  the  other  as  a 
coefficient.  Hence  for  a  given  difference  in  temperature  radi- 
ation will  be  enormously  more  effective  than  contact  in  trans- 
ferring heat.  This  can  be  shown  graphically  by  the  diagram 
Fig.  41,  where  differences  of  temperature  are  abscissas  and 


163408 


216a.< 


6821 


400'' 
Pig.  41. 


heat  units,  Q  transferred  are  ordinates.     The  curve  ae  is  for 
radiation,  the  line  ab  for  contact. 

The  transfer  for  800**  difference  of  temperature  is  over  70 
times  as  great  by  radiation  as  by  contact.  This  is  one  of  the 
reasons  for  the  superiority  of  flaming  coals  over  short-flame 
fuels,  and  for  the  lessened  economy  of  gas-firing  from  gas 
made  from  coal  in  a  separate  generator.  Anthracite  as  a 
short-flame  fuel  requires  a  large  furnace  area,  as  its  heat  is- 


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TRANSFER   OF  HEAT,  147 

mainly   radiated   from   the  solid  carbon  and    not   from   the 
flame. 

Rankine*s  formula  for  transfer  by  contact  per  square  foot 
of  boiler  heating-surface  per  hour  is 


c = (^^); 


in  which  T^  and  T  are  the  temperatures  of  the  two  fluids  in 
contact  with  the  two  faces  of  the  metal,  and  a  is  a  factor 
varying  from  i6o  to  200.  This  he  calls  a  rough  approxima- 
tion, and  Q  is  B.T.U.  and  differs  from  the  Dulong  and  Petit 
formula  in  substituting  2  for  1.233  ^"d  changing  the  con- 
stant. 

In  the  transfer  of  heat  in  the  heating  of  air  by  coils  or 
radiators,  using  contact  of  air  and  hot  metal  in  the  rooms  to 
be  heated,  or  in  the  direct-radiation  system,  it  is  usual  to 
calculate  the  condensation  representing  the  transfer  at  2  to  3 
heat-units  per  square  foot  of  transferring  surface  per  degree 
difference  in  temperature,  per  hour.  That  is,  experiments 
show  such  condensation  to  average  from  1.66  heat-units  with 
ineffective  radiators  up  to  2.25  with  flat  pipe-coils  or  good 
radiators.  Otherwise  stated,  it  appears  that  with  low-pres- 
sure steam  of  one  or  two  pounds  pressure  the  condensation  per 
square  foot  ranges  from  0.25  to  0.30  pound  per  square  foot 
per  hour.  In  the  transfer  of  heat  to  air  from  coils  in  venti- 
lating systems,  where  the  air  from  out  of  doors  is  passed  over 
metal  surfaces  to  warm  it  before  distribution,  the  rough  rule 
may  be  used  that  one  square  foot  of  radiating-surface  with 
steam  at  212°  will  heat  100  cubic  feet  of  air  from  zero  to 
150°  per  hour  or  300  cubic  feet  from  zero  to  100°  in  the  same 
time;  or  the  relation  of  specific  heats  for  equal  masses  may 
be  used  to  calculate  the  water  required.  If  the  specific  heat 
of  air  be  called  0.238,  while  the  specific  heat  of  water  is 
called  unity,  it  is  obvious  that  one  pound  of  water  will  heat 


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148  HEAT  AND    HEAT-ENGINES, 

^  =  4.2   pounds  of   air    through   a  given    range.      If   a 

pound  of  air  occupies  12.39  cubic  feet,  the  lowering  of  one 
pound  of  water  one  degree  will  raise  4.2  X  12.39  =  5^  cubic 
feet  of  air  one  degree.  If  low-pressure  steam  is  used,  so  that 
966  units  are  transferred  in  cooling  steam  to  water  (§  58)  at 
212° — which  may  be  called  looo  units  without  sensible  error 
— it  appears  that  the  pounds  of  water  to  be  made  into  steam 
per  hour  bear  to  the  cubic  feet  of  air  required  to  be  warmed 
one  degree  per  hour  the  relation  of  unity  to  50,000.  Roughly 
speaking,  the  evaporation  of  30  pounds  of  water  per  hour 
will  heat  a  cubic  capacity  as  follows: 

Brick  dwellings,  in  blocks,  as  in  cities X5,cxx)  to  20,000  cu.  ft. 

"      stores,          '•        '*         10,000"  15,000  " 

*'      dwellings,  exposed  all  round 10,000**  15,000  ** 

*'      mills,  shops,  factories,  etc 7,000**   10,000  *' 

Wooden  dwellings,  exposed 7,000"  10,000  " 

Foundries  and  wooden  shops 6,000"  10,000  " 

Exhibition  buildings,  largely  glass,  etc 4,000  *'  15,000  '* 

The  water  to  be  evaporated  per  hour  having  been  found, 
the  calculation  of  boiler,  grates,  and  the  like  will  be  made  by 
methods  to  be  treated  in  later  chapters. 

In  a  negative  transfer  where  cold  brine  is  circulated  in 
coils  to  cool  a  room  (see  Chapter  XXII),  each  square  foot  of 
surface  can  take  care  of  1200--1300  heat-units  per  hour,  to  be 
withdrawn  from  the  material  to  be  cooled. 

95.  Transfer  of  Heat  by  Conduction. — When  one  end  of 
a  bar  of  metal  is  exposed  to  heat  by  putting  it  into  or  near  a 
fire,  the  heat  energy  imparted  at  the  one  end  is  conducted  to 
the  parts  farther  from  the  source  of  heat  by  overcoming  a 
certain  resistance  to  such  increase  of  heat  energy.  This 
resistance  has  been  called  the  thermal  resistance;  or  the  con- 
ductivity of  the  metal  is  the  reciprocal  of  such  resistance. 
The  transfer  is  cumulative,  since  the  bar  grows  hotter  and 
hotter,  up  to  the  point  at  which  the  transfer  of  heat  away 
irom  the  bar  by  radiation  or  contact  or  both  becomes  equal 


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T/^AjVS\F£/C   of  heat,  I49 

to  the  amount  which  it  receives  by  conduction  in  the  same 
time. 

The  conductivity  of  metal  and  the  rate  of  such  conduction 
are  primary  elements  of  transfer  of  heat  in  all  cases  where  the 
medium  to  be  heated  is  enclosed  in  a  vessel  upon  whose 
exterior  surface  the  heat  of  the  fire  is  brought  in  order  to 
raise  the  temperature  of  such  enclosed  medium.  The  outer 
layer  of  the  metal  nearest  the  fire  should  be  as  nearly  at  the 
temperature  of  the  fire  or  the  hot  gases  resulting  from  com- 
bustion as  the  efficiency  of  the  transfer  of  heat  by  radiation 
or  by  contact  will  permit,  provided  there  were  no  conduction 
to  the  presumably  cooler  inner  layers.  The  more  instantane- 
ous the  conduction,  and  the  less  loss  of  heat  energy  in  the 
process,  the  more  nearly  will  the  inner  layer  which  touches 
the  enclosed  medium  approach  to  the  temperature  of  that 
which  heats  the  outer  layers.  When  the  conducting  metal 
is  thin — having  but  a  small  fraction  of  an  inch  in  thickness — 
the  transfer  is  practically  complete,  and  with  a  medium  en- 
closed such  as  water  and  having  a  high  specific  heat  (§  12) 
the  metal  has  throughout  the  same  temperature,  which  is  that 
of  the  cooler  fluid.  With  thicker  walls  of  metal,  the  greater 
mass  to  be  affected  by  changes  of  heat  energy,  or  througlt 
which  the  thermal  resistance  may  act,  will  increase  the  differ- 
ence of  temperature  between  the  outer  hot  layer  and  the  inner 
cool  layer.  In  other  words,  for  a  given  transfer  per  unit  of 
time  the  outer  layer  must  be  hotter  with  thick  plates  than 
with  thin.  Thin  boiler-plates  absorb  heat  more  effectively 
from  the  hot  gases  which  pass  over  them  because  the  outer 
layer  is  further  removed  from  the  temperature  of  such  gases 
than  when  the  plate  is  thick,  particularly  when  the  gases  are 
moving  rapidly  and  the  time  for  absorbing  heat  from  eaclii 
pound  of  gas  is  short. 

Conduction  is  expressed  by  a  formula 
^  _  C{T'  -  T) 


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ISO  HEAT  AND   HEAT-ENGINES, 

in  which  e  is  the  space  separating  the  two  surfaces  which  are 
at  the  temperatures  T'  and  T  respectively,  and  C  is  a  coeffi- 
cient for  each  material  to  be  determined  by  experiment,  and 
the  conductivity  to  be  relative  to  a  standard. 

Relative  conductivities  as  measured  by  Wiedemann  and 
Franz  are: 

In  Air.         In  Vacuo. 

Silver icx)  icx) 

Copper 73.6  74.8 

Gold 53.2  54.8 

Brass 23.6  24 

Tin 14.5  15.4 

Iron 1 1.9  ID.  I 

Steel   1 1.6  10.3 

Lead 8.5  7.9 

Platinum 8.4  7.4 

Palladium 6.3  7.3 

Bismuth 1.8 

Conductivity  of  metals  drops  as  the  temperature  increases. 
For  iron,  with  an  increase  of  100°  F.  the  foregoing  figure 
diminishes  15  to  25  per  cent  (Forbes). 

The  quantities  of  heat  in  B.T.U.  transmitted  per  second 
through  an  area  of  one  square  foot  one  millimeter  in  thick- 
ness for  one  degree  F.  difference  in  temperature  are  ap- 
proximately for  the  following  materials  (Neumann): 

Copper 41-2     Iron 6.1 

Zinc 11.4 

Brass   11.2 


German  silver 4.  i 

Lead   1.4 


The  absolute  values  of  conductivity  in  liquids  are  uncer- 
tain and  are  certainly  low.  The  received  values  (Guthrie, 
Philos.  Trans.,  1869)  have  been  determined  in  terms  of  the 
resistance  to  transfer  of  heat,  which  is  the  reciprocal  of  the 


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TRANSFER   OF  HEA  T. 


151 


conductivity  and    is    called   the   thermal    resistance, 
thermal  resistance  is  for 


This 


Water i 

Glycerine 3.84 

Acetic  acid 8.38 


Sperm-oil 8.85 

Alcohol 9.09 

Turpentine ii«75 


The  conductivity  of  liquids  is  greater  at  higher  tempera- 
ures  than  at  low;  but  when  convection  is  not  possible  it  is 
small  in  any  case. 

Despretz  puts  that  of  water  =  ^^^  that  of  copper. 

Conducting-power  of  gases  is  very  slight,  and  it  is  often 
supposed  they  have  none.  Magnus  gives  that  for  air  =  ^-^^ 
that  of  lead. 

In  a  boiler,  when  the  hot  gases  are  at  one  constant  tem- 
perature and  the  water  at  another,  it  would  appear  that  the 
•thickness  oL  the  plate  would  not  affect  the  rapidity  of  transfer. 
But  the  gases  are  moving  in  the  apparatus  at  speed,  and 
<lo  not  stay  long  in  contact  with  the  plate;  hence  a  thick  wall 
prevents  the  heat  of  gas  from  being  so  efficiently  abstracted 
by  retarding  the  equalization  downward  to  the  temperature 
of  the  cooler  (the  water),  and  so  heat  is  wasted  by  escaping 
unreduced.  This  loss  should  be  diminished  by  proper  use  of 
what  are  called  **retarders.'* 

96.  Transfer  of  Heat  by  Convection.  Circulation. — 
The  process  whereby  heat  is  transferred  from  the  outer  layers 
of  a  fluid  to  the  inner  ones,  or  from  the  bottom  tD  the  top, 
must  differ  from  the  simple  conduction  which  takes  place  in 
a  solid.  The  molecules  being  easily  mobile  among  them- 
selves, the  cooler  ones  being  heavier  tend  to  descend  and  dis- 
place the  lighter  and  warmer  ones  within  the  confining  vessel, 
and  there  is  thus  produced  a  continual  movement  of  the 
-confined  medium,  whereby  imparted  heat  is  carried  about 
within  it,  the  hotter  part  going  to  the  top  and  the  cooler  to 
the  bottom.  This  movement  due  to  differences  of  specific 
gravity  caused  by  heat  is  called   the  convection  of  heat.      It 


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152  HEAT  AND   HEAT-ENGINES. 

is  much  less  rapid  than  the  process  of  conduction  in  solid 
matter,  but  is  the  only  way  in  which  large  bulk  of  water  or 
gas  can  be  heated.  The  source  of  heat  should  obviously 
always  be  on  the  bottom  of  such  masses  of  fluid.  When 
water  is  being  heated  and  vaporized  as  in  a  steam-boiler 
there  occurs  not  only  the  convection  process,  but  as  soon  as 
st£am-gas  bubbles  begin  to  form,  which  are  much  lighter  than 
the  water,  a  different  movement  begins,  accelerated  in  charac- 
ter as  compared  with  the  earlier  convection,  because  of  the 
difference  in  weight  of  the  same  bulk  of  steam  and  of  water. 
The  steam-bubbles  tend  to  rise  to  the  surface,  and  tend  ta 
accelerate  the  convection  when  they  conform  to  its  direction, 
and  to  disturb  it  when  opposed  to  its  direction.  This 
motion  in  a  steam-boiler  is  called  the  circulation,  and  is  of 
primary  importance  as  respects  the  transfer  of  heat.  It  can 
be  directed  but  cannot  be -antagonized.  Surprising  results 
have  been  secured  by  mechanical  circulation,  where  the 
speed  of  motion  is  greater  than  it  would  be  if  differences  of 
specific  gravity  were  alone  depended  upon. 

The  difficulty  of  transfer  of  heat  from  gases  or  to  them 
makes  it  necessary  that  the  gases  should  be  finely  divided 
into  thin  layers  or  small  bulks  if  the  transfer  of  heating  or 
cooling  effect  must  be  rapid.  This  principle  underlies  the 
use  of  small  tubes  in  tubular  boilers,  and  is  a  sound  one  if 
only  abstraction  of  heat  from  hot  carbonic  acid  is  the  object 
of  such  tubes.  Small  tubes  are  not  favorable  to  combustion, 
and  will  make  a  gaseous  fuel  a  smoky  one.  The  forcing  of 
hot  gases  in  large  flues  to  move  in  eddies  by  baffle-plates  or 
cross-partitions  causes  a  continual  convection  motion  which  is 
favorable  to  the  abstraction  of  heat  by  cooling  surfaces  pre- 
sented to  the  gases. 

97.  General  Remarks  on  the  Transfer  of  Heat. — In 
discussing  the  usual  formula  for  an  exchange  of  heat, 

G  =  C  X  7e;  X  (/'  -  /), 


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TRANSFER  OF  HEAT.  ISJ 

which  may  be  written 

(2  =  C,  X  ^  X  /?  X  (/'  -  /), 

in  which  Q  =  quantity  of  heat  transferred ; 

w  =  weight  of  gas  passing  per  unit  of  time; 
V  =  its  volume  in  cubic  feet,  and 
D  =  its  weight  per  cubic  foot ; 
Z'  —  /  =  the  range  of  temperature  change. 

It  will  appear — 

1st.  The  quantity  will  increase  as  the  difference  in  tem- 
peratures. Hence  circulation  is  beneficial,  and  the  hotter  gas 
should  meet  the  hottest  water,  and  the  coolest  gas  the  coldest 
water,  to  keep  the  difference  a  maximum. 

2d.  The  denser  the  gas  the  more  heat  it  transfers.  Hence 
plenum  and  forced-draft  systems  are  more  efficient  than  aspi- 
ration  systems. 

3d.  Liquids  transfer  heat  faster  and  more  efficiently  than 
gases  by  reason  of  greater  density.  The  presence  of  moisture 
in  an  air  causes  it  to  take  more  heat  from  the  body  than  a 
dry  air.  Hence  the  coldness  of  damp  winter  days.  The  cyl- 
inder-walls give  heat  to  the  damp  air  of  the  exhaust  of  the 
steam-engine  at  a  rate  seventy  times  faster  than  if  that  gas 
were  dry  and  free  from  moisture. 

98.  Heating-surface. — The  area  of  metal  exposed  on  one 
side  to  the  heating  effort  of  the  fire  and  on  the  other  to  the 
medium  to  be  heated  by  conduction  of  heat  through  that 
surface  will  be  called  the  heating-surface.  The  cooling- 
surface  is  the  same  thing,  only  with  the  direction  of  transfer 
reversed.  The  practical  result  therefore  to  be  sought  by  the 
engineer  and  designer  is  the  proportioning  of  the  absorbing 
surface  for  heat  so  that  with  a  given  liberation  of  heat-units 
in  the  fire  there  may  be  a  transfer  of  heat  energy  to  the  work- 
ing medium  with  the  containing  vessel  which  shall  raise  its 
heat  energy  to  the  greatest  possible  extent.    With  the  steam- 


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154  NEAT  AND   NEAT'ENG%NES. 

boiler  this  means  the  evaporation  of  a  given  weight  of  water 
into  steam  at  a  given  pressure  with  the  combustion  of  a  given 
weight  of  fuel  or  combustible,  per  unit  of  time.  Confining 
the  discussion  for  the  present  to  the  steam-boiler,  it  may  be 
said  that  the  quantity  of  heat  transferred  to  the  water  will 
therefore  depend  upon  the  extent  or  weight  of  that  contact- 
surface  of  metal,  and  the  difference  of  temperature  between 
that  metal  (or  the  water  which  touches  it)  and  the  imparting 
source  of  heat — fuel,  flame,  or  gas.  Hence  the  amount  of 
Jieating-surface  for  a  given  evaporation  of  water  or  absorp- 
tion of  heat  will  be  fixed — 

1st.  With  relation  to  the  rate  of  combustion  to  be  em- 
ployed— since  the  faster  this  rate  the  higher  the  temperature 
of  the  fire  and  the  gases. 

2d.  In  some  relation  to  the  absolute  quantity  of  heat  sup- 
plied in  a  given  time — which  is  a  relation  to  the  square  feet 
of  grate-surface  on  which  the  fuel  is  burned,  if  the  rate  of 
combustion  is  assumed. 

It  will  appear  at  once  that  the  terminal  temperature  of 
the  gases  when  leaving  the  generating  apparatus  must  be  con- 
sidered and  fixed.  If  the  gases  are  too  cool,  they  do  not 
transfer  heat  to  the  heating- surface  and  water;  chimney- 
draft  is  dependent  on  a  certain  minimum  temperature  in  the 
stack  as  compared  with  the  outer  air.  .If  the  gases  are  too 
hot,  heat  is  wasted  in  the  chimney,  because  there  was  not 
surface  enough  to  abstract  the  heat  as  fully  as  might  be,  and 
coal  has  been  burned  to  waste,  heating  the  stack  and  outer 
air  and  not  the  water. 

Hence  it  is  usual  to  fix  the  terminal  temperature  at  about 
600°  F.  (the  maximum  draft  temperature,  §  80),  since  steam 
at  250  pounds  pressure  has  a  temperature  of  401°  F.,  and 
these  gases  will  give  off  their  heat  to  the  steam  even  when 
the  difference  is  reduced  to  200°.  For  lower  pressures  they 
are  so  much  more  effective,  and  can  be  cooler  if  the  draft 
need  not  be  considered. 


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TRANSFER   OF  HEAT. 


155 


If  the  terminal  temperature  in  the  flue  Ob  (Fig.  42)  be  set 
at  600°,  represented  by  an  ordinate  bfy  and  the  curve  for  the 
transfer  of  heat  be  drawn  through /according  to  the  formula 
Q  =  Cw{t'  —  /),  there  will  be  found  a  point  A  which  will 
indicate  the  initial  difference  of  temperature  between  the  fire 


Fig.   42. 

and  the  water  such  that  the  heat  would  be  abstracted  down 
to  600°  in  that  extent  of  contact  and  transfer. 

But  if  a  higher  rate  of  combustion  be  assumed,  and  a 
higher  initial  temperature  represented  by  A'\  then  the  curve 
will  not  pass  through /as  before,  but  through  a  point/'  be- 
yond it,  so  that  with  an  extent  of  heating-surface  represented 


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156 


HEAT  AND   HEAT-ENGINES. 


by  the  length  Ob^  the  gases  would  leave  unduly  hot,  and  the 
heating-surface  should  be  extended  till  b"  is  reached,  at 
which  point  the  terminal  temperature  is  the  same  600°  as 
for  the  first  case.  For  a  higher  difference  the  third  curve 
results,  and  an  extent  of  heating-surface  as  much  greater  than 
the  first  case  as  Ob"'  is  longer  than  Ob. 

This  increase  of  heating-surface  to  absorb  greater  amounts 
of  heat  is  not  usually  done  by  lengthening  the  boiler  as 
indicated,  but  by  increasing  the  number  of  tubes,  and  the 
diameter  of  shell  as  well  as  the  length. 

Experimental  data  on  this  subject  have  been  obtained  in 
two  ways:  by  keeping  the  heating-surface  constant  and  vary- 
ing the  rate  of  combustion,  or  by  finding  the  increase  of  heat- 
ing-surface to  keep  an  evaporation  constant.  The  following 
table  is  by  Isherwood,  for  a  marine  tubular  boiler  using 
anthracite  fuel  and  having  a  constant  heating-surface  25 
times  the  area  of  the  grate. 


Pounds  of  coal  per  hour  per  square  foot 
of  grate 

Pounds  of  water  evaporated  from  and  at 
aia"  per  lb.  of  coal   


6 

8 

10 

13 

M 

16 

18 

ao 

as 

10.5 

I0.4 

10. 1 

9-5 

8.9 

8. a 

7-7 

7.3 

7.0 

"4 
6.8 


The  following  table  from  D.  K.  Clark,  **  Railway  Ma- 
chinery," gives  for  higher  rates  of  evaporation  the  relation 
between  heating-  and  grate-surface  to  maintain  a  constant 
evaporation  of  9  pounds  of  water  for  each  pound  of  coke: 


Pounds    of     coke    per 

square  foot  grate      . . 

M 

«9 

25 

3 1 

38 

47 

56 

65 

76 

87 

98 

no 

125 

129 

»53 

Heating  -  surface     per 

square  foot  grate  . . . 

30 

35 

40 

45 

50 

5S 

60 

65 

70 

75 

80 

85 

90 

95 

100 

Hence  it  appears  necessary  to  decide  upon  the  conditions 
of  rate  of  combustion  to  be  anticipated  as  usual,  and  fix  the 
heating-surface  accordingly. 

The  following  table  gives  accepted  data  on  this  subject: 


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TXANSFEX  OF  HEA  T. 


157 


Cornish 

Ordinary  flue. .  . . 

factory. 

"         marine. 


Type  of  Boiler. 

Pounds  of  Coal  per  Hour 
per  Square  Foot  o£  Grate. 

Draft. 

Authority. 

Anthracite.     1     Bituminous. 

Land 

1                             1 
6-12                    '  12-27           Chimneir 

Whitham 

'           65-80 

Forced 
Chimney 

Seaton 

Marine 

7-16                       12-27 

Shock 

I  Forced 
Chimney 


locomotive. 


Average. 


18-20 
20-30 

4 

10  I 

12-16  ** 

16-24 
40-120       Forced 


12-18       !  Chimney 

I 


Seaton 
Rankine 


Rankine 


Thurston's  formula  for  the  rate  of  combustion  per  square 
foot  of  grate  with  a  given  chimney  is : 


Rate  =  2i^height  in  feet  —  I. 


99.  Ratio  of  Heating-surface  to  Grate-surface. — There 
is  further  a  certain  agreement  that  the  ratio  between  the 
grate-area  and  the  heating-surface  shall  be  generally  main- 
tained, approximately  as  follows: 

With  a  grate-area  of  unity  the  heating-surface  will  be: 

In  Plain  cylinder  boilers 10    to    15,  average  12 

Cornish  flue-boilers 30 

Elephant  boilers 25 

Flue-boilers 17 

Tubular  boilers 25 

Traction-engine  boilers 

Marine  (Martin  type)  boilers 

Locomotive-boilers 40 

The  Morin  and  Tresca  rule,  which  has  influenced  much 
European  practice,  was  to  fix  for  each  type  a  rate  of  combus- 
tion per  square  foot  of  heating-surface  which  was  not  to  be 


40, 

35 

40. 

33 

25. 

21 

30. 

*        28 

32 

25 

00, 

75 

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1 58 


HEAT  AND   HEAT-ENGINES, 


exceeded,  and  is  given  in  the  second  column  of  the  foUowing^ 
table.  Then  the  ratio  and  rates  were  as  in  the  other 
columns. 


Type  of  Boiler. 

Pounds  of  Fuel 
pcrSq.Ft.  H.  S. 

Ratio 
H.  S.  to  G.  S. 

Combustion 
per  Sq.  Ft.  Grate. 

(a\  Land 

0.6 
0.5 
0.8 

24:1 
28:1 
70:1 

14.4 
56 

{h\  Marine 

tr\  Locornotive.  •  •  • 

Old  English  practice  was  to  require  and  expect  an  evapo- 
ration of  one  cubic  foot  of  water  (62.4  pounds)  per  square  foot 
of  heating-surface  when  water  was  delivered  at  60°  F.  and 
evaporated  at  212°. 

Old  U.  S.  Navy  practice  was  to  allow  8  pounds  of  anthra- 
cite coal  to  the  cubic  foot  per  hour  to  raise  it  from  212**  to 
steam  at  30  pounds  pressure.  This  required  f  of  a  square 
foot  of  grate  (at  12  pounds  per  square  foot  per  hour),  and 
with  a  ratio  of  25  to  i  the  heating-surface  for  this  unit  was 
i6f  square  feet. 

From  Isherwood's  historic  experiments  the  following 
table  is  taken: 


Type  of  Boiler. 

Heatingr-surface 
per  I.  H.  P. 

Water  per  Pound 
Combustible. 

Combustible  per 

Hour  per  So.  Y\, 

Grate. 

Marine  tubular 

19 

19 

16 

16.8 

20 

15.6 

15 

18 

12 

10.5 
II. 2 

II. 8 
12.4 
11.2 
10.4 
II. I 

I J 

10.5 
9.16 

9-3 
10 
9.9. 

9-3 
II   2 

44              t« 

«•              <i 

Vertical  water-tube 

Hori20ntal  flue    

Marine  tube.  ............. 

Average  10.2 

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TRANSFER  OF  HEA  T. 
Another  series  of  data  is  the  following: 


159 


T  jpe  of  Boiler. 


S':2uareFeet 
oi  H.  S. 
per  H.  P. 


C->a:  per 
H.ur  pe 


Ecooony. 


ReUtive 

Steam  I  R<;        Aatbority. 

Kapiduy. 


Water- tube 10-12  .3 

Tubular 14-15  .25 

Fiue S-12  .4 

Plain  cylinder 6-10  .        .5 

Locomotive i2-i6  .275 

Vertical  tubular 15-20  .25 


1. 00  1. 00 

.91  '         .50 

•79  .25 

.C9  I         .20 

■55  ,  .55 

.So  •  .60 


Isherwood 
Trowbridge 


loa  Evaporation  in  Boilers  per  Pound  of  Coal. — 
Again,  the  design  of  the  boiler  may  be  approached  directly 
on  the  basis  of  water  to  be  evaporated  per  pound  of  coal 
burned. 

It  will  be  recalled  (§  22)  that  a  pound  of  carbon  of  calo- 
nfic  power  14,400  will  evaporate  as  many  pounds  of  water  at 
212°  into  steam  at  212^  as  966  (which  is  the  number  of  heat- 
units  required  to  do  such  evaporation)  is  contained  in  I4,400«. 


14400 
"^66" 


=  15  + lbs. 


If'  commercial  coal  is  used  instead  of  pure  carbon,  as  stand- 
ard, having  a  calorific  power  of  12,000  by  reason  of  ash  and 
moisture  in  it,  the  pounds  of  water  per  pound  of  coal  will  be 

12000  ,    „ 

^6-  =  ^^  +  1^^- 

It  is  doing  very  well  in  a  test  when  1 1  pounds  is  reached,  and 
in  every-day  service  7,  8,  and  9  are  acceptable.  Less  than 
7  is  poor. 

If  then  the  pounds  of  water  per  hour  required  in  the  form 
of  steam  are  known,  the  grate-area  will  be  determined,  and 
the  ratio  of  heating-surface  to  grate-area  is  taken  from  the 
foregoing  tables. 

The  weight  of  water  and  steam  for  an  engine  service  can 


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I60  HEAT  AND   HEAT-ENGINES. 

be  found  from  volume  and  pressure  at  cut-off  or  at  release 
from  an  indicator-card  by  consulting  steam-tables  for  the 
weight  per  cubic  foot  at  those  pressures. 

Or  if  no  tables  are  available,  it  can  roughly  be  calculated 
as  follows:  Volume  of  cylinder  in  cubic  feet  X  2Rpm  X  60 
=  cubic  feet  of  steam  per  hour  at  boiler-pressure  and  no 
cut-off.     This  volume  in  cubic  feet  multiplied  by 

I       /       62.5  I 

-  X  -  X  X  =  lbs.  water  per  hour, 

n       \  I  1700  ^ 

when  n  =  point  of  cut-off  in  terms  of  piston-stroke; 
p  =  pressure  in  atmospheres  at  point  of  cut-ofi; 

62.5  =  pounds  per  cubic  foot  of  water; 

1700  =  multiplier  to  reduce  steam  at  atmospheric  pressure 
to  water  at  same  pressure,  since  i  cubic  inch  of  water  makes 
1700  cubic  inches  of  steam  at  one  atmosphere  pressure. 

lOi.  Water  per  Horse-power  per  Hour. — Or  again,  ex- 
periment has  shown  that  in  various  grades  of  engine  an 
engine  horse-power  should  be  developed  with  the  following 
pounds  of  water: 

High-grade  compound 16-20 

Condensing  single 22-24 

Good  large  non-condensing 28 

Average  size  condensing 30 

Small 30-45 

Pumps,  elevators,  and  non-expansive  engines         50  upwards. 

The  American  Society  of  Mechanical  Engineers,  choosing  a 
safe  figure,  has  said  a  boiler  of  iV  horse-power  should  evapo- 
rate 30jV  pounds  of  water  from  a  feed-water  temperature  of 
100°  to  steam  at  70  pounds  pressure.  This  is  34^  pounds  of 
water  (34.488)  evaporated  from  and  at  212**  with  easy  firing, 
moderate  draft,  and  ordinary  fuel,  and  showing  good  econ- 
omy. By  forcing  the  boiler  should  be  able  to  do  one  third 
more. 


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TRANSFER   OF  HEA  T. 


l6l 


This  standard  boiler  horse-power  is  equivalent  to  a  devel- 
opment of  33f305  thermal  units  (34.488  X  Q^S-?  =  33-305) 
and  therefore  corresponds  to  a  condition  of  economy  belong- 


ing to  a  combustion  of 


33305 


=  2.8  pounds  of  coal  (usually 


12000 

called  3)  per  horse-power  per  hour  in  the  engine.  Hence  from 
these  data  also  a  boiler-,  grate-,  and  heating-surface  can  be 
<lerived.  If  this  principle  be  applied  to  the  data  in  §  99,  the 
accepted  proportion  of  ^  of  a  square  foot  of  grate  per  horse- 
power is  seen  to  be  the  result. 

Still  another  path  to  solution  is  the  assumption  of  1 1^  to 
12  square  feet  of  heating-surface  to  the  horse-power  on  the 
above  unit;  or  about  3  pounds  of  water  will  be  evaporated 
from  and  at  212°  per  square  foot  of  heating-surface.  At  slow 
rates  of  evaporation  more  square  feet  will  be  required.  Kent 
gives  the  following  table  (p.  678) : 


Pimiidft  Hf O  ffDdi  3n«I  at  sis*  per  square 
foot  hcAi  in g^ surface  ptr  hour      .....  — 
Square  feet  ticaEing-surf iicc  per  H.  P. 
"  itio  H.  f       ^  ^~     ■  ^'        '      ' 
i  H   P.. 


Rjitio  H.  S,  10  G.  S.  »l  M  sq.  ft.  or  G.  S.  to 


Probable  relative  economy ,. . 

Probable  leajperaiure  of  chituncj^-ffal*. 


a 

»-5    1 

J-S 

1        1 

6 

7 

i 

^ 

17.  J 

13.8  fi.S 

9» 

1.6    IS.S 

5  8 

4.<> 

4.3 

V« 

5" 

4»-4  14"5 

»9U 

35. S  3a.4 

^7-4 

IV7 

13. q 

"*4 

lOO 

lOCjl      TOO 

vS 

^      Ss 

&a 

T't 

7" 

6' 

4^ 

45^'    ^5^ 

5^H 

t&^    C^j 

f*a 

7B7 

B5S 

^. 

6q 


As  two  examples  the  following  cases  will  illustrate  the 
different  results  from  assuming  different  conditions: 

No.  I.  Chimney-draft:  12  pounds  ot  coal  per  square  foot 
grate  per  hour  evaporation  =  9  pounds  of  water  per  pound 
of  coal.  Required  to  evaporate  5000  pounds  of  water  per 
hour. 

5000 
— — =  48  square  feet  of  grate. 

If   H.S.  :  G.S.  ::  25  :  I,  then  heating-surface  =  1200  square 
feet. 

No.  II.  Artificial  draft:  60  pounds  of  coal  per  houi    per 


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1 62 


HE  A  T  AND   HEA  TENGINES. 


square  foot  grate ;  7  pounds  water  per  pound  of  coal.     Then 

5000 
—     ^    =12  square  feet  of  grate. 

And    if   H.S. :  G.S.  ::  70  :  I,    then    heating-surface  =  840 
square  feet. 

Case  I  would  probably  be  two  boilers  of  24  square  feet 
each. 

2X24X12  =  576  lbs.  coal  per  hour,  and 
576  X  9  =  5184  lbs.  water  per  hour. 

Case  II.  12  X  60  =  720  lbs.  coal  per  hour,  and 

7  X  720  =  5040  lbs.  water  per  hour. 

This  illustrates  an  advantage  of  central  power  stations 
over  road  generation  of  steam  for  short  lines. 

102.  Refrigerating-surface. — The  transfer  of  cold  in 
refrigeration  and  condensing  is  the  same  in  principle  as  the 
reverse  transfer  of  heat. 

The  standard  experiments  are  Joule's  {/our.  Franklin 
Inst.  1862)  and  Isherwood's  (Shook's  '*  Steam-boilers," 
p.  58). 

Isherwood's  results  are: 

1.  The  number  of  heat-units  per  hour  transmitted  per 
square  foot  of  surface  is  in  direct  ratio  to  the  difference  in 
temperature  of  the  sides  of  the  intervening  metal. 

2.  Within  limits,  the  rate  of  transmission  of  heat  through 
a  metal  is  independent  of  its  thickness  (^,  J,  f). 

3.  The  thermal  conductivities  of  four  metals  is  as  follows: 


Material. 

Thermal  Conductivity  or 
Heat-units  per  Hour  per 
Square  Foot  for  i*  Dif- 
ference Fahrenheit. 

Relative  Thermal 
ConducUvity. 

Coooer  Trcfined^ 

642.543 
556.832 
373-625 
315-741 

J 

Brass  f6o  Cu.  jo  Zn^ 

0.866607 
0.581478 
0.491393 

AATrouo^ht    iron  .... 

Cast  iron  (several  times  remelted). . 

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TXANSFE/i   OF  HEAT.  163 

Prof.  Jay  M.  Whitham's  formula  for  condensing-surface  is 

WL 


S  = 


ck{T,-ty 


In  this,   5  =  condensing-surface  in  square  feet ; 

L  =  latent    heat    of  saturated    steam    at    tempera- 
ture 7;; 
T^  =  temperature  of  steam  at  pressure  recorded  by 
the  vacuum-gauge; 

/  =  mean    temperature    of   condensing  water — the 

half-sum  of  initial  and  final  temperatures; 
k  =  perfect  conductivity  of  i  square  foot  of  condens- 
ing-surface of  metal  used  from  above  table; 
c  =  fraction  denoting  efficiency  of  condensing-sur- 
face: probably  about  .3. 

Standard  experiments  give  a  value  for  ck  =  180,  hence 

5=     ^^ 


180(7;  -  /)• 

Joule  found  the  resistance  to  conductivity  to  be  due  to  a 
film  of  water  on  each  surface,  and  that  to  circulate  the  con- 
densing water  rapidly  was  to  increase  the  conductivity  of  the 
metal. 

In  cooling  brine  by  coils  containing  a  cold  fluid,  experi- 
mental values  give  a  result  of  79  square  feet  of  coil-surface 
to  dispose  of  100,000  heat-units  negative  per  hour. 

103.  Conclusion. — While  further  topics  belonging  to  the 
proper  appliances  for  the  actual  liberation  and  transfer  of  heat 
might  properly  be  introduced  here,  to  do  so  would  make  the 
discussion  too  voluminous  to  be  convenient.  Students  will 
find  the  subjects  of  boiler-setting,  boiler  accessories,  care  and 
management  of  boilers,  and  the  like  fully  treated  elsewhere^ 
to  which  references  will  be  found  in  the  Appendix. 


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CHAPTER   IX. 
MEDIA  USED   TO   TRANSFER   HEAT   ENERGY. 

105.  Introductory. — A  heat-engine  has  been  heretofore 
defined  (§  6)  as  one  in  which  an  effort  in  pounds  was  exerted 
through  a  space  or  path  in  feet,  and  where  such  effort  was 
the  result  of  a  pressure  on  an  area,  such  pressure  being 
caused  by  heat.  The  preceding  chapters  have  been  con- 
cerned first  with  the  generation  or  liberation  of  heat  from  the 
storage  of  such  heat  energy  in  fuel;  and  secondly,  with  its 
transfer  to. a  proper  medium  to  act  upon  the  piston  which  is 
the  mechanical  organ  to  receive  that  effort.  The  subject 
next  to  be  entered  upon  must  then  be  the  effect  of  increase 
of  heat  energy  in  proper  motor  media,  and  the  laws  of  their 
action  under  changes  which  they  may  undergo  in  the  amount 
of  heat  represented  in  heat-units  on  the  absolute  temperature 
scale. 

The  properties  of  these  media  and  the  effects  of  heat 
changes  upon  them  are  physical  phenomena  for  investigation 
by  the  physicist  in  his  laboratory.  The  engineer,  however, 
is  concerned  with  a  comparatively  narrow  range  of  those  phe- 
nomena and  properties  which  are  properly  within  the  domain 
*of  physics  in  the  field  of  heat. 

106.  Solids,  Liquids,  and  Gases. — It  will  be  generally 
agreed  that  the  matter  of  the  earth  (and,  so  far  as  known, 
of  the  universe)  appears  in  solid  or  in  fluid  form.  The 
solid  matter  is  that  which  can  be  changed  in  shape  or  figure 
only  by  considerable  exercise  of  force,   while  the   particles 

164 


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MEDIA    USED    TO    TRANSFER  HEAT  ENERGY.         165 

of  the  fluids  are  mobile  among  each  other,  and  only  remain 
in  any  relation  to  each  other  by  the  exertion  of  some  force. 
The  fluid  matter  is  again  subdivided  into  liquids,  which  have 
a  considerable  weight  per  cubic  foot  and  some  cohesion  of 
particles  and  no  inherent  elasticity  or  tension  at  usual  pres- 
sures; and  gases,  whose  weight  per  cubic  foot  is  small,  and 
which  have  at  all  usual  pressures  a  tendency  to  expand  and 
fill  larger  volumes  as  soon  as  such  increased  volume  exists  in 
connection  with  the  gas.  Instead  of  the  solid  and  fluid  sub- 
division, that  into  solids,  liquids,  and  gases  is  preferred  by 
many,  and  for  present  purposes  is  most  convenient. 

This  threefold  division  is  further  of  advantage  since  the 
accidental  conditions  of  temperature  and  pressure  may  cause 
the  same  matter  to  appear  in  one  or  the  other  of  the  three 
states.  Water,  for  instance,  at  atmospheric  pressure  is  a 
solid  below  32°  F,,  a  liquid  between  32°  and  212°,  and  a  gas 
above  the  latter  point.  Mercury  is  a  solid  below  39°  below 
zero  Fahrenheit,  a  liquid  up  to  648°  F.,  and  a  gas  above  this 
point.  All  of  the  usual  metals  are  solid  as  they  commonly  are 
found,  will  become  liquid  or  melt  at  a  sufficient  temperature, 
and  are  volatilized  at  the  temperatures  of  the  electric  arc  or 
furnace  and  in  that  of  the  sun.  On  the  other  hand,  many  of 
the  substances  which  at  atmospheric  pressure  and  ordinary 
temperatures  are  known  as  gases  will  become  liquid  by  suffi- 
cient pressure  and  lowering  of  their  temperature.  Such  con- 
densable gases  are  ammonia,  sulphurous  acid,  some  petro- 
leum products,  carbonic  acid  gas,  the  air,  and  others.  When 
the  pressure  is  released  or  the  temperature  is  raised,  they  will 
return  to  the  condition  of  gases.  It  is  proper  to  say,  there- 
fore, since  the  foot-pounds  required  to  compress  a  gas  can  be 
translated  into  heat-units  by  multiplying  by  778  (§  10),  that 
the  state  of  a  body  as  to  its  condition  as  a  solid,  a  liquid,  or 
a  gas  is  dependent  upon  its  heat  condition.  A  gas  which  has 
not  yet  been  made  into  a  liquid  by  pressure  or  cold  or  both 
is  called  a  permanent  gas.    Improvements  in  apparatus,  how- 


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l66  HEA  T  AND   HEA  7^-ENGINES. 

ever,  are  continually  shifting  gases  from  the  list  of  permanent 
gases  into  that  of  condensable  gases.  A  more  exact  defini- 
tion will  be  given  in  a  following  paragraph. 

107.  General  Characteristics  of  a  Medium  to  be  used 
in  a  Heat-engine. — It  has  been  already  established  (Chapter 
II,  §  7)  that  the  efifort  of  a  piston-engine  in  foot-pounds  can 
be  expressed  by  the  product  of  the  two  factors  PVy  either  per 
stroke  or  per  minute  or  per  pound.  It  is  the  effort  of  the 
engineer  who  is  to  use  the  motor  energy  of  heat  to  make  this 
product  as  large  as  possible  with  the  least  expenditure  of  his 
store  of  heat  in  the  fuel.  With  a  cylinder  which  has  been  actu- 
ally constructed  in  cast  iron  or  other  material  the  value  for  V 
has  become  a  fixed  quantity  in  any  one  engine,  so  that  P  must 
be  the  quantity  which  it  is  desired  to  have  increase  as  more 
heat  energy  is  supplied.  Hence  the  medium  to  be  used  in 
the  heat-engine  should.be  one  in  which  the  following  equa- 
tion should  be  true : 

PV  =  ZT, 

in  which  T  represents  degrees  of  temperature  on  the  absolute 
scale  (§  16)  and  Z  is  a  factor  or  multiplier  constant  or  varia- 
ble, but  determinate,  with  which  the  temperature  is  to  be  mul- 
tiplied in  order  to  produce  the  desired  or  observed  value  for 
the  first  member,  with  any  selected  medium.  V  is  the  vol- 
ume at  the  end  of  the  stroke,  through  which  the  piston  has 
swept,  and  P  the  pressure  at  the  end  of  the  stroke  and  which 
has  prevailed  throughout  it  if  the  pressure  was  constant,  or  is 
the  mean  pressure  if  the  latter  was  variable.  All  solids  are 
at  once  thrown  out  as  media,  because  they  lack  the  property 
of  any  considerable  range  of  volume  except  in  the  form  of 
coiled  springs  which  are  not  available  where  heat  energy  is 
the  motor  energy,  and  consideration  can  be  confined  to 
media  in  liquid  and  gaseous  states.  Liquids  in  the  liquid 
state  are  thrown  out  for  the  same  reasons:  the  change  of  vol- 
ume by  heat  alone,  tf  they  remaifi  liquids,  is   too   small   to 


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MEDIA    USED    TO    TRANSFER  HEAT  ENERGY,         167 

make  them  useful.  Gases,  on  the  other  hand,  have  the  prop- 
erty of  undergoing  wide  ranges  of  volume,  and  of  experienc- 
ing considerable  changes  of  condition  for  small  changes  of 
temperature.  Their  great  elasticity  enables  the  gases  to  be 
conveniently  stored  in  considerable  weights  in  bulks  which 
are  not  inconvenient;  and  when  liberated  from  the  motor- 
cylinder  after  their  work  is  done  they  pass  out  easily,  and 
cause  the  least  negative  pressure  or  effort  to  expel  them.  It 
will  furthermore  be  evident  that,  other  things  being  equal,  a 
medium  which  has  a  high  value  for  the  factor  Z  will  make  a 
more  powerful  motor  with  a  given  size  of  cylinder  than  one 
which  has  a  low  value  for  that  factor.  It  goes  without  say- 
ing that  the  greater  the  value  for  the  quantity  of  heat  in 
units  which  is  brought  into  the  cylinder  and  utilized  there 
per  stroke,  the  more  powerful  and  economical  is  the  motor  for 
its  size  or  bulk.  Shall  now  the  gases  to  be  selected  as  media 
be  permanent  or  condensable  gases? 

It  must  not  be  overlooked  that  the  volume  of  gas  which 
has  filled  the  volume  V  of  the  cylinder  at  the  end  of  the  com- 
pleted stroke  must  be  expelled  therefrom  on  the  return  of  the 
piston  to  its  starting-point.  The  effort  necessary  to  do  this 
work  of  expulsion  is  a  charge  upon  the  net  or  effective  work 
outside  of  the  cylinder,  because  it  must  be  subtracted  from 
the  gross  or  driving  effect  of  the  working-pressure  medium, 
and  it  is  of  advantage  to  make  it  as  small  as  possible  in  the 
interests  of  size  of  engine  for  a  given  effective  power,  and 
for  the  sake  of  reducing  ineffective  effort  on  general  princi- 
ples. Now  with  the  permanent  gases,  the  best  which  can  be 
done  is  to  open  the  cylinder-volume  by  generous  passages  and 
valves  to  a  larger  and  cooler  volume  in  which  by  the  lower- 
ing of  T  and  the  increase  of  F,  the  value  of  P  shall  be  low- 
ered as  far  as  it  can  be  done  for  that  gas.  For  now  a  defini- 
tion can  be  made  of  a  permanent  gas  which  shall  be  more 
exact  and  definite  than  that  of  the  preceding  paragraph.  A 
permanent  gas  is  one  in  which  the  value  for  the  multiplier  Z 


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1 68  HEAT  AND  HEAT-ENGINES. 

determined  experimentally  for  one  condition  of  pressure  vol- 
ume and  temperature  is  true  for  all  other  natural  conditions, 
or  in  which  Z  \s^  constant.  The  equation  is  then  usually 
written 

PV  ^  RT, 

and  values  of  R  for  different  media  will  be  given  shortly. 
With  the  condensable  or  non-permanent  gases  a  relation 
of  pressure  and  temperature  exists  in  which  the  gas  changes 
to  a  liquid  with  a  very  great  diminution  of  volume  at  that 
period  of  change,  and  of  course  a  very  great  drop  in  the 
value  for  P.  If  then  a  condensable  gas  be  used,  and  it  be 
convenient  at  the  end  of  the  working  or  forward  stroke  to 
establish  the  conditions  under  which  the  gas  goes  back  to 
liquid,  the  negative  pressure  for  the  expulsion  stroke  drops 
much  further  than  it  can  conveniently  be  made  to  do  with 
the  permanent  gases.  If  then  the  engine  works  without 
condensation  of  its  medium,  it  makes  little  difference  whether 
the  gas  be  permanent  or  not,  but  the  value  for  Z  is  the  im- 
portant primary  matter;  if  the  engine  can  work  with  conden- 
sation, the  use  of  the  condensable  gases  gives  a  smaller 
engine.  The  condensable  medium,  however,  must  be  so 
chosen  that  the  appliances  for  its  condensation  and  re- 
vaporization  shall  not  be  inconvenient  to  an  extent  whtch 
may  offset  its  advantage. 

It  is,  however,  not  enough  to  have  the  value  of  the  factor 
Z  ox  R  large  in  the  above  formula.  It  is  obvious  that  if  the 
equation  is  a  true  one  it  will  hold  for  all  values  of  F,  and  will 
be  true  for  a  volume  of  one  cubic  foot.  If  D  denote  the 
weight   per  cubic  foot  or  the  density  of  the  medium,  then 

these  must  vary  inversely  as  each  other,  or  z;  =  — .  Then 
the  formula  will  be  written 


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MEDIA    USED    TO    TRANSFER  HEAT  ENERGY.         1 69 

an  expression  in  which  the  volume  does  not  appear,  and 
which  states  that  the  density  of  the  gas  must  diminish  as  the 
temperature  is  made  to  increase,  and  when  R  is  large  the 
density  must  diminish  faster  than  the  pressure  rises  for  such 
a  medium.  Hence  the  conclusion  that  a  desirable  medium  is 
one  in  which  the  changes  of  temperature  within  a  given  range 
do  not  produce  wide  differences  in  specific  gravity.  Such 
media  must  cause  the  change  in  T'to  cause  changes  in  pres- 
sure, which  is  the  thing  sought  for. 
The  equation 

P 

permits  of  an  interesting  extension  of  its  discussion.  If  the 
equation  as  written  is  true  for  air,  it'  will  take  for  any  other 
permanent  gas  whose  density  is  D'  and  which  has  for  its 
factor  a  quantity  represented  by  R'  a  form 

P 
-D'  ^  ^'^' 

Dividing  these  equalities  member  by  member, 

D^_R 

D  ~  R!' 

or  the  factors  R  and  K  will  vary  inversely  as  the  weights  per 
cubic  foot  or  the  densities.  These  latter  are  usually  well 
known  and  of  easy  access  in  tables,  from  which  the  values  of 
R  can  be  found.  If  the  densities  are  given  with  air  as  a 
standard,  then 

U 

jr  =  specific  gravity  =  •?• 

From  this  R'  can  be  found  by  dividing  R  for  air  by  S\  or 

R  =  5- 


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170 


HEAT  AND   HEAT-^ENGINES, 


The  following  table  gives  such  determinations  made  by 
this  method: 


spec.  Grav,  ^.    R  Ccnlifjrade. 


Atmospheric  air i. 00000 

Nitrogen -97137 

Oxygen 1. 10563 

Hydrogen .06926 

Carbonic  acid 1 .  529C31 

Steam-gas  (ideal,  Rankine) .62209 

"    (     "       Zeuner) .62300 

Steam,  saturated  (Zeuner) .64000 


96.0376 
98 . 867 
86.862 

1386.579 
62.808 

154.379 
154.153 
150.160 


R  Fahrenheit. 


53-354 
54.926 
48.257 
770.322 
34.895 
85.766 
85.641 
83.422 


Much  effort  has  been  directed  towards  securing  a  medium 
which  should  pass  from  a  liquid  to  a  gaseous  state  with  least 
absorption  of  heat  in  such  vaporization  process,  so  as  to 
secure  a  high  vapor  tension  or  pressure  of  the  gas  in  its  gen- 
erator with  a  low  specific  heat  or  heat  in  the  liquid  when  in 
a  state  to  make  itself  into  a  gas.  The  difficulty  so  far  en- 
countered in  all  these  attempts  has  been  an  inherent  one: 
that  the  vapors  from  the  volatile  liquids  which  heat  easily  are 
so  much  more  dense  than  the  vapor  of  water  with  which  they 
compete  and  are  compared,  that  just  about  as  much  greater 
weight  of  the  substituted  liquid  has  to  be  vaporized  as 
appears  to  be  saved  by  the  lower  temperature  of  vaporization 
if  the  same  mechanical  energy  is  developed  at  the  piston. 

Another  way  of  stating  the  same  truth  or  result  is,  that 
to  carry  into  the  working  cylinder  as  much  heat  as  possible 
per  stroke  is  one  of  the  objects  sought  in  a  medium,  and  to 
have  it  carry  out  with  it  the  least  possible  heat  is  the  other. 
The  volatile  vapors  with  low  specific  heat  compel  a  large 
weight  of  their  substance  to  be  used  to  carry  into  the  cylinder 
a  great  number  of  heat-units,  and  it  is  not  easy  to  prevent 
their  carrying  too  many  out  of  the  engine  with  them,  since, 
unless  great  quantities  of  cool  condensing  water  are  used, 
these  easily  vaporizable  media  refuse  to  return  back  to 
liquids.      If  they  do  not  return  to  liquids,  they  carry  away 


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MEDIA    USED    TO    TRANSFER  HEAT  ENERGY,         I /I 

the  heat  used  to  vaporize  them,  which  is  lost;  and  the  work 
of  handling  great  weights  of  water  for  condensing  more  than 
offsets  the  apparent  gain. 

io8.  Some  Heat-carriers  which  have  been  used  as 
Media  in  Heat-engines. — The  two  media  most  used  in  heat- 
engines  are  steam,  which  is  the  gaseous  state  of  water,  and 
air.  These  are  accessible,  cheap,  safe,  innoxious,  odorless, 
non-inflammable. 

Other  media  may  be  mentioned: 

Ammonia  (NH,). 

Acetone  (C,H,0). 

Alcohol  (C,H,0). 

Bisulphide  of  carbon  (CS,). 

Chloride  of  carbon  (CCIJ. 

Chloroform  (CHCl,). 

Ether  (CJ-I,oO). 

Naphtha  and  Gasoline  (C.H,,  to  C.H,.). 

These  are  all  more  volatile  than  water,  or  make  a  vapor  at 
a  lower  temperature ;  but  they  are  costly  to  buy  and  hence 
must  be  condensed  after  working  in  the  cylinder,  and  require 
for  this  an  excess  of  cool  condensing  water.  Many  of  them 
have  an  odor,  some  an  offensive  one;  some  are  inflammable, 
some  explosive,  some  irrespirable. 

The  objection  to  air  and  the  other  permanent  gases  is 
the  high  range  of  temperature  under  which  it  must  work, 
and  the  high  initial  pressures  corresponding  to  such  high 
temperatures,  and  yet  withal  the  low  mean  pressure  which 
must  follow  expansive  working  of  the  air.  There  can  be  no 
condensation  and  hence  the  working  cylinder  has  to  be  bulky. 
This  will  be  illustrated  in  detail  later.  Some  of  the  prop- 
erties of  heat  media  are  exhibited  in  the  table  on  page  173, 
and  others  will  be  found  in  appendices  under  their  respective 
heads.  The  only  objection  to  steam  as  a  heat-carrier  is  its 
possession  of  a  property  whereby  the  withdrawal    of   heat 


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172  HEAT  AND   HEAT-ENGINES. 

while  doing  work  during  expansion  in  the  cylinder  causes  a 
condensation  of  some  of  the  steam,  resulting  in  the  formation 
of  a  mist  which  has  an  enormous  absorptive  capacity  for  heat 
and  causes  the  phenomenon  of  cylinder  condensation,  to 
which  later  reference  will  be  made.  This  very  property, 
however,  gives  steam  an  advantage  as  far  as  size  of  cylinder 
is  concerned. 

109.  Vapors. — The  term  vapor  which  has  been  used 
above  is  often  employed  to  define  the  gaseous  state  of  a  body 
which  is  commonly  a  liquid  within  ordinary  ranges  of  pressure 
and  heat.  In  this  sense  steam  is  the  vapor  of  water,  and  any 
condensable  gas  should  be  called  a  vapor.  This  is  the 
proper  use  of  the  term.  It  is  often,  however,  loosely  applied 
to  define  a  gaseous  body  having  or  carrying  finely  subdivided 
liquid  particles  in  it  which  do  not  combine  into  drops,  but 
give  an  opacity  or  visibility  to  the  mixture  of  gas  and  liquid. 
The  white  cloud  of  watery  particles  which  appears  to  issue 
from  the  exhaust-pipe  of  a  steam-engine  is  not  the  true  vapor 
of  water  (steam  is  an  invisible  gas),  but  it  is  often  called  a 
vapor  when  it  should  properly  either  be  called  vesicular 
vapor  or  nebulous  vapor  or  be  known  as  a  mist.  The  term 
vapor  is  often  popularly  used  to  cover  those  gases  other  than 
steam  which  are  used  for  motive-power  purposes. 

110.  Liquefaction,  Fusion,  or  Melting.  Latent  Heat  of 
Fusion  and  Vaporization. — If  the  notion  of  the  mechanical 
theory  of  heat  be  sound,  it  follows  that  a  solid  which  has 
become  a  liquid  by  the  process  of  applying  heat  to  it,  as  in 
the  melting  of  ice  or  sugar  or  tallow  or  lead  or  iron,  must 
have  had  its  heat  condition  or  heat  energy  greatly  increased 
by  that  process.  Very  considerable  quantities  of  heat  in 
units  have  been  expended  upon  it,  and  yet  the  temperature 
changes  recognizable  by  the  thermometer  arc  not  so  very 
great  between  the  condition  of  hot  solidity  and  that  of  incipi- 
ent fluidity.     Conversely,  a  body  like  water,   in  passing  to- 


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MEDIA    USED    TO   TXAA'SFEK  HEAT  ENERGY, 


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174 


HEAT  AND   HEAT-ENGINES. 


the  State  of  ice,  requires  the  withdrawal  of  a  large  number  of 
units  of  heat  just  at  the  freezing-point,  to  enable  the  change 
to  occur.  This  is  usually  explained  by  saying  that  an  in- 
creased energy  is  characteristic  of  the  fluid  state  of  that  body 
over  that  attaching  to  it  in  its  solid  state;  and  that  the  heat 
or  energy  which  disappears  in  effecting  this  change  of  state  is 
used  in  overcoming  molecular  attractions.  It  is  generally 
called  latent  heat  (meaning  concealed  heat)  because  it  is  not 
recognizable  as  heat  except  when  the  reverse  change  occurs, 
although  necessary  to  produce  it.  When  the  change  is  from 
a  solid  to  a  liquid,  it  is  called  the  latent  heat  of  fusion  or 
liquefaction.  The  following  table  gives  the  accepted  values 
determined  by  M.  Person.  The  figures  are  the  pounds  of 
water  which  are  raised  one  degree  Fahrenheit  by  the  release 
of  heat  when  the  bodies  solidify;  or  the  degrees  Fahrenheit 
through  which  one  pound  of  water  would  be  raised  by  the 
same  process.  They  must  also  be  the  same  quantities  for 
the  lowering  of  the  heat  condition  of  water  when  its  heat  is 
demanded  to  liquefy  the  substance  at  the  temperature  of  its 
fusion. 


Water  (ice) 140  to  142 

Zinc 50.682 

Silver 38-057 

Tin 25.702 

Cadmium 24.588 


Bismuth 22.726 

Sulphur 16.954 

Lead 9. 740 

Phosphorus 9.018 

Mercury 5.086 


These  figures,  which  are  in  B.T.U.,  must  not  be  con- 
founded with  the  temperatures  of  fusion  already  referred  to 
in  §  69. 

When  the  change  is  from  a  liquid  to  a  gas,  the  heat  re- 
quired for  vaporization  is  called  the  latent  heat  of  evapora- 
tion. This  will  be  further  discussed  in  a  following  chapter; 
but  it  will  be  apparent  that  media  which  have  a  high  value 
for  their  latent  heat  of  evaporation  will  carry  more  heat  into 
the  engine-cylinder  than   media  in    which    this    quantity  is 


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MEDIA    USED    TO    TRANSFER  HEAT  ENERGY.         1/5 

smaller,  and  that  upon  usefully  entrapping  this  large  latent 
heat  by  condensation  after  the  working  stroke,  the  motor  re- 
jects less  heat  to  waste  than  when  the  medium  is  reluctant  to 
part  with  its  latent  heat  or  has  none  to  give,  as  in  the  case 
respectively  of  the  volatile  vapors  or  the  permanent  gases 
used  as  media. 


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CHAPTER  X. 

PHYSICAL  LAWS    EXHIBITING  THE   EFFECTS  OF  HEAT' 
UPON   HEAT-CARRIERS. 

III.  Introductory. — The  accepted  principles  of  the  me- 
chanical theory  of  heat  exact  that  when  a  body  like  a  motor 
medium  undergoes  an  increase  of  its  heat  energy,  that  increase 
shall  be  distributed  to  produce  three  effects: 

1.  An  increase  in  the  sensible  temperature  as  discernible 
by  thermometer  or  measurable  by  other  means  of  observing 
actual  energy. 

2.  An  increase  of  volume,  which  means  the  doing  of  a 
certain  amount  of  internal  work  upon  the  substance  itself  in 
overcoming  the  attractions  of  the  particles  for  each  other. 

3.  An  overcoming  of  the  forces  exerted  externally  upon 
or  against  the  body  in  its  first  state  which  have  resisted  the 
increase  in  volume,  and  which  have  therefore  demanded  an 
expenditure  of  energy  in  foot-pounds  before  the  body  could 
assume  its  greater  bulk.  If  these  three  effects,  each  in  foot- 
pounds, be  represented  respectively  by  the  symbols  A,  B, 
and  C,  and  Q  denote  the  quantity  of  heat  applied  in  heat- 
units,  then  it  can  be  written  that 

A  +  B+C=  77iQ> 
or 

A  +  B+  C 


°-       ;78 


176 


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EFFECT  OF  HEATS    UPON  HEAT-CARRIERS.  177 

In  solids  and  liquids  the  quantity  C  will  be  so  small  as  to 
be  negligible,  so  that  the  expression  can  be  written 

^  778    • 

In  perfect  gases  there  should  be  no  force  required  to  over- 
come the  attraction  of  their  particles  and  B  will  disappear; 
or,  for  such  gases, 

A  +  C 


Q  = 


778 


The  above  holds  true,  however,  only  within  the  limits  of  no 
change  of  state  of  the  body  or  while  it  remains  a  soh'd,  a 
liquid,  or  a  gas.  At  the  melting-point  of  a  solid  the  quan- 
tity A  disappears  suddenly  or  gradually,  and  the  addition  of 
heat  after  that  does  not  raise  the  temperature  of  the  re- 
mainder of  the  solid  or  of  that  part  which  has  become  liquid 
until  all  has  been  melted.  The  additional  heat  is  expended 
in  increasing  the  quantity  B  -{-  C.  The  same  is  true  for 
liquids  passing  to  vapors.  These  quantities  require  to  be 
separately  investigated  for  each  material. 

But  for  the  permanent  gases  used  for  motive-power  pur- 
poses, such  as  air,  and  for  the  most  usual  vapor,  that  of 
water,  there  are  certain  physical  laws  which  are  the  result  of 
experiment  and  analysis  and  which  require  to  be  studied. 
The  permanent  gases  are  the  easiest  to  begin  with  and  will 
be  taken  first. 

112.  Law  of  Gay-Lussac,  or  Charles'  Law. — This  may 
be  stated :  The  increase  of  volume  which  a  perfect  gas  re- 
ceives when  the  temperature  is  increased  1°  under  a  constant 
pressure  of  such  gas  is  a  fixed  proportion  of  its  initial  volume 
at  the  temperature  of  melting  ice;  or,  stated  otherwise,  Equal 
increments  of  the  volume  of  a  perfect  gas  correspond  very 
nearly  to  equal  increments  of  its  temperature  as  determined  by 


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i7« 


HEAT  AND   HEAT-ENGINES. 


a  mercurial  thermometer,  provided  the  pressure  is  kept  con- 
stant. The  first  statement  has  already  been  anticipated  ia 
the  discussion  of  the  air-thermometer  and  absolute  temper- 
ature (§§  IS  and  i6),  and  the  values  for  the  increment  of  vol- 
ume for  each  thermometric  degree  as  determined  by  Regnault 
and  others;  viz.,  yJhr  ^^  -00365  on  the  centigrade  scale,  and 
y^  or  .002035  on  the  Fahrenheit.  Expressing  this  law  in 
symbols,  if  v,  =  an  initial  volume  of  any  permanent  gas  at 
the  temperature  of  melting  ice,  and  if  a  represent  the  coeffi- 
cient of  increase  for  each  degree  of  the  thermometric  scale,, 
then  the  volume. for  any  temperature  /  will  be  {at)  times- 
greater  than  the  volume  at  melting-ice  temperature  on  the 
centigrade  scale,  and  \a{t  —  /,)]  times  greater  on  the  Fahren- 
heit or  other  scale  on  which  the  reading  at  meltjng-ice  temper- 
ature is  not  zero.  This  can  be  made  general  for  all  scales  by 
calling  /  the  range  of  temperature  from  melting  ice  as  a  start- 
ing-point, or 

1/  =  ^,(1  -f  at). 


The  coefficient  a  is  practically  or  very  nearly  the  same  for  alF. 
the  permanent  gases,  air,  oxygen,  hydrogen,  etc. 

113.  Coefficients  of  Expansion. — It  has  already  been  ob- 
served that  the  expansion  of  solid  bodies  by  heat  is  so  small 
a  quantity  within  any  normal  range  of  temperature  as  to  be 
of  no  moment  in  motive-power  problems.  The  following 
tabular  values  from  D.  K.  Clark  will  show  the  quantitative 
relations  of  certain  materials.  The  figure  is  the  length  to  be 
added  to  a  unit  length  for  each  degree  Fahrenheit. 


Aluminium .00001234 

Brass 00001052 

Bronze 00000986 

Concrete 00000795 

Copper 00000887 

Iron,  wrought 00000648 

*•     cast 00000556 


Lead 00001571 

Plaster 00000922 

Silver 00001079 

Steel 00000689 

Tin 00001163 

Zinc 00001407' 


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EFFECT  OF  HEATS    UPON  HEAT-CARRIERS. 


179 


Liquids  expand  between  32°  and  212**  F,,  with  the  vol- 
ume at  freezing  as  unity: 


Water 1.0466 

Salt  solution 1.05 

Mercury 1.0182 

Alcohol I. II 


Nitric  acid i.ir 

Oils 1.08 

Ether  and  turpentine 1.07 

HClandH,S04 1.06 


114.  Law  of  Mariotte,  or  Boyle's  Law. — The  law  of 

Mariotte,  discovered  by  him  in  1640,  and  announced  by 
Robert  Boyle  in  England  independently  at  about  the  same 
date,  may  be  stated :  The  temperature  of  the  gas  remaining 
constant y  the  volumes  of  the  same  weight  of  gas  at  different 
pressures  will  be  inversely  as  the  pressures. 

Near  the  points  of  liquefaction  of  gases  by  pressure,  de- 
partures occur  from  this  law  which  are  wider  the  nearer  that 
point  is  reached,  as  the  diminution  of  volume  is  then  more 
than  proportional  to  the  increase  of  pressure, — as  should  be 
anticipated  from  the  conditions.  Expressing  the  law  by 
symbols,  if  /,  be  an  initial  pressure  expressed  in  any  unit  of 
pressure  on  a  unit  of  area,  and  v^  the  corresponding  initial 
volume  of  the  gas,  then  for  any  other  pressures  and  volumes 
v/hich  go  together  it  will  be  true  that 


/.:/ 


V  :  v^ 


or,  more  conveniently, 

p^v^  =  ^z;  =  a  constant, 

provided  no  change  of  temperature  or  heat  energy  occurs  by 
reason  of  processes  connected  with  such  change  of  volume. 
It  follows  further,  that  since  for  a  given  weight  of  gas  the 
density  will  vary  inversely  as  the  volume,  the  pressures  must 
vary  directly  as  the  densities,  and  will  be  directly  propor- 
tional to  them  at  the  same  temperatures.     Or,  in  symbols. 


p,\  p\\  D^\  D\     or, 


/        A 

—  =^  —  ^  di  constant. 


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l80  HEAT  AND   HEAT-ENGINES. 

1 15.  Combination  of  Mariotte  and  Gay-Lussac  Law. 
Value  of  Symbol  R. — It  becomes  simple  and  useful  to  com- 
bine the  foregoing  two  laws  so  as  to  exhibit  the  behavior  of  a 
weight  of  gas  undergoing  change  of  volume  and  temperature 
under  constant  pressure,  or  change  of  pressure  and  temper- 
ature under  constant  volume.  Let  /,,  v^y  and  /.  be  respect- 
ively the  pressure  volume  and  temperature  of  a  given  weight 
of  gas  at  the  temperature  of  melting  ice.  Then  for  a  differ- 
ent pressure,  /,,  let  v^  denote  the  corresponding  volume,  and 
/,  the  range  of  temperature  attaching  to  the  change  of  pres- 
sure to/j,  and  let/,,  z\^  and  /,  denote  the  same  quantities  at 
a  different  pressure,  /„  and  range  of  temperature  /,.  It  fol- 
lows from  Mariotte 's  law  alone  that 

But  by  the  Gay-Lussac  law  the  respective  volumes  for  a 
range  /,  and  /,  belonging  to  the  pressures  /,  and  p^  will  be 
respectively 

«'i  =  ^^.(i  +  ^^,); 


whence 

and 


A^i  =A^'o(l  +  ^Oi 


Dividing  one  by  the  other,  and  transposing  the  factors  p^ 

Substituting  for  a  its  value  in  either  thermometric  scale  {^fj 
or  ^\^)  and  multiplying  both  numerator  and  denominator  by 
it,  we  have 

!i=  Ay  273 +_£, 
V,       A       273  +  // 


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EFFECT  OF  HEATS   UPON  UEAT-CAKKIEKS.  l8l 

or 

V,    A  ^  461  + 1: 

But  the  last  factor  is  the  absolute  temperature  correspond- 
ing to  the  temperatures  belonging  to  /,  and  p^  respectively, 
so  that  the  equations  might  be  written,  if  a  capital  T  denote 
the  respective  absolute  temperatures, 

^»  ^  A  y  z; 

which  may  be  again  transformed  so  as  to  read 

^^  =  ^-j^i    and  which  must  equal  ^^, 

which  may  be  translated  to  say  that  at  constant  pressure  the 
volume  will  vary  inversely  as  the  absolute  temperature ^  or  at 
constant  volume  the  pressure  will  vary  inversely  as  the  absolute 
temperature. 

It  follows  furthermore,  that  since  for  any  permanent  gas 
the  quantity  2",,  or  the  absolute  temperature  at  the  point  of 
melting  ice;  the  quantity  v^^  or  the  volume  occupied  by  a 
given  weight  of  gas  under  atmospheric  pressure  at  that  tem- 
perature ;  and  the  quantity /o»  or  the  pressure  on  a  unit  of  area 
corresponding  to  one  atmosphere,  are  all  known  and  evalu- 
ated, the  product  of  them  must  be  a  constant  for  any  known, 
gas.  It  may  be  called  R,  Whence  it  will  be  true  for  any 
other  conditions  of  pressure  and  volume  which  belong 
together  that 

PV^  RT. 

(Compare  §  107.) 

For  air  -^  =  53.354,  since /,  =  2116.5  pounds  per  square 

foot;  ^»  =  77  ==  — o o>  whose  denominator  is  the  weight 

of  a  cubic  foot  of  dry  air  at  the  sea-level  and  32**  F.,  and 


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1 82  HEAT  AND   HEAT-ENGINES. 

under  one  atmosphere  of  pressure  called  14.7  pounds  per 
square  inch;  and  T^  is  493  for  Fahrenheit  scale.  For  other 
gases,  such  as 

Steam,  superheated i?  =  104.641 

Ammonia  R -=  162.602 

Ether ^=  107.830 

Alcohol jR  =  103.785 

It  will  be  apparent  from  inspection  of  the  term  ^^  =  R 

that  it  represents  the  outer  work  performed  by  a  pound  of  gas 
when  its  temperature  is  raised  one  degree,  or  from  32*"  to  33° 
on  the  Fahrenheit  scale.  Let  a  cylinder  be  imagined  of  one 
square  foot  of  area,  in  which  fits  a  weightless  piston  loaded 
with  a  weight  to  represent  one  atmosphere  or  14.7  X  144 
=  2116.5  pounds,  and  enclosing  below  it  one  cubic  foot  of 
air.  Let  this  cubic  foot  be  expanded  by  heat  to  become  two 
cubic  feet.  The  work  done  will  be  2u6.5  X  i  =  2116.5 
foot-pounds  by  one  cubic  foot,  or 

2116.5  ^  ^^  e 

— r r  =  26217.66  foot-pounds 

.080728  '  ^ 

by  one  pound  of  air.  The  denominator  is  the  weight  in 
pounds  of  one  cubic  foot.  But  to  double  the  volume  would 
require  by  the  Mariotte  law  an  expenditure  o£  493*";  hence  to 
expand  through  one  degree  would  require  but  ^iir  of  that 
required  to  do  the  work  of  doubling  the  volume.  Hence  the 
outer  work  entailed  by  the  rise  of  one  degree  temperature 
Pahrenheit  will  be 

26217.66       p^v^  „ 

-^=%==  53.354  =  it. 

Similar  calculation  can  be  made  for  any  gas,  or  R  can  be 
found  by  the  other  method  discussed  in  §  107  by  using  the 
densities. 


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EFFECT  OF  HEATS    UPON  HEAT-CARRIERS,  1 83 

116.  Specific  Heat  at  Constant  Pressure  and  at  Con- 
stant Volume. — A  most  important  consequence  is  suggested 
by  the  foregoing  calculations  and  deductions  concerning  the 
symbol  R  in  the  equation  PV=^  RT.  If  the  volume  of  the  gas 
is  prevented  from  increase,  the  work  represented  by  R  is  not 
disposed  of  against  outside  resistances,  and  will  remain  in  the 
gas  as  heat  not  expended  in  work.  By  definition  (§  12)  the 
specific  heat  of  a  substance  is  the  amount  of  heat  necessary 
to  raise  one  pound  of  it  through  one  degree  Fahrenheit. 
This  quantity  must  obviously  be  diflferent  for  a  gas  which  is 
free  to  expand  and  overcome  the  work  represented  by  Ry 
from  the  quantity  which  the  gas  takes  when  such  work  is  not 
done  upon  outer  resistances.  Gases  therefore  have  two  spe- 
-cific  heats:  the  specific  heat  at  constant  pressure,  which  may 
be  represented  by  Cpy  and  the  specific  heat  at  constant  vol- 
ume, represented  by  C^.  The  former  is  always  the  larger, 
since 

if 

^"^     •■"  778* 

For  air  Regnault's  experiments  give  for  C/ 0.2375;  ^^^ 
^,  o.  1691 ;  whence 

C-  1691  -  '•4°«- 

In  any  case  where  a  gas  is  heated  from  a  temperature 
absolute  7^  to  another  higher  absolute  temperature  T^  under 
a  constant  pressure,  the  work  done  will  be  that  of  overcoming 
the  pressure  through  a  space  represented  by  the  difference 
between  the  volume  v^  at  the  temperature  T^  and  the  volume 
7/,  which  corresponds  to  the  temperature  7",.  Expressing 
this  in  symbols,  the  heat  taken  in  will  be,  per  pound  of  gas, 

and  the  work  done  will  be 

p{y^  —  v,\  which  must  equal  ^(7;  —  T,). 


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1 8 1  HEAT  AND   HEAT-ENGINES, 

The  internal  energy  in  the  gas  must  be  the  net  difference 
between  these  two  quantities,  or 

(c;-i?)(7;-r,). 

When,  on  the  other  hand,  the  same  weight  of  gas  (one  pound) 
was  heated  at  constant  volume  from  7",  to  7",,  it  must  be  true 
that  the  heat  taken  in  is  expressed  by 

since  no  external  work  is  done,  and  the  whole  applied  heat 
energy  goes  to  store  up  internal  energy.  But  the  same 
amount  of  heat  energy  was  applied  in  the  two  cases;  so  that 

C;(7;  -  T;)  should  equal  {Cp  —  R){T^  —  7;), 
or 

C,  =  C,-R, 

as  has  just  been  shown  above. 

It  may  therefore  be  stated  that  the  expression  CX  ^%  ~  T',) 
expresses  or  measures  the  change  of  internal  energy  in  a  unit 
weight  of  gas  in  changing  its  temperature  from  7)  to  T^  in 
any  manner,  no  matter  how  the  volume  or  pressure  may  vary 
during  the  process.  C^,  has  been  called  the  real  specific  heat, 
and  Cp  the  apparent  specific  heat. 

117.  Joule's  Law« — A  law  determined  experimentally  by 
Joule,  involving  the  foregoing  determinations  and  extending 
them,  may  be  stated  as  follows:  When  a  gas  expands  without 
doing  work  and  without  taking  in  or  giving  out  heat  {and 
therefore  without  changing  its  stock  of  internal  energy)^  its 
temperature  does  not  change.  This  was  proved  by  immersing 
two  closed  vessels  in  a  vessel  of  water.  They  were  connected 
by  a  tube  with  a  cock  in  it.  One  was  empty,  and  in  the 
other  was  the  gas  at  a  considerable  tension  by  compression. 
When  the  cock  was  opened,  the  gas  expanded  and  equalized 
its  pressure  in  the  two  vessels,  but  did  no  external  work.  The 
water  surrounding  the  vessels  underwent  no  change  in  tem- 
perature, but  the  cooling  upon  expansion  was  offset  by  the 


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EFFECT  OF  HEATS    UPON  HEAT-CARRIERS,  1 85 

warming  effect  in  the  other  vessel.  Hence  it  was  inferred 
that  the  gas  had  neither  gained  nor  lost  heat,  and,  since  it 
had  done  no  work,  the  intrinsic  energy  was  the  same  at  the 
end  as  at  the  beginning,  although  both  pressure  and  volume 
had  undergone  changes.  Hence  the  conclusion  that  the  in- 
trinsic energy  of  a  given  weight  of  gas  depends  on  its  tem- 
perature only,  and  not  on  its  pressure  or  volume;  or,  in 
other  words,  a  change  of  pressure  and  volume  not  associated 
with  a  change  of  temperature  leaves  the  internal  energy  un- 
altered«  This  has  an  important  significance  in  operating 
with  compressed  air.  Or,  again,  the  same  idea  may  be  ex- 
pressed by  saying  that  the  change  of  internal  energy  is  inde- 
pendent of  the  relation  of  pressure  to  volume  during  a  tem- 
perature change,  but  is  dependent  only  upon  the  amount  of 
such  temperature  change. 

118.  Graphical  Representation  of  the  Thermal  Changes 
in  a  Gas. — Since  the  characteristic  equation  of  a  perfect  gas 
(^pv  =^  RT)  involves  three  factors  which  are  variable  and  one 
constant  factor,  and  of  which  variable  factors  one  can  be 
made  an  arbitrary  to  be  assumed,  it  early  attracted  the  atten- 
tion of  mathematicians  that  this  equation  was  in  the  same 
form  as  that  for  a  curve  upon  a  surface  whose  points  were 
given  by  their  coordinates  or  perpendicular  distances  from 
three  rectangular  axes.  If  one  factor  or  co-ordinate  were 
assumed  arbitrarily,  the  other  two  would  give  the  relation 
between  themselves  on  a  plane  surface,  giving  a  curved  plane 
figure;  while  if  all  three  were  variable  the  curve  would  be 
upon  a  surface  whose  section  at  every  plane  through  it  would 
be  a  curve. 

This  fact  is  of  interest  and  significance  in  the  field  of  spec- 
ulative research,  but  by  far  the  most  usual  cases  are  those  in 
which  one  of  the  variables  is  assumed  to  be  constant  or  to 
undergo  no  change,  while  the  other  two  are  varying  according 
to  the  law  of  their  relation  for  that  particular  gas.  If  the 
temperature,  for  instance,  be  assumed  to  be  kept  up  by  jack- 


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i86 


HEAT  AND   HEAT-ENGINES, 


eting  the  working-cylinder  with  live  steam  or  hot  air,  the 
changes  designated  by  a  properly  drawn  curve  show  the 
changes  in  pressure  which  take  place  as  the  volume  is  in- 
creased or  diminished.  This  gives  the  form  of  diagram  or 
curve  which  bounds  the  ideal  indicator-diagram,  taken  or 
described  by  a  pencil  which  records  pressures  as  vertical  lines, 
while  the  horizontal  lines  described  from  the  engine  cross- 
head  are  proportional  to  the  volume  created  behind  the 
piston  by  its  motion  from  its  dead-centre.  By  a  similar 
process,  the  volume  being  kept  constant  for  a  given  mass  or 
weight  of  gas,  a  curve  can  be  drawn  showing  the  law  of  ob- 
served variation  of  pressure  with  temperature;  or  again,  the 
pressure  being  kept  constant,  the  law  of  variation  of  volume 
with  temperature.  This  is  a  straight  line,  of  course,  whose 
equation  is  z^,  =  2/0  +  at  from  the  Gay-Lussac  law  (§  112). 

These  various  lines  on  one  or  another  of  the  coordinate 
planes  have  received  special  names,  some  of  which  are  as 
follows, 

119.  Lines  of  Constant  or  Equal  Pressure.  Isopiestic 
Lines,  or  Isobars. — When  the  change  of  condition  in  a  gas 
is  a  change  of  its  volume  without  change  in  its  pressure,  and 


r4^^^ 


VOLUMES 

FiG.48. 


It 


I  I 
I  I 


I 
I 


F1G.44. 


the  same  assumption  is  made  as  in  the  foregoing  paragraph, 
that  vertical  ordinates  represent  pressures,  and  horizontal  ab  • 
scissas  represent  volumes,  then  a  horizontal  line  ab  (Fig.  43) 


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EFFECT  OF  HEATS   UPON  HEAT-CARRIERS. 


187 


drawn  at  a  height  above  the  initial  line  of  pressures  at  a  dis- 
tance proportional  to  that  constant  pressure  and  of  a  length 
proportional  to  the  increase  in  volume  (or  decrease)  will 
represent  an  isopiestic  line.  Such  a  line  is  drawn  by  the 
pencil  of  a  steam-engine  indicator  when  the  piston  moves  in 
the  cylinder  and  steam  enters  from  the  boiler  by  evaporation 
of  the  water  within  it  without  drop  of  pressure. 

The  temperature  may  or  it  may  not  change  during  the 
increase  of  volume.  The  diagram  is  silent  on  this  point. 
The  work  done  would  be  obviously 

Work  =  /(z/,  —  t/o)« 

120.  Lines  of  Constant  or  Equal  Volume.  Isometric 
Lines. — When  the  pressure  in  the  cylinder  is  increasing  by 
addition  of  heat  or  pressure,  while  the  volume  occupied  by 
the  gas  is  not  altered,  a  vertical  line  will  represent  such 
changes  of  pressure  under  the  same  suppositions  as  above. 
This  is  the  line  traced  by  the  -pencil  of  the  indicator  at  the 
dead-centre  of  the  piston-stroke  when  the  valve  has  opened 
to  admit  steam  behind  the  piston,  but  no  motion  has  occurred 
to  generate  a  volume  in  the  cylinder  to  be  filled.  Since 
there  is  no  volume  swept  through  by  the  pressure,  the  work 
is  zero  (Fig.  44). 

121.  Lines  of  Constant  or  Equal  Temperature.  Iso- 
thermal Lines. — By  the  use  of 
special  appliances  (steam-jacket, 
hot-air  jacket,  and  the  like)  it 
is  possible  to  supply  to  the 
weight  or  mass  of  gas  en- 
closed in  a  working-cylinder  the  ' 
amount  of  heat  which  it  is  ex- 
pending in  the  form  of  work  both 
upon  its  own  molecules  in  expand- 
ing, and  the  doing  of  the  ex- 
ternal work.  In  the  case  of  a  per- 
manent gas  acting   in  this  way  the  pressure  will  fall  as  the 


•-T-— ^^ 


FIG.45. 


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1 88  HEAT  AND    HEAT-ENGINES. 

volume  increases  (Fig.  45),  and  in  simple  and  inverse  ratio 
to  such  increase  because 

^-~  =     7*  -  —  R  r^  2,  constant, 

and  the  final  temperature  T^  was  the  same  as  the  initial  7", , 
by  the  hypothesis.  In  other  words,  the  external  work  has 
received  all  the  heat  supplied  to  the  working-gas  from  out- 
side, and  the  intrinsic  energy  of  the  gas  has  remained  con* 
stant,  or  undiminished  by  the  doing  of  any  work. 

On  the  other  hand,  for  a  mixture  of  a  liquid  and  its  vapor, 
as  in  a  steam-boiler,  in  which  the  temperature  is  kept  con- 
stant by  a  continuous  supply  of  heat  from  a  fuel  or  a  fire,  the 
pressure  of  the  combination  of  liquid  and  vapor  remains  con- 
stant ;  hence  the  isothermal  for  such  a  case  will  be  a  straight 
line,  like  the  isobar  or  isopiestic  line  of  Fig.  43.  This  is  the 
condition  in  the  admission  line  and  the  back-pressure  lines 
of  the  indicator-diagram. 

122.  Isodynamic  or  Iso-energic  Lines. — This  name  is 
applied  to  lines  of  a  thermal  diagram  representing  changes 
during  which  the  intrinsic  energy  remains  unaltered;  that  is, 
all  the  heat  received  is  transformed  into  external  work,  and 
produces  no  change  in  the  carrier  during  the  process.  The 
isothermal  for  a  gas  as  above  is  also  an  isodynamic  line,  by 
definition. 

123,  Adiabatic  Lines. — When  the  gas  which  is  working 
by  expansion  within  a  cylinder  overcomes  the  external  resist- 
ance through  a  path,  and  is  yet  so  contained  within  that  cyl- 
inder that  it  can  receive  no  heat  from  an  outside  source,  it  is 
apparent  that  in  such  expanding  it  should  become  cooled  by 
the  giving  up  of  some  of  its  intrinsic  energy.  The  cylinder 
may  be  supposed  to  be  absolutely  non-conducting;  hence  no 
heat  is  transferred  to  or  from  the  working-medium — which 
was  supposed  to  happen  in  the  isothermal  working.  Rankinc 
gave   the   name  adiabatic  to   this  change  of  heat   condition 


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EFFECT  OF  HEATS   UPON  HEAT^CARRIERS, 


189 


1 
1 
1 

.-*>C 

V 

1 
1 

.-ur> 

X 

^ 

-H' 

.  1 

1 

1 

* 

„, 

* 

n: 

^ 

0 

V 

{from  a,  not,  and  diabaineiny  to  pass  through) ;  and  adiabatic 
lines  are  those  which  represent  the  relation  of  volume  to 
pressure  during  changes  which  occur  without  transmission  of 
heat,  as  such,  to  the  medium. 

The  adiabatic  line  is  usually  steeper  than  the  isothermal 
which  has  a  common  point  with  it,  as  can  be  made  apparent 
if  the  gas  has  a  considerable  change  of  volume  with  tem- 
perature. In  Fig.  46,  if  the 
curve  «'  be  an  isothermal  and 
start  at  /  to  represent  the  ex- 
pansion which  takes  place  with 
a  transfer  of  heat  to  it  during 
that  process,  it  will  be  appar- 
ent that  the  curve  aa'  represent- 
ing expansion  without  that 
added  heat  should  have  a  less 
pressure  when  a  final  volume  is 
reached  which  is  the  same   for  Fig.46. 

both.  This  will  be  equally  true  if  the  gas  be  compressed 
from  a  greater  to  a  lesser  volume.  The  isothermal  curve  must 
have  heat  withdrawn  from  the  gas,  thus  diminishing  its 
volume  at  the  end  of  compression ;  adiabatic  compression 
will  leave  in  the  gas  the  heat  which  corresponds  to  the  work 
expended  in  such  compression,  and  for  the  same  final  volume 
the  pressure  will  be  higher.  It  will  be  interesting  in  this 
■connection  to  examine  the  table  for  the  relative  volumes  of 
■compressed  air  under  adiabatic  and  isothermal  compression 
^iven  in  Chapter  XIII,  §  182. 

In  the  analytic  representation  of  an  adiabatic  change  it 
will  no  longer  be  true  that  pv  ^=  RT,  but  the  equation  for 
relation  must  be  written 

/oZ/o"  =  /^"  =  a  constant ; 

in  which  the  exponent  n  represents  either  a  whole  number  or 
a  fraction,  but  is  constant  for  any  one  substance  and  is  to  be 


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1 90  HEAT  AND   HEAT-ENGINES. 

experimentally  determined.  The  condition  of  true  adiabatic 
expansion  (or  compression)  is  rarely  reached  in  practice, 
because  the  cylinder-walls  of  metal  castings  such  as  are  usual 
must  conduct  heat  in  or  out  during  the  time  in  which  the  gas 
or  medium  is  changing  its  volume  and  pressure.  Such  a 
curve,  however,  with  its  exponent  experimentally  determined 
is  probably  more  nearly  reached  in  the  majority  of  cases  than 
the  curve  of  the  isothermal  change  in  which  n  is  unity. 

124.  Isentropic  Lines.  Entropy. — It  would  be  aside 
from  the  present  purpose  to  review  in  detail  the  processes 
used  by  the  great  mathematicians  in  their  masterly  deduc- 
tions which  resulted  in  the  mathematical  quantity  which  they 
have  called  the  **  thermodynamic  function"  (Rankine)  or 
the  '*  entropy  "  (Clausius).  In  brief  their  reasoning  may  be 
summarized  by  stating  that  the  addition  of  heat  to  a  body  is 
rendered  evident  by  changes  in  pressure  and  volume.  These 
simultaneous  changes  of  infinitesimal  extent  give  rise  to  an 
equation  of  differential  form  which  expresses  the  relation, 
between  the  ordinates  and  abscissae  for  a  given  state,  and 
which  it  is  desired  to  integrate  by  the  methods  of  the  calcu- 
lus so  as  to  express  the  law  of  change  between  certain  finite 
limits.  When  the  equation  involves  unknown  functions  of 
the  variable  volume  and  pressure,  and  is  in  a  general  form^ 
the  expedient  has  been  used  of  introducing  an  integrating 
factor.  If  this  factor  is  made  itself  a  function  of  the  pressure  ' 
and  volume,  the  differential  equation  for  a  small  increase  in 
heat  H  becomes 

in  which  y  is  the  reciprocal  of  the  integrating  factor  and  ^x 
is  what  the  differential  equation  becomes  when  the  equation 
is  thus  made  integrable.  Thence  the  investigation  is  con- 
cerned with  the  labor  of  finding  out  which  of  the 
functions  of  pressure  and  volume  it  is  most  useful  to 
assign  to  the   factor  y.      Subsequent    research   shows  it  to 


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EFFECT  OF  HEATS   UPON  HEAT-CARRIERS,  IQt 

be  the  absolute  temperature,  deduced  from  Camot's  prin- 
ciple (§  213),  and  therefore 

^^ 
This  is  usually  written  by  substituting  0  for  x^ 

whence 

6H=  Td4>. 

This  IS  evidently  a  most  elementary  expression  for  an  area^ 
and  is  to  be  used  in  that  form  hereafter  in  this  treatise. 

This  factor  <t>  was  first  segregated  mathematically  by 
Clausius,  and  received  from  him  its  accepted  name,  entropy — 
from  the  Greek  words  en  and  tropin  meaning  a  * '  turning 
into**  or  a  transformation.  Its  symbol  in  all  languages  is 
the  Greek  letter  0.  While  it  is  of  signal  importance  in  heat- 
engine  discussions,  it  is  impracticable  to  form  a  defensible 
conception  of  the  entropy  as  a  property  of  heat  media, 
since  it  does  not  reveal  itself  to  the  senses  nor  to  usual  in- 
struments of  observation.  A  most  helpful  illustration  or 
analogue  has  been  elaborated  by  Zeuner,  Reeve,  and  others, 
by  the  suggestion  that  the  energy  resident  in  a  pound  of  water 
to  be  used  upon  a  water-motor  is  the  product  of  the  available 
height  or  head  above  the  motor,  multiplied  by  the  attraction 
of  gravitation  upon  the  mass  of  the  water.  .  The  head  corre- 
sponds to  the  temperature  in  heat-engines,  and  is  the  measure 
of  the  availability  of  the  medium  when  our  lower  temperature 
level  is  fixed;  the  attraction  of  gravitation  corresponds  to- 
the  entropy  of  the  heat  medium,  which  has  been  called  its 
**  heat  weight."    We  know  as  little  about  gravitation  outside 


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192  HEAT  AND   HEAT-ENGINES. 

of  its  phenomena  and  laws  as  we  know  about  entropy,  but  this 
does  not  interfere  with  every-day  applications  and  uses. 

It  is  customary  to  take  the  value  for  the  entropy  factor 
as  the  difference  between  the  value  for  the  final  stage  and 
the  initial  stage  of  the  expansion,  each  counted  from  freez- 
ing-point usually.  This  gives  a  finite  value  to  be  used  as  a 
factor,  by  methods  to  be  discussed  hereafter  in  more  detail 
in  Chapter  XIV.  For  the  present  it  will  suffice  to  say  that 
when  heat  is  added  to  a  permanent  gas  such  as  air, 


Entropy  =     /  -y,-  =  C  hyp.  log  -~, 


t: 


which  becomes  equal  to  R  hyp.  log  r  when  r  is  the  ratio 
between  the  initial  and  final  volumes  or  pressures  or  tem- 
peratures of  the  gas  doing  work  by  its  expansion.  This  is 
made  evident  from  the  fact  that  the  entire  heat  addition  in 
such  isothermal  expansion  appears  as  the  external  work; 
this  external  work  being  the  expression  RT  hyp.  log  r  (§  i66) 
can  therefore  be  placed  equal  to  T4>. 

In  the  case  of  steam-gas,  working  in  a  cylinder  as  dry 
saturated  steam,  the  heat  addition  is  that  which  has  dis- 
appeared as  latent  heat ;  hence  the  entropy  becomes 

Heat  of  vaporization  of  steam  at  T 

^ =  0  =  entropy, 

exclusive  of  the  heat  addition  made  to  the  liquid  from  which 
the  steam  is  formed.  Hence  for  the  condensable  vapors  the 
total  entropy  is  made  up  of  two  parts.  The  difference 
between  the  entropy  value  of  the  liquid  at  the  beginning  and 
end  of  the  heating  process  will  be 

which  indicates  a  progressive  increase  in  the  heat  condition 


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EFFECT  OF  HEATS    UPON  HEAT-CARRIERS,  1 93 

from  the  lower  temperature  to  the  higher  on  the  hypothesis 
that  C,  the  specific  heat  of  the  liquid  at  constant  volume,  is 
the  same  at  both  ends  of  the  range  represented  by  the  heat- 
ing. (See  columns  ii  of  §  136,  and  fornmlae  at  its  conclu- 
sion.) When  the  vapor  begins  to  form,  a  part  x  has  its  state 
changed  and  receives  the  heat  of  vaporization  r^  or  the 
latent  heat.     The  sum  of  these  is 

for  a  state  corresponding  to  7",,  and  for  a  state  T^ 

Hence  the  difference  will  be 

or 

0,  —  0,  =  -^  —  --^-  +  C^  hyp.  log  Y^ 

tinder  the  foregoing  supposition. 

If  in  the  permanent  gas  the  temperature  has  to  be  raised 
from  a  lower  temperature  2"^,  the  entropy  above  that  at  freez- 
ing will  be  made  up  of  the  heat  to  raise  from  T^  to  7",,  and  in 
addition  that  to  increase  the  pressure  from  that  at  /«  to  that 
at/j.  Hence  the  general  expression  becomes  for  a  heating 
process  not  isothermal 

<t>—<t>^  —  Cp  hyp.  log  —  +  (C;  —  Q  hyp.  log  ^. 

When,  on  the  other  hand,  the  curve  representing  the 
relations  of  pressure  and  volume  is  no  longer  an  isothermal. 


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1  y  I  HE  A  T  AND   HE  A  T- ENGINES. 

but  is  an  adiabatic,  the  condition  must  be  met  that  by 
definition  there  is  no  longer  a  transfer  of  heat  from  without 
the  medium.     Hence  in  the  equation 


the  quantity  ^H  has  become  zero,  so  that  while  T  remains 
finite  the  quantity  S<t>  must  become  zero.  This  means  that 
when  the  volume  and  pressure  change  according  to  the  adia* 
batic  law,  the  change  in  entropy  for  such  changes  is  zero,  or 
the  entropy  is  constant  for  such  changes  of  condition.  Im- 
portant deductions  from  this  truth  will  be  seen  to  follow 
hereafter  (Chapter  XIV),  but  for  the  present  it  may  be 
observed  that  a  curve  representing  an  adiabatic  variation  of 
pressure  and  volume  may  be  called  a  curve  of  constant 
entropy,  or  an  isentropic  line. 

An  interesting  deduction  can  be  made  from  the  foregoing 
facts.  If  two  isothermal  lines  represent  two  differing  states 
of  a  heat  medium  at  different  times,  the  change  which  has 
made  them  differ  is  a  change  in  temperature.  Each  curve 
represents  by  itself  all  variations  of  pressure  and  volume  at  a 
constant  temperature,  and  the  substance  can  therefore  pass 
from  one  curve  to  the  other  curve  only  by  having  a  temper- 
ature change  brought  in  sufficient  to  make  thf  transfer.  If, 
on  the  other  hand,  two  adiabatic  lines  represent  two  paths 
of  variation  of  pressure  with  volume,  with  constant  entropy 
attaching  to  each,  but  variable  temperature,  the  heat-medium 
can  only  pass  from  being  operated  on  one  adiabatic  to  being 
operated  on  the  other  by  such  a  heat-energy  change  as  shall 
change  the  entropy  of  the  medium.  Temperature  addition 
will  only  increase  the  relation  of  the  pressure  to  the  volume  on 
either  curve,  but  will  not  change  the  path  of  the  process  from 
one  adiabatic  to  the  other.  Representing  this  graphically: 
if  ii  and  i'i'  be  two   isothermals  (Fig.  47)  representing  the 


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EFFECT  OF  HEA  TS    UPON  HEA  T-CARRIERS. 


195 


relations  of  pressure  and  volume  of  a  gas  in  a  cylinder  each 
corresponding  to  its  proper  temperature  2"  and  T' y  it  follows 
from  what  precedes  that  to  have  the  product  /V  belonging 
to  T'  become  the  product /t/  belonging  to  7",  the  property 
of  the  gas  to  be  altered  is  its  temperature.  If,  however,  the 
curves  aa  and  a' a!  in  Fig.  48  are  each  an  adiabatic,  whose 


q  V 

riG.47. 


riQ«48. 


constant  entropy  is  respectively  0  and  0',  the  relation  /z/*" 
for  one  curve  can  only  become  the  relation  /V"  proper  for 
the  other  by  a  change  in  entropy  which  will  correspond  to 
the  difference  in  that  factor  for  the  two  states  of  the  heat 
medium  in  question. 

125.  Plotting  of  Isothermal  and  Adiabatic  Lines. — The 
graphical  representation  of  the  variation  of  pressure  and 
volume  isothermally  is  quite  simple  when  the  temperature  is 
known  or  assumed  and  the  value  for  R  for  the  particular  gas 
in  question  has  been  computed  from  known  data.  For» 
since 

it  appears  that  the  curve  of  the  isothermal  is  that  of  an  equi- 
lateral   hyperbola    referred    to  the   coordinate  axes  of  zero 


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196 


HEAT  AND    HEAT-ENGINES. 


pressure  and  zero  volume  as  asymptotes.  The  easiest  way- 
is  to  calculate  the  product  /z/,  and  then  to  find  the  coordi- 
nates of  the  vertex  of  the  hyperbola,  when  /  =  z/,  by  extract- 
ing the  square  root  of  that  product.  When  the  vertex  has 
been  found  for  the  assumed  value  of  T^  other  points  are 
found  by  making  2v  =  i/,  ^v  =  \p^  and  so  on  (Fig.  49),  or 
the  curve  may  be  drawn  by  any  reliable  hyperbolograph. 

A  method  much  used  to  draw  the  hyperbola  for  the  curve 
of  expansion  on  ^pv  diagram  where  the  vertex  does  not  come 
at  an  observed  point  is  required  for  indicator-diagrams.  Any 
point  on  the  actual  curve  having  been  located,  as  B  (Fig.  50), 


FzG.49. 


FiG.sa 


and  the  two  coordinate  axes  of  zero  volume  (9/^  and  zero  pres- 
sure O  V  having  been  established,  a  horizontal  line  is  drawn  at 
a  convenient  pressure  height  above  the  greatest  record  of  the 
diagram.  It  may  be  at  boiler-pressure,  but  this  is  not  essen- 
tial. From  the  point  B  draw  horizontal  and  vertical  con- 
struction lines,  and  from  the  point  A  draw  a  diagonal  to  the 
point  O,  the  origin  of  coordinates;  where  the  horizontal 
through  B  intersects  the  diagonal,  or  at  the  point  E^  erect  a 
perpendicular  EF,  and  complete  the  rectangle  ABEF  hy  this 
means.  Then  lines  drawn  from  O  and  cutting  EF  and  meet- 
ing -^-Fwill  determine  other  rectangles,  and  the  intersections 
of  the  lines  /»  and  z/„  /,  and  z/,  will  give  in  each  case  a  point 


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EFFECT   OF  HEATS    UPON  HEAT-CARRIERS,  I97 

on  the  curve.  In  indicator-diagram  work  the  point  B  is 
usually  taken  at  the  point  of  release  of  steam  at  the  end  of 
the  expansion,  because  at  this  point  it  is  usually  safe  to 
assume  that  the  steam  is  dry  or  vaporization  is  complete. 
The  point  C  at  which  cut-off  takes  place  or  expansion  begins 
can  also  be  taken,  although  this  is  less  certain  and  accurate, 
and  necessarily  locates  a  different  hyperbola. 

For  the  drawing  of  the  adiabatic  curve,  the  calculation 
must  be  made  for  the  initial  state  with  the  relation  of  pres- 
sure and  volume  represented  hy  p^v^^  in  which  the  exponent  n 
is  either  known  or  assumed.     Then  by  the  relations 

/o^#"  =  /i^i    =  A^«*  =  ^  constant 

points  on  the  adiabatic  curve  are  found.  It  will  be  brought 
out  in  a  following  chapter  that  for  air  n  is  usually  1.4 1,  while 
for  steam  it  is  variously  held  to  be  i.ii  or  1.06 


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CHAPTER    XL 

VAPORS  AS   HEAT-CARRIERS.    STEAM. 

130.  Introductory. — It  has  been  already  said  in  Chapter 
IX  that  condensable  vapors  could  also  be  used  as  heat- 
carriers,  or  those  for  which  the  expression  pv  =  RT  vrais  not 
true  in  all  states.  In  the  choice  of  a  vapor  medium  there  is 
room  for  a  wider  choice  than  among  the  permanent  gases. 
The  latter  are  so  nearly  alike  in  their  physical  qualities  that 
the  selection  of  the  cheapest,  most  accessible,  most  innocuous, 
and  most  inexhaustible  of  the  gases,  which  are  the  condi- 
tions which  attach  to  air,  have  precluded  any  serious  attempts 
to  use  any  of  the  other  gases.  But  with  the  vapors  there  is 
at  once  presented  a  wide  variation  in  volatility,  specific  heat, 
vapor  density,  condensability,  and  behavior  while  doing  the 
work  of  expansion  which  has  attracted  experiment  and  inven- 
tion to  attempt  to  utilize  them.  The  vapor  of  water  has  the 
same  convenient  qualities  on  its  practical  side  as  are  pos- 
sessed by  air  among  the  gases.  It  is  furthermore  without 
disagreeable  odor,  is  not  inflammable  nor  explosive,  and  has 
the  property  of  carrying  great  heat  in  small  bulk,  and  of 
having  the  highest  temperature  at  the  convenient  limits  of 
pressure  to  be  used  in  generators  and  working-cylinders.  It 
must  be  shown  therefore  by  any  other  vapor  that  it  possesses 
advantages  greater  than  the  losses  incidental  to  the  use  of 
steam  if  it  is  to  seek  to  be  used  as  a  heat-carrier.  In  other 
words,  the  presumption  is  in  favor  of  steam,  and  the  burden 
of  proof  must  lie  with  the  rivals  who  may  seek  to  displace  it 

19^ 


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V  A  pons  AS   HE  A  T-CARRIEKS,     STEAM,  1 99 

{see  Chapter  XXI).  There  are,  however,  ceitain  general 
facts  and  principles  to  be  noted  for  all  condensable  vapors  to 
which  attention  should  be  first  directed  before  discussing  the 
special  properties  of  steam. 

131.  Saturated  Vapor.  Saturated  Steam. — It  should 
be  a  deduction  from  Chapter  IX  that  in  a  vessel  containing  a 
given  weight  of  a  mixture  of  a  vapor  and  the  liquid  from 
which  the  vapor  is  being  given  off  by  the  application  of  heat 
at  any  given  pressure,  it  will  be  impossible  to  change  the 
value  of  the  expression  pv  by  changing  the  value  of/  without 
•changing  the  proportion  of  liquid  and  vapor.  If  /  is  in- 
creased and  the  volume  remain  constant,  some  vapor  will  go 
back  to  liquid;  \i  p  is  diminished,  more  vapor  is  formed. 
Furthermore,  if  heat  is  withdrawn  from  the  mixture,  conden- 
sation of  vapor  to  liquid  occurs;  if  heat  is  added,  vaporiza- 
tion occurs.  In  other  words,  there  is  for  every  vaporizable 
liquid  a  temperature  of  vaporization  (or  a  boiling-point)  cor- 
responding to  every  pressure.  A  vapor  is  said  to  be  a  satu- 
rated vapor  when  it  is  in  that  condition  of  pressure  and  tem- 
perature at  which  exists  this  equilibrium  of  tendency  to 
vaporize  and  to  condense.  In  the  case  of  the  steam  in  a 
boiler  in  which  is  the  water  being  vaporized,  the  steam  is 
saturated.  Instantly,  on  the  withdrawal  of  any  steam  into 
the  cylinder,  its  place  is  supplied  by  fresh  evaporation.  When 
the  throttle-valve  is  closed,  either  the  generation  of  steam 
ceases,  or  if  heat  is  still  flowing  into  the  water,  the  pressure 
at  constant  volume  rises  until  generation  is  made  to  cease  by 
a  new  equilibrium  at  such  higher  pressure.  When  the  steam 
passes  into  a  pipe  at  the  temperature  of  saturation  and  leaves 
the  boiler  to  do  work  in  the  engine,  it  is  called  dry  saturated 
steam.  Strictly,  of  course,  it  is  the  space  which  it  occupies 
which  is  saturated,  or  which  is  filled  with  as  much  steam  as 
it  will  hold  as  steam  at  that  temperature.  Any  reduction  of 
temperature  from  radiation  or  other  heat-loss  will  cause 
some  of  the  dry  steam-gas  to  fall  back  to  the  state  of  water, 


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2CX)  HEAT  AND   HEAT-ENGINES, 

probably  in  a  state  of  fine  division  or  mist,  or  perhaps  in  the 
form  of  liquid  hot  water.  Such  steam  is  called  wet  steam ; 
and  wet  is  not  synonymous  with  saturated.  Heat  applied  to 
it  to  dry  it  by  evaporating  out  the  condensed  water  will  cause 
it  to  become  saturated  once  more. 

When  dry  saturated  steam  enters  its  working-cylinder, 
and  after  cut-off  begins  to  work,  increasing  the  volume  it  occu- 
pies and  lowering  its  pressure  by  adiabatic  expansion,  the 
drop  in  temperature  equivalent  to  the  work  done  outside 
will  cause  a  similar  condensation  of  some  steani  unless  the 
necessary  heat  is  supplied  from  the  cylinder-walls  by  jacket 
or  otherwise  to  prevent  a  drop  below  the  condition  of  satura- 
tion. The  latent  heat  of  vaporization  must,  however,  be 
given  out  before  this  condensation  occurs,  and  as  this  is  a 
considerable  proportion  of  the  total  heat  (§  138),  the  heat  of 
the  steam  is  strongly  effective  for  doing  work.  By  careful, 
adjustment  of  the  supply  of  heat  to  the  jackets  of  a  steam- 
engine,  the  curve  of  pressure  and  volume  ratio  can  be  made 
to  be  that  of  the  saturation  curve  of  steam,  and  the  steam  at 
the  period  of  release  from  the  cylinder  will  be  dry  saturated 
steam.     It  would  otherwise  be  wet. 

This  matter  will  be  further  considered  under  paragraphs 
treating  of  cylinder-condensation  and  re-evaporation,  and  the 
negative  specific  heat  of  steam. 

132.  Superheated  Vapor.  Superheated  Steam. — When 
steam  or  other  vapor  is  raised  by  the  application  of  addi- 
tional heat  to  a  temperature  above  that  which  belongs  to 
Its  equilibrium  of  temperature  and  pressure  when  in  con- 
tact with  its  liquid,  it  is  called  superheated.  It  is  possible  to 
superheat  steam  in  contact  with  its  liquid  by  reason  of  the 
slow  transfer  of  heat  through  a  large  volume  of  gas,  but  as- 
soon  as  convection  or  circulation  occurs  some  of  the  liquid 
will  be  vaporized,  and  the  state  of  saturation  will  be  agaia 
established.  Hence,  as  a  rule,  superheating  is  effected  upon 
steam-gas  which  is  isolated  from  its  liquid,  and  in  some  other 


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VAPORS  AS  HEAT-CARRIERS.     STEAM.  20t 

chamber  or  vessel.  The  effect  of  superheating  is  to  make  it 
possible  for  some  heat  to  be  withdrawn  from  the  superheated 
vapor  before  it  passes  to  the  saturation  stage,  after  which 
further  removal  of  heat  results  in  condensation.  This  makes 
it  a  convenient  expedient  to  diminish  probable  losses  from 
the  cylinder-condensation,  hereafter  to  be  discussed,  since  a 
range  or  margin  above  saturation-point  must  first  be  traversed 
before  the  inconveniences  of  active  change  to  liquid  set  in. 

Superheating  occurs  in  effect  when  steam  or  other  vapor 
passes  through  a  narrow  opening  or  a  constriction  of  passage 
such  as  is  caused  by  a  partly-closed  valve.  On  the  one  side 
is  the  higher  potential  of  greater  pressure,  while  upon  the 
lower  side  is  a  volume  too  large  to  be  filled  as  rapidly  as  it  is 
created  if  the  flow  must  be  through  the  constricted  passage. 
Hence  a  lower  pressure  prevails  beyond  the  constriction,  and 
yet  no  heat  has  been  abstracted  except  that  required  to  do 
the  work  represented  by  the  friction  of  the  vapor  through  the 
orifice.  Hence  the  practical  effect  is  to  produce  a  steam  in 
the  space  beyond  the  valve  which  is  hotter  than  the  temper- 
ature belonging  to  the  pressure  there — or  which  is,  by  defini- 
tion, superheated;  and  it  will  behave  as  a  superheated  vapor 
in  an  engine-cylinder.  The  action  or  effect  here  spoken  of  is 
one  of  the  advantages  inhering  in  the  throttling  method  of 
governing  by  means  of  a  valve  in  the  steam-pipe,  and  lies  at 
the  basis  of  a  form  of  apparatus  for  measuring  the  amount  of 
moisture  present  in  a  flowing  current  of  wet  steam  in  a  pipe. 

Superheated  vapor  may  be  made  so  hot  that  within  the 
limits  of  its  use  in  any  machine  it  may  behave  as  a  permanent 
gas,  and  undergo  no  change  of  state.  It  may  then  be  called 
steam-gas  rather  than  a  vapor.  It  loses  some  of  its  advan- 
tages as  a  heat-carrier  when  it  is  used  as  a  permanent  gas,  and 
some  practical  difficulties  result  from  its  inconveniently  high 
temperature. 

133.  Relations  of  Pressure  and  Temperature  in  Satu- 
rated Steam-vapor  (Regnault). — The  relation  between  pres* 


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202  HEAT  AND  HEAT-ENGINES. 

sure  volume  and  temperature  for  saturated  steam  and  other 
vapors  were  investigated  by  the  physicist  Regnault  at  Paris 
with  such  thorough  exhaustiveness  that  his  results  are  the 
standards  for  all  engineers.  These  researches  are  to  be  found 
in  vol.  XXVI  of  the  *'  M^moiresdeTInstitut  de  France/*  1847. 
His  method  was  to  take  the  temperature  of  the  boiling-point 
under  varying  pressures,  the  pressure  being  observed  by  a 
mercury-column,  and  the  temperatures  by  mercury-thermom- 
eter. After  corrections  were  applied  and  the  readings  re- 
duced to  the  air-thermometer,  the  best  results  were  plotted, 
a  curve  drawn  through  them,  and  an  equation  worked  out 
whereby  the  relations  desired  could  be  calculated.  His  equa- 
tion is  of  the  form 

log  /  =  ^  +  ba""  -f  ^/?", 

in  which/  is  the  pressure  in  millimeters  of  mercury,  and  n  = 
/  — .  /,,  or  is  the  range  between  the  temperature  at  which  the 
pressure  p  prevails  and  the  lowest  temperature  at  which  the 
formula  is  true  with  the  given  values  for  the  constants  a^  b, 
and  c.  Thus  at  a  latitude  of  45°  the  values  for  steam 
between  32°  and  212°  F.  and  in  pounds  per  square  inch 

a  =  3.025908; 
log  b  =  0.61 17400; 
log  c  =  8.13204  —  10; 
log  a  =  9.998181015  —  10; 
log/?=  0.0038134; 

«  =  ^—  32; 

while  between  212°  and  428°  F.  the  quantities  will  be 

a  =  3.743976; 
log  b  =  0.412002 1 ; 
log  c  =  7.74168  ■—  10; 
log  a  =  9.99856183 1  —  10; 
log/?  =  0.0042454; 

«  =  /  —  212. 


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VAPOKS  AS  HEAT^CAKRIERS.     STEAM, 


203 


Fig.  5 1  presents  to  the  eye  a  graphical  representation  on  a 
small  scale  of  the  relations  between  temperature  and  pressure 
from  the  Regnault  experiments,  below  15  pounds  pressure, 
and  Fig,  97  hereafter  will  carry  the  relation  up  to  150  pounds. 


LBS.  PRESSURE  PER  SQ.  IN. 

5     U     13     li     11     10      9       8       -i 

A      .1 

i 

3      ~      1      n    ..,,, 

y21J 

'     i     1     ! 

•'10* 

i    1    ■    :    1 

90B» 
800* 
195» 
190« 
185' 
180» 

170* 
l«6^ 
160« 
IM** 

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^ 

1 

!    1    1    !    . 

I 

197.8' 

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r  - 

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1 

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1 

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i 

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1 

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n^'V 

146» 
140« 
136« 
130** 

1   !  '  \,..., 

r 

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1 

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1 

1  1  1  \ 

118«. 

V 

190° 
115» 
110' 
lOS'^ 
100** 

1  1 

\ 

\ 

\ 

_ 

J 

h 

Fi3.   51. 

134.  Rankine  Formula  for  Pressure  of  Saturated  Steam. 

— An  approximate  formula  conforming  very  closely  to  Reg- 
nault's  experiments  was  put  forward  by  Rankine  {Edinburgh 
New  Philosophical  J ournaly  July,  1849),  ^^^  claimed  by  him 
to  be  sufficiently  accurate  between  —  22°  F.  and  446°  F.  It 
is  of  the  form 

log/   =  ^  -y  -   -^i, 


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204 


HE  A  T  AND   HE  A  T-ENGINES, 


in  which  T  is  absolute  temperature  on  the  basis  of  7"=  /°  -|* 
461°. 2,  and  for  pounds  per  square  inch 

A  =  6.1007; 
log^  =  3-43642; 
logC=  5-59873. 

For  pounds  per  square  foot  A  =  8.2591.  The  difference 
between  the  two  authorities  is  given  by  the  comparison  in  the 
following  table : 


Pressure,  in  Pounds  per  Square  Inch. 

Temperature 
Fahrenheit. 

Reffnault, 
at  Latitude  45®. 

Rankine  Formula. 

32 

0.0890 

0.083 

77  • 

0.4555 

0.452 

122 

I . 7789 

1.78 

167 

5-579 

5.58 

212 

14.697 

14.70 

257 

33.711 

33.71 

302 

69.27 

69.21 

347 

129.79 

129.80 

392 

225 . 56 

225.9 

428 

336.26 

336.3 

135.  Other  Formulae  for  Pressure  and  Temperature  of 
Saturated  Steam. — Many  other  formulae  have  been  worked 
out  for  the  temperature  and  pressure  of  steam,  having  a  cer- 
tain accuracy  and  value  within  their  several  ranges.  Mallet's,. 
ranging  between  1 5  and  60  pounds  pressure,  is 


\III.78/ 


78^ 

with    centigrade    degrees,   and   in   pounds  per  square  inch. 
Tredgold  uses  175  as  the  denominator  instead  of  11 1.78. 

Dulong  and  Arago  give  for  pressures  above  60  pounds  per 
square  inch,  and  centigrade  degrees 

/  =  (0.4873  +  0.012244/)*. 


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VAPORS  AS  HEAT-CARRIERS,     STEAM.  205 

Zeuner*s  formula  is 

in  which  by  substitution  is  found 

/>v  =  50.933  T'-  192. 50A 

in  which  /  is  in  kilograms  per  square   meter  and  v  is  the 
specific  volume  in  kilograms  per  cubic  meter. 
De  Volson  Wood  proposed 

18500 


pv  =  96.95  r- 


^2: 


in  which  p  is  in  pounds  per  square  foot,  and  v  the  cubic  feet 
for  one  pound.  For  pounds  per  square  inch,  and  v  still  in 
cubic  feet  per  pound, 

128.5 


pv  =  0.6732  r  — 


2/^'' 


Other  formulae  are  by  Dalton,  Roche,  Coriolis,  and  others. 

136.  Steam  Tables. — Using  the  accepted  formulae  and 
•experiments  of  Regnault,  Zeuner  Rankine  and  others  have 
•computed  tables  giving  the  pressure  corresponding  to  any 
temperature  or  the  temperature  corresponding  to  any  pres- 
sure in  common  use.  An  abstract  of  such  a  table  follows, 
giving  also  certain  other  data  concerning  steam  which  will  be 
found  useful  and  convenient.  The  pressure  is  given  in  even 
figures,  as  counted  from  a  vacuum,  and  the  corresponding 
temperature  is  therefore  fractional.  Following  the  compu- 
tations by  Prof.  C.  H.  Peabody  (the  accepted  authority  in 
American  practice),  the  value  of  the  Fahrenheit  freezing-point 
is  taken  as  492''.7.  The  reader  and  student  is  referred  to 
Peabody's  complete  tables  for  further  and  fuller  tabular  infor- 
mation. The  data  for  pressures  above  300  pounds  absolute 
are  not  reliable  wherever  the  specific  heat  has  entered  as  a 


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206 


HEAT  AND   HEAT-ENGINES. 


Pressure 
in  Pounds 

Gauge. 

'- 

\r% 

CO  CO  CO  coco 

CO  CO 

H 
1 

h  -r  CO  «  t-i 

'  T  T  T  T 

0    0^  ^  CO  W 

7 1  1  1  1 

M     0     0     0     M 

1        1      ■+i-f- 

c«  CO  Tf  m  0 

:?8 

a 

»n  m  o^ 

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<  moo  N  CO 

1  0  c*  0*00 

«  0  P«  0  r^ 
M  M  M  CO  to 
0  •I'oo  rN.o 
CO  QO  r^  r^  r>. 

QO  tn  r>«  rN.  M 
00  «  r^o  M 
in  m  «^  Tf  't 
r^  t>.  r^  t>.  t>. 

M  CO  a^  "f  o^ 

in  M  0  «  CO 
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rN.  rn  f>,  i>H  r^ 

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M      M 

= 

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^  CO  f>.  0 

>     •-•     M     Cl 

CO  CO  N    «  0 

0  »r>  ^  M  r^ 
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CI    04    CI    M    C4 

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CO  CO  CO  CO  CO 

CO  e«  t  CO  0 

N  CO    W  0    CO 

«  CI  CO  CO  m 
CO  CO  CO  CO  CO 

m  M 

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0  00 

CO  CO 

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of 

External 

Work. 

778 

2 

u 

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00  r^O  0  ^ 

r>.  0   ^  mco 

0  «  -to  u^ 

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CO  CO  CO  CO   Tf 

r^  r^  !■>.  rN.  r^ 

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Heat 
Equiv. 

of 
Internal 
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o> 

1-   0^  m 

TfM   1-co  »o 

^  m  coo   0 

0  CO  w  0  in 

00 

%%\l% 

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0*  0*  0\  0^  Ov 
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!>.  m  CO  t-i  n 

00  00  00  00  i>> 
CO  00  00  CO  00 

coo 
0  m 

00  CO 

Heat  of 
Vaporiza- 
tion. 

B.  T.  U. 

eo 

r 

s  CO  0    M    CO 

c*  CO  0  00  a* 

•H  m  i>>  M  00 

0  ino  0   0 

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4  QO  coo  »n 

0000 

rN.  Q  0^  »n  c« 
Q  Q  i^  r^  r^ 

0  0  o>  0*  0^ 

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^  Q\  Q\  Q\  Q\ 

Q  00  0   Tf  0 
0  m  m  in  Tf 
0^  0^  0^  0^  0^ 

CO    d 
to  CO 

0  0     1 

Heat  of 
Liquid. 

rs 

< 

l"o   ^OO 

^  r^  0*  »r>  f^ 

0    CO  O^CO    M 

COCO  M    O*  M 

Tf   1-           i 

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Ttoo  0  11  m 
t>«  i>»co  00  00 

M     M     l-l     M     M 

CO    O^  5'o^O 

a»oo 
«  d 
d  d 

1.^     M     M     M     d 

Total 
Heat. 

A 

(O 

r 

8 

■«  CO  M  m  1^ 

0  in  0»  coo 

r>  00  0  0*  0^ 

O»co  t>.  m  M 

coo 

)     H4     M     M     1-4 

00     M     0     C<     CO 
N    CO  rf  Tf  -^ 

l-l     tH     H4     M     11 

^  mo  0  fN. 

'«t   Tf   Tf   Tf   -t 

00  a>  0  M  m 
Tf  ^  m  m  m 

M     M     M     Hi     l-< 

00     M 
M     H 



Weight  of 
I  cu.  ft. 

in 
Pounds. 

■A 

>  00  o^o  ^ 
■>  in  o^r*.  Tf 

>  iM  N  inco 

5  8  8  8  8 

2 1.1  IB 

ssss? 

m  Q  ^0  t>. 
m  0   0»  N  0 

coo  rN.00  0 

1^  t^O    CO  0^      0  00 

0  1-O0  d  J>    0  0 
CO  m  r^  0  M      CO  m 

Volume  of 

1  pound 

in 

Cu.  Feet. 

^ 

)  vO  0    Tf 

*^    M  0  CO    Tf 

CO  c«  M  00  M 

N  ovci  m  0 
CO  t>.  Tf  M  m 

d   0   Q  ^   CO 
d    0    C>  0^  "H 

C»in 
m  »>i 

>  -t  coco 
^  CO  rN.  i-i 

>  CO    M     >-l 

Q  cooo  Tf  e« 
o>  rN.  CO  CO  CO 

ovr^o  0  1- 

€4    CI    M    C«    C« 

cOd   0    C^O 

d     d     d     i-l     M 

CO   M 

Tempera- 
ture, 
Degrees 
Absolute. 

« 

<.  i>HvO    0^  CO 

?:?s;^s 

OM>«  0   CO  c« 
m  w  r-  r^  0 

-^t  0  't  m  Tf 

M  M  0^0  r^ 

OQO 

1  0  c<  0  M 

^  -"l-O  00    Q 
h  »n  »n  vnO 

CO  to  cooo  « 
►-.   CI  in  invo 

00000 

0  0  N  cor^ 
0  t^  fN.  r^  r* 

00000 

0  CO  mco  Q 

00  00  CO  CO  0 
0  0  0  0  r^ 

0    0* 

Tempera- 
ture, 
Degrees 
Fahr. 

e^ 

«  c 

co« 

0  r^  « 
a*e<  0 

o^  Ttmoo  oo 

0    CO  M    i-N.  O^ 

CM^  0    CO  CI 
00   «n  0   0   CO 

?§.?S5? 

{J? 

'222 

CO  c*  CO  r*.  M 

too  0*  a^  0 

in  <>  «   COO 
C<    d    CI    C<    C4 

0»  W  m  t>.  0 

l-l     d     d     d     Tf 

d   d  d   d   d 

as 

d  d 

Pressure 

above 

Vacuum 

in  Pounds 

per 

Sq.  Inch. 

- 

10 

00 

0  *n 

d  d  M  «  CO 

^m  0  M  N 

CO  t  4  mo 

r*.oo  a*  0  m 

CO  to 

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I'APORS  AS  NEAT-CAICKJEKS.     STEAM. 


207 


S^ 


20. 


*:  o 


> 


C**  C'i  C**  fi  c*^ 

t«^  C*4  C*4  t«^  C*4 

cn  «n  t^  en  t«^ 

cn  tn  cn  cn  cn 

en  c^ 

0  ««  C  ^  « 

00000 

ac    C^  0   —  M 
0  0  r^  r*  t^ 

1^  f  0  't-  C^ 

0  »'^  -r  f  "^ 

0  0  0  >c  0 

»nQO  »nO    'f 
r>.  ^  >0  »n  '* 

M    r4    _    M    M 

00000 

»nO  0  0  r^ 

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00000 

^oooo 

tn  en 

3  3 

= 

^  0  {>  "  r^ 
w  w   0   C^O 

00    «    -    N 

cn  -r  -t  t  "^ 

t^  w    -fO    fN. 
en  C  0   r^ao 
en  -f  1-  f  -r 
1-  f  -r  -r  ^r 

C^w  M  tm 
c^  ^  M  en  t 
-T  m  m  m  m 
t  f  -r  -r  -r 

1^00  00  '-' 
mo  r^  0  0 
m  m  mm>3 
1-  t  1-  f  -r 

Heat 
F.quiv. 

of 

External 

Work. 

778 

0 

1^  C4  r^  MO 

0  't-  r^oo  C* 

C>0   «  «  « 

en  en  t  t  m 

mo 

0  r^  rN.ao  00 
t^  r^  rN.  r^  I'* 

0  0  C>C>  Ov 
r^  rn  t^  r>.  rN. 

00000 

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00000 

0  0 
CO  00 

Heat 
Equiv. 

of 
Internal 
Work, 

» 

cnoo  I"*.  0*  r>» 

W*  t^   M     -^tO 

0  en  m  0  w 

too  M  moo 

w  m 

0  t  0  f  0 
u->  -r  tn  en  tn 

CO  00  CO  00  OO 

0  w  a»co  r^. 

M    (<•    ^    »    M 

00  CO  QO  OO  CO 

r^O  m  t  t 

00  00   oc   00   TO 

end  «  ^-  0 

Q^  00  00  QO  QO 

t^  «  m  o»  en 

OO  <30 

TIeat  of 

Vapozira- 

lion. 

B.  f.  V. 

- 

0  0   Tfm  tn 

in  M  QO  c«  tn 

O^r^^    0   1- 

t^    M 

r>»  w  rN.  en  c^ 
«   N   i-i    -    5 

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vn  M  CO  ac   r^ 

CS  ^00  00  CO 

0  0  »n  m  f 

OO  CO  oc  oc  CO 

en  en  e^  •-  iH 

cc  00  CO  00  00 

II 

Heat  of 
Liquid. 

■^0  «  en  o» 

«  M  o^QO  rN. 

0  m  t  en  « 

w  0  00  r>.  m 

t  M 

rs 

0  en  c  0  Ht 
en  -t  »n  ino 

d    C«    C4    P4    C4 

rn  M  0  r^co 
0  r^  r^  »^  t^ 

M    C«    C<    M    M 

0  0  M  w  «n 

I>»CO  CO  oc  CO 
C<    M    M    C4    M 

00  00  00  CO  00 

d    M    M    M    d 

QC    C^ 
00   OC 

Total 
Heat. 

« 

Tf  0   0     ^   W 

r^  en  rN.  0  « 

mco  0  p^O 

00  M  xr%>c  00 

1^   en 

en  »r>  r-  c*  -- 

0  0  0  0  r^ 

«  Tt  »nO  0 
r^  r^  r^  r>*  r>. 

0  0  t^  r>.  rN. 
r^  t^  rn  rN.  r^ 

r^cc  QO  00  OO 
r*.  r^  r^  t«»  rn 

0  0 

•rt 

-1. 

-T  r^oo  0^  Q^ 

^   r^oo  Cn  0 

Cs  0    «    N    -1- 

O^co  0  t>.  0^ 
►-  M   en  in  r* 
mo  r^  1-*  rN. 

•H  «  en  mo 

0    N    -TO  CO 

00  CO  CO  QO  CO 

QO  0  •-•  en  t 
0  en  «n  r^  0 

0  c^  00  0 

0  r^ 

0      ►H      «      H.      ►H 

21  i 

en  N  -TO   0 

en  ^  M  M  ^ 

CO  to   (>« 
m  ^  t^o  0 

rfoo  m  d  M 
mco   WOO 
m  -r  -f  en  en 

0  w  m  0  t 

too    N  0    ^ 
N    •-•    N-    0    0 

il 

0  O^oo  rn  1^ 

0  0  m  m  m 

t  T 

Tempera- 
ture, 
Dcfrrees 
Absolute. 

« 

en  0^  u->  0^  ^ 
ao   C  tn  in  c« 

r^  M  00  QO  00 

0  t  0  0  »-• 
r^O   m  en  N 

0   0  «   "t  m 
0  00  r>  m  en 

m  m 

r^  -t  •-•  r^  en 
M  tn  'f  'f  w. 
r^  t^  t^  r^  r^ 

00  enoo  00   0^ 
\n\0  \0  \0  ^ 
rN.  r^  rn  r*  t^ 

0  H^  w  en  t 
rN.  rn  r^  r^  t^ 
rn  t>.  t^  r^  r* 

»n  mo  t>-co 
r^  t^  r^  r^  t^ 

0  ^ 

Tempera- 
ture, 

Decrees 
Fahr. 

en  0^  »n  0>  M 

iM   N  oc  00    ir> 

r^  i-i  CO  00  00 
r^  r^  en  e^  «-i 

0   000  0  m 

0   0  «  t  m 

en  i-i  0  OO  0 

m  m 

t  :i 

rN.  -t  0  0  « 
0  r^co  QO   O^ 

M    C4    C4    C<    M 

w  en  en  en  en 

0  0  M  w  en 
en  en  en  en  en 

t  mo  0  r* 
en  en  en  en  en 

00   0 
en  en 

Pressure 

above 

Vacuum 

in  Pounds 

per 

Sq.  Inch. 

0    »n  0    »0  0 

Tf  Tf  »n  mo 

m  0  mo  fN. 
0  !>«  r^  r^  r^ 

CO    0  0    M    M 

r^  r^QO  00  00 

en  t  mo  r^ 

CO  00  CO  CO  QO 

00   0 

00  QO 

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2o8 


HEAT  AND   HEAT-ENGINES, 


- 

toco  to  tn  CO 

CO  O  0  O  O 

OO   OOO 

O  O   O   O  O 

0  o 
o  o 

r^  f^  !>.  r^  r^ 

O   »n  0   Q  »n 
oo  oo   O  0   O 

O  »«  »n  0   0 
«  M  coins5 

m  o  tn  O  »n 
O  rN.  r^oo  QO 

».<     i^     M     M     M 

1    t^U 

1  r^ 

2 

vO  O  O  O   u^ 

-t  r^  O  w  « 

oo    T  0    -t  •- 

O  O  Ooc  00 
tf)  in  in  lit  in 

^  t^QO     M  OO 

W    O  -fOO    CO 

rN.vo  O   in  in 
in  in  in  in  in 

00  OO  CI  Ml  m 
M    O  OO   to 
m  ■^  If  ^  ^ 
m  m  m  m  m 

o  o 

as 

= 

CO  CO  CO  to  CO 
CO  *»■  ir>vO   t>. 

CO  CO  O    O  1^ 
CO    COCO  sC    *^ 

o  r-  r^co   O 

•^  '^  Tf  -f  -r 

in  in  in  in  in 

to  CO  CO  ^  'i- 
m  m  m  m  m 

moo 

25; 

" 1 

o 

r»  r^aooo  0» 

ON    1-  Ow 

O  CO   M  O  oo 

O   O     NN     C«     to 

Tj-m 

c§Scg<g<g 

O    IM    «    «    w 
oo  oo  CO  00  00 

W    N    to  CO  CO 
oo  QO  QO  oo  oo 

CO  1-  -t  -t  't- 

oo  oo  00  00  00 

oo  QO 

Heat 
Equiv. 

of 
Internal 
Work. 

» 

O  too     M     ^ 

oo  00   O  '^  O 

r^  CO  M  O  « 

1-0    O^^    M\ 

OO  ei 

CO  QO  r>*  r^o 

in  N   a  "t  1^ 

O  O   O"^  o  o 

f  e«  CO  w  00 
QO  oo  r>.  r^o 

O  O  O  O  »n 

r^o 
m  in 

Hrat  of 

Vaporiza 

tiun. 

B.  T.  U. 

eo 

O  O  'I-  o  «n 

r^  O  to  to  0 

CO  •-•  w  o  O 

COO    O    COQO 

«  r^ 

0»  Oco  r>»  t^ 

00  OO  GO  OO  OO 

oo  00  CO  uo  oo 

eo  oo  0^  r^  r^ 

00  oo  oo  oo  oo 

rn  in  M  in  M 

O  O  O  tn  in 

00  CO  QO  QO  oo 

O  00  t>.  »n  to 
»n  •*  Tf  t  -f 

OO  OO  OO  oo  00 

CO  QO 

Heat  of 
Liquid. 

rs 

O  ooo  ^  « 

O  OO  r^  O 

TftTtO  o 

^  e«  M  Tto 

00  o 

IISI? 

o  o  o  o  2 

W   «   to  CO  to 

M  n-  O  oo  to 

N    C«    N    CO  Tt 
to  to  to  CO  CO 

moo   O   CI   '* 
^  f  m  m  m 

CO  CO  CO  CO  CO 

O  00 
m  m 
CO  CO 

« 

O  00    O    CO  to 

r^  O  oo  O 

r*  in  w  o  O 

OO 

;   U^ 

r^  i^oo  oo  CO 

O   •-   c^  mo 

CO  oo  CO  oo  CO 

QO   O  «   CO  in 
QO  00    O  O  O 

mo  1^  t^oo 

0^0*000 

M     l-«     M     M     M 

8:8; 

1 

„„M«M 1 

Weight  of 
X  cu.  ft. 

in 
Pounds. 

lA 

OO  O  ^  c«  Tt 
o  *§  O  «  ^ 

C4    M    C«    C<    M 

in  M  oo   O  m 
O  r^  r^cc   o 
M   «   CO  tnO 
w  c*  N  e«  c< 

o  CO  I-I  in  M 
Q    «    W    CO  f 

0    •-«    N  O  oo 

to  CO  CO  CO  CO 

m  o  CO  r^  O 
t  ^  m  in  m 

O  0  M  d  CO 

II 

Volume  of 

X  pound 

in 

Cu.  Feet. 

OO  OO   Q   M   »n 

u^  0  O    M  o 

00  oo  rN.  i^o 

o  coo  «  M 
o  -t  CI  oo  rt 

CO  W    I-i    «    CO 

w  »-«  tH  m  0 
CO  N  O  r-O 

m  O  00   O  Tf 
CO  r^  O   ^  O 
»n  Tf  ^  CO  w 

^8> 

Tf   -*   -*    Tf   -^l- 

^  ^  Tf  to  CO 

CO  CO  to  W   M 

N    CI    M    CI    CI 

M    W 

Tempera- 
ture, 
Degrees 
Absolute. 

« 

'I*  CO  O  t>.  '*• 
t^  in  CO  O  oo 

Ooo  too  »n 
in  w  oo  in  t>. 

CO  mo  OO  m 
r^.  m  O  in  CO 

r^  to  ^  »-  CO 

O    O  M    to  ''t 

m  m 

O   «-•  W   CO  CO 
CO  CO  CO  oo  oo 
r^  r*.  f>.  t>.  r* 

-TOO    i-i  oo    i-i 
CO  QO     O  O  O 

r*  t>»  r*  t>.oo 

O  tooo  O  •-• 

M    M    -    N    to 
QO  CO  CO  OO  OO 

CO  mco  0  N 

CO  CO  CO   -t   Tf 
oo  oo  oo  CO  00 

oo  00 

Tempera- 
ture, 
Degrees 
Fahr. 

M 

?<?5R? 

Ooo  coo  in 
CO  in  ^  CO   O 

CO  mo  oo  m 

O  oo  c<  oo  o 

t^  to  't  »-«  «*^ 

o  w  -^o  rn 

oo  GO 

N    N    W    W    C? 
CO  CO  CO  CO  CO 

to    I^    M     t^    IM 

e<  c<  to  CO  "i- 
to  CO  CO  to  to 

O  CI  oo  m  O 
m  m  mo  r>* 
to  to  CO  CO  to 

d  m  i^  0\  M 
r>i  r^  r^  !>.  QO 

to  CO  CO  CO  CO 

to  m 

QO  00 

CO  to 

Pressure 

above 

Vacuum 

in  Pounds 

per 

Sq.  Inch. 

- 

5s  ^h  o*  o^  ^^ 

in  0  »o  in  O 

o5   O    ►^   N 

m  O   O  »«  m 

CO  -f  mo   I^ 

O  »n  O  m  Q 
oo  oo   O  O  O 

n 

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VAPORS  AS  HEAT'CARRIERS,     STEAM, 


209 


114 

- 

^   0  >rk\r\\rk 
0  "^  C«  c^  ^ 
M   M   C4   M   CI 

MWTk  \rt  xrt  sTk 
mvo  r^oo   CO 
«  d  d  d  CO 

00   cocc   croo 
c^  1-  ir  m  m 

m  m  m  m 

oc  00  00  CO 

nC    f>-O0    0^ 

M 

cn  «<^  O^  «   •*• 
\t\  \r\  \c\  \t\  yrt 

OMn  CO  M  CO 
eoH^  O^r*  d 
d  d  M  H^  0* 
\a  *r\  \r\  M^  '^ 

CO  ^00  CO  0^ 
m  m  d  vO  0 

00  r^  r>»»o  nO 

m  cooo  00 

= 

1-  en  M  in  r* 
0  »n  d  0  0 
in  ino  0  r^ 
m  m  tn  *n  m 

CO  i^O  roco 
-too  d  NO  r^ 
r*  r»»oo  00  00 
\r\  \r%  \r\  \r\  \n 

CO  d  CO  a  CO 
^  m  M  M  d 
Q  M  CO  "t  m 

nO  0  nO  NO  nO 

00     M     M     O^ 

1^  COOO  d 

nO  nO  0   f^ 

e 

NO   I^  0*0    W 

«   CO  ^"t-co 

M    M    COOO 

00  00  qo  00  00 

in  in  m  in  m 

00  CC   CO  00  CO 

no  no  r*  r>»  r>. 

00  00  00  00  CO 

00  CO  GO  GO 
GO  GO  00  GO 

Heat 
Equiv. 

of 
Internal 
Work. 

0 

0  0  to  "^  t^ 

d  r^  CO  0  1^ 

m  ^  C  C«  NO 

d  d  CO  m 

»n  m  ^  ?  ^ 
!>.  r^  t^  r*  r* 

CO  CO  CO  ro  d 

r*  t>»»o  0  no 

m  cOd  M 
NO  m  ^  CO 

NO   NO   nO   NO 

Heat  of 

Vaporixa- 

lion. 

B.  T.  U. 

flO 

w  CO  CI  in  o^ 

d^o  c«  o^o 

CO  t^  C^  w    w 

00  GO  OO  00  00 

00  00  QO  00  CO 

0*  M  0  m  CO 

r^  0*  w  c^vo 
O*co  CO  t>»o 
t>»  r^  r*  r>.  r>. 

CO  ^nO    CO 
m  ^COd 

1^  i>»  r-»  r>. 

Heat  of 
Liquid. 

K 

0  •-•  0  t^  '* 

0^  COnO    0^  CO 

00  d  m  M  d 

^0^0  CO 

M     tn   M     ^QO 

0  0  r^  r>^  t^ 
eoeo  CO  CO  CO 

M    moo    »H  nO 
00  OO  00   0«  0 

CO  CO  coco  Tf 

On  d    CO  "t  ^ 

►*  to  Tf  mo 

d  CO  ^00 

GO    aM    d 

Total 
Heat. 

« 

d   **■  W  W   CO 

CO  CO  coco  t^ 

r*  CO  mNO  m 

!>*  CO  r>.  r^ 

iiin 

d  d  d  d  d 

M  d  d  d  CO 
d  d  d  d  d 

m  0   ^QO 
CO  'tj-  4  t 
d  d  d  d 

Weight  of 
I  cu.  ft. 

in 
Pounds. 

in 

0^0  *0    to  M 

0  r-^GO  0>  C 
0  00  •-•  co>5 
^  -^t  ir»  m  »n 

mN5  »0  •©  r^ 

d  m  0  0  0 

t^  o-d  <^n5 

in  ino  nO  nO 
00    ON  0   •-■   d 

8^S8 

^0  GO    0 

M     M     M            M     M     M     C« 

Volume  of 
I  pound 

in 
Cu.  Feet. 

^ 

CI  iM  CO  "t  «^ 
^  in  d  »noo 

•^  0  O'co  r^ 

d  d  t>»  Tt  in 
d  vO  0  ir>  d 

t^NO  NO   ir>  CO 

r>-  d  d  0*  0 

NO   t  t  m  <> 
M   0   o*eo  l>» 

0    I^  d    0 
GO    0*  COCO 

NO  m  m  •i- 

04     Ci    M     M     M 

M  ^  0    0   0 

0000 

Tempera- 
ture, 
Degrees 
Absolute. 

« 

CO  ON  M  0*  r-» 
in  '•t  «  0  M 

in  d  d  d  0 

moo  0  M  r* 

n8§>2§5 

COOO 
CO  CO  -"t  m 

CO  c«  00  iH  m 

■<r  m  mo  0 

00  CO  00  00  CO 

00  M  moo  d 
NO  r-  r*  r^  On 

00  QO  00  GO  00 

m  r^oo  00  r* 

0    •-•    d    CO  TT 

5n    0^    0»    ON    ON 

o'onSo 

Tempera- 
ture, 

Degrees 
Fahr. 

r<« 

00  On  1^  0  r-» 

00   r-  ^  On  f 

m  d  d  d 

CO  ►*  CO  -t  0 

0^^   ^t"  m  On 

M  >0    t>»0O 

00     On  On  0     0 
CO  CO  CO  "^  -«• 

r>.  M  Tj-  r^  d 

0     M     IH     1^     CO 

'(J-no  t^  ^^NO 
tmNO  r-^oo 
^  'I-  -r  ^  oi- 

n  oncono 

0    M    CO  ^t 
m  m  m  m 

Pressure 

above 

Vacuum 

in  Pounds 

per 

Sqllnch. 

- 

m  in  0   0  Q 
M   d    d    d   d 

d    d    d    CO  CO 

2  0  9  0  Q 

Q   m  0  m  5 
^  '«r  »n  mNO 

OOOI 
006 

oog 

OOil 

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210 


HEAT  AND   HEAT-ENGINES. 


factor,  since  its  value  at  these  higher  pressures  has  not  been 
fixed. 

The  columns  after  No.  5  have  been  calculated  as  follows: 

A  =  1091.7  +  o.305(/— ,  32); 

y  =  I  +  0.00004/  +  0.0000009/,  in  centigrade  units> 

reduced  to  Fahr. ; 
r  =  A  —  ^  =  Col.  6  —  Col.  7 ; 

pu 
r.  =  r  ^  ^^-—z  =  Col.  8  —  Col.  10; 
778 

Col.  10  =  (Col.  I  X   144)  X  Col.  4  -^  778 ; 

T 


Col.  II  =  Spec.  Ht.  X  Hyp  Log 


t: 


Col.  12  = 


Column  8 
Column 


-  +  Column  II;    or  0,  =  y  +  0„. 


137.  Saturated  Vapor  Pressures  and  Temperatures  for 
Media  other  than  Steam. — In  the  Comptes  Rendus  of  the 
Academie  des  Sciences,  Tome  x*xvi,  will  be  found  the  for- 
mulae elaborated  by  Regnault  to  express  the  relations  between 
temperature  centigrade  and  pressure  by  mercury-column  for 
other  vapors  such  as  alcohol,  ether,  chloroform,  carbon  bisul- 
phide, and  carbon  tetrachloride,  all  of  which  have  attracted 
experimenters  who  have  wished  to  replace  the  vapor  of  water 
by  another  medium  (see  also  Chapter  XXI).  His  equations 
and  constants  are  given  in  the  following  table: 

PRESSURE    OF   SATURATED    VAPORS. 


[Quantity. 

Alcohol. 

Ether. 

Chloroform. 

cs. 

CC14. 

Lofir>» 

a-3a«+f^»« 

a  +  bc!^  ^  r^*• 

a-hc^-  cfi"" 

a_AE«-cP« 

a  -  ^«  -  r^« 

a 

5.456ao«8 

5.0386398 

5.3353893 

5.401x663 

xa. 0963331 

luoga 

s- 99708557 

4.9809960 

o- 0x4577s 

S-9974«44 

1.9977628 

I. 9997120 

t 

0.0003284 

3.9531381 

3.4405663 

9.1375180 

l^Kfi 

i. 9409485 

1. 996877 

1.9B68176 

1.99x1997 

1.9949780 

c 

.      ^ 

0.OA85397 
^-l-ao 

3..^^^ 

0.0668673 
/  —  20 

0.2857386 

/-I-20 

1.9674890 
^  +  30 

Limits  (C). 

-  20,    +  i5o» 

-3o«,   4-iao» 

+  »o».  -f  164- 

-  30«,     +  X40' 

-  9o«,  4-  i88» 

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VAPORS  AS  HEAT'CARRIERS,     STEAM,  211 

X38.  Total  Heat  of  Steam. — In  the  case  of  a  hot  liquid 
and  its  vapor,  there  will  be  a  certain  amount  of  heat  resident 
in  the  liquid  which  has  been  required  to  raise  it  to  the  point 
at  which  the  vapor  forms  at  that  pressure;  there  will  be, 
furthermore,  the  heat  represented  by  the  internal  work  of 
disgregation  of  the  particles  of  liquid  to  change  its  state  to 
vapor  (§  III)  and  the  heat  which  has  disappeared  in  over- 
coming the  external  pressure.  The  usual  expression  for  this 
sum  (which  is  called  the  total  heat  of  the  vapor)  is  counted 
from  the  freezing-point  of  water,  and  for  a  unit  of  weight  is 
the  heat  required  to  raise  that  weight  of  water  from  freezing- 
point  to  a  given  temperature,  and  evaporate  it  completely 
into  steam  at  that  temperature.  Science  is  indebted  also  to 
Regnault's  investigations  for  the  accepted  expression  for  this 
total  heat,  which  has  the  form 

A  =  ^  -f  5/, 
in  which  the  constants  in  centigrade  units  give 

X  =  606.5  -f  0.305/; 
and  in  Fahrenheit  scales 

\  =  1091.7  -f  o.305(/-.  32*). 

For  the  same  other  vapors  as  in  the  preceding  paragraph, 
Regnault's  figures  for  the  total  heat  are,  for 

Ether X  =  94      +0.45/        —0.00055556/* 

Chloroform X  =  67      +0.1375/ 

CS, A  =  90      +  0.14601/  — 0.0004123/" 

CCl, X  =     52      +  0.14625/  — 0.000172/' 

Aceton A=  140.5  +  0.36644/ —  0.000516/' 

139.  Heat  of  the  Liquid. — If  the  specific  heat  of  water  be 
considered  unity  at  all  ranges  of  temperature,  the  heat  of  the 


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212  HEAT  AND   HEAT-ENGINES. 

liquid  water  would  be  the  same  as  its  range  above  freezing* 
point  for  each  pound.  At  lower  temperatures,  the  specific 
heat  is  unity.  Regnault  found  that  from  o"*  to  lOo''  C.  it 
was  1.005  2ind  from  o**  to  200®  it  was  1.016.  Assuming  an 
equation  of  the  form 

y  =  I  +  ^/'  +  Bt\ 

and  finding  the  values  for  the  constants  by  aid  of  known  ob- 
served values  of  q^  the  usually  accepted  equation  results: 

q  z=L  t  ^  0.00002/*  +  0.0000003/'. 

This  can  be  used  to  work  back  to  the  specific  heat  by  the 
methods  of  the  calculus,  since  the  differential  of  the  value  of 
q  taken  with  respect  to  the  temperature  will  be  the  heat  re- 
quired to  produce  this  differential  change,  which  is  the  spe- 
cific heat ;  or 

da 
C  =  ^  =  I  +  0.00004/  +  o.ooocooq/.' 

As  before,  the  heat  of  the  liquid  for  the  other  vapors  investi- 
gated by  Regnault  gives  values  for  q  as  follows: 

HEAT   OF    THE   LIQUID   q. 

Alcohol 0.54754/  4-  O.OOII2I8/'  4-  0.000002206/* 

Ether 0.52901/  -f  0.0002959/* 

Chloroform 0.23235/  +  0.0000507/* 

CSi 0.23523/  4-0.0000815/* 

CC1« 0.19798/  -h  0.0000906/* 

Aceton,  CiH«0 0.50643/  -{-  0.0003965/* 

140.  Heat  of  Vaporization.  Internal  Latent  Heat- 
It  is  made  apparent  from  the  foregoing  that  if  the  heat  of  the 
liquid  be  subtracted  from  the  total  heat»  the  remainder  will 
be  the  heat  absorbed  in  the  vaporization  process.  If  this  be 
designated  by  the  symbol  r 

r  =  X  —  ^. 


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VAPORS  AS  HEAT  CARRIERS.     STEAM,       •  21 J 

It  may  be  seen,  however,  that  r  is  really  made  up  of  the 
sum  of  two  quantities.  One  is  the  internal  latent  heat,  or 
heat  of  disgregation,  and  the  other  is  the  heat  equivalent  ta 
the  work  done  by  a  unit  liquid  volume  expanding  into  vapor 
volume  u  against  a  pressure/.  If  then  r,  denote  the  excess 
of  the  heat  in  units  of  heat  which  is  contained  in  the  vapor 
over  the  heat  contained  in  the  unit  of  weight  of  the  water  at 
32°  F.  from  which  the  vapor  was  produced,  the  above  equa- 
tion can  be  written 

^  =  ^+^-'  +  7$' 

since  the  last  term  will  express  the  heat  which  has  been  ex- 
pended in  increasing  the  volume  from  a  smaller  bulk  j  to  a 
larger  bulk  o-,  which  we  may  call  f/,  and  overcoming  the 
pressure  P  which  must  be  constant  during  the  evaporation. 

An  empirical  formula  in  the  French  system  for  r,,  pro- 
posed by  Zeuner,  gives  the  following  values,  which  are  fairly 
approximate : 

INTERNAL    LATENT    HEAT    r,. 

Water 575-40  -  0.791/ 

Ether 86. 54  —  o.  10648/  —  0.0007160/* 

Chloroform 62.44  —  0.11282/  —  0.0000140/' 

CSa 82.79  —  0.11446/  —  0.0004020/* 

CCh 48.57  —  0.06844/  —  0.0002080/* 

Aceton 131.63  —  0.20184/  —  0.0006280/* 

141.  Specific  Volume  of  Hot  Liquids. — For  the  accepted 
data  concerning  the  increase  of  volume  of  the  liquid  which 
expands  by  heat  (although  much  less  than  the  expansion  in 
change  of  state)  the  best  values  are  those  given  by  Hirn  in 
the  Annales  de  Chimie  et  de  Physique  for  1867,  as  the  result 
of  experiments  using  the  liquids  in  question  as  the  registering 
medium  as  in  a  thermometer.  Usually  the  expansion  of  the 
liquid  in  connection  with  its  vapor  can  be  neglected  in  com- 
parison with  the  expansion  of  the  vapor,  without  detectable 


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214 


HEAT  AND   HEAT-ENGINES. 


error.     Or,  in  other  words,  the  value  for  <t  is  considered  to 
be  constant.     Hirn's  data  are  as  follows: 


a  = 


SPECIFIC    VOLUMES   OF    HOT   LIQUIDS. 


Water, 

lOO*  C.  to  200'  C. 

(Vol.  at  4^*  =  unity.) 


Alcohol, 

30°  C.  to  160*'  C. 

(Vol.  at  o**  =  unity.) 


Ether, 

30*  C.  to  130*  C. 

(Vol.  at  o*  =  unity.) 


Carbon  Bisulphide, 

30*  C.  to  i6o'  C. 
(Vol.  at  o*  =  unity.) 


Carbon  Tetrachloride, 

30*  C.  to  i6o'  C. 

(Vol.  at  o**  =  unity.) 


:  I  -f- 0.00010867875/ 
-}-  o .  0000030073653/* 
\-  0.000000028730422/* 

—  0.0000000000066457031/* 

:  I  -h  0.00073892265/ 
-j-  0.00001055235/* 

—  0.000000092480842/* 

H-  0.00000000040413567/* 

:  I  -f  0.0013489059/ 
4-0.0000065537/* 

—  0.000000034490756/* 
+  0.00000000033772062/* 

I  -f  0.0011680559/ 
-j-  0.0000016489598/* 

—  0.00000000081119062/* 
-f  0.000000000060946589/* 

I  +  0.0010671883/ 
-j-  0.0000035651378/* 

—  0.00000001494928 1/* 

+  0.00000000008  5 1 823 1 8/* 


Lof^arithms. 
6.0361445  —  10 
4.4781862  —  10 
1. 4583419  —  10 
8.8225409  —  20 

6.8685991  —  10 
3.0233492  —  10 
2.9660517  —  10 
O.606527S  —  10 

7.1299817  —  10 
4.8164866  —  10 
2.5377028  —  10 
0.5285571  —  10 

7.0674636  —  10 
4.2172103  —  10 
0.9091229  —  10 
9.7849494—20 

7.0282409  —  10 
4.5520763  —  10 
2.1746202  —  10 
9-9303494  —  20 


142.  Critical  Temperature. — Computations  made  by  the 
foregoing  formulae  (§  141)  show  that  the  internal  latent  heat 
of  vapors  (r^)  decreases  as  the  temperature  rises,  since  the 
terms  containing  the  temperature  as  a  factor  act  to  diminish 
the  value  of  the  constant  for  each  vapor.  There  must  be  a 
temperature  therefore  for  each  vapor  at  which  r^  will  become 
zero  for  that  vapor,  or,  in  other  words,  a  temperature  at  which 
there  is  no  internal  work  done  in  disgregating  the  particles 
of  the  medium,  but  at  which  it  behaves  as  a  perfect  gas. 
The  distinction  between  the  liquid  and  its  vapor  has  disap- 
peared, and  it  would  be  correctly  inferred  that  above  this 
temperature,  pressure  alone — without  a  concurrent  lowering 
of  temperature — would  not  liquefy  the  vapor  or  gas.  This 
temperature  at  which  the  value  for  r,  or  the  internal  latent 


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VAPORS  AS  HEAT-CARRIERS,     STEAM.  21$ 

lieat  disappears  has  been  called  the  critical  temperature  for 
any  vapor;  and  it  has  been  wisely  advocated  to  use  the  term 
gas  for  a  vapor  above  its  critical  temperature,  while  below 
that  temperature  it  is  a  vapor. 

The  accepted  determinations  so  far  have  been  those  of 
Avenarius  (Poggendorfl's  Annalen,  vol.  151,  1874),  in  which 
volatile  liquids  were  heated  in  strong  glass  sealed  tubes  until 
the  liquid  all  disappears  and  the  tube  is  full  of  gas.  His  ex- 
periments, compared  with  the  computations  based  on  Reg- 
nault's  experiments  from  equations  deduced  for  the  internal 
latent  heat,  give  the  following: 

TABLE    OF   CRITICAL   TEMPERATURES. 

Experiment.  Calculation. 

Ether 196.2  C.  196.8  C. 

CS, 276.1  274 

CCl 292.5  298.7 

Aceton 246.1  230.4 

The  critical  temperature  for  water  as  calculated  from 
Zeuner's  formula  is  720°  C.  (1328°  F.),  which  is  beyond  the 
present  limits  of  experiment. 

143.  Increase  of  Entropy  of  a  Liquid  and  its  Vapor— 
It  is  usual  in  considering  liquids  with  their  vapors  to  treat  of 
a  unit  of  weight,  from  which  a  portion  x  is  raised  from  liquid 
to  vapor.  Hence  i  —  ;r  is  the  weight  of  liquid,  and  i  X  x 
=  ;r  is  the  weight  of  vapor.  If  such  unit  of  weight  of  liquid 
is  raised  from  freezing-point  to  a  temperature  /,  and  the  part 
X  is  evaporated  at  that  temperature,  the  increase  of  entropy 
will  take  place  in  two  stages,  and  the  total  increase  will  be 
their  sum.  The  heat  of  the  liquid  portion  is  determinable 
from  the  Regnault  experiments  and  data  given  in  §  139  as 
denoted  by  q,  so  that  when  /  denotes  the  range  above  centi- 
grade 0°,  the  increase  in  entropy  from  that  at  zero  repre- 
sented differentially  by  the  symbol  -=.  can  be  written: 


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2l6  HEAT  AND  HEAT-ENGINES. 

as  foreshadowed  in  §  124.  In  this  expression  c  is  the  specific 
heat,  considered  as  constant  for  the  range  in  question.  If 
it  is  not  constant,  as,  for  instance,  was  made  clear  by  Regnault 
in  the  case  with  water  (§  139),  the  entropy  of  the  h'quid  is  to 
be  calculated  in  steps  or  stages  from  the  zero-point  to  that 
desired.  Referring  to  Rcgnault's  experiments,  the  specific 
heat  between  0°  and  5°  C.  is  1.0072;  from  5°  to  lo**,  1.0044; 
from  10°  to  15°,  1. 0016.  This  would  make  the  entropy  for 
a  temperature  between  10**  and  15** — say  at  13°,  or  65°  F.^ 
to  be  made  up  of 

T  T  T 

1.0072  hyp.  log  ^  +  1.0044  hyp.  log -^'+i- 0016  hyp.  log  ^* 

=    0.04663. 

For  other  liquids  the  data  of  the  tables  in  §  139  can  be  used 

which  ^iwQ  values  for  q  directly.       By  differentiating  these 

do 
equations,  the  resulting  equation  has  the  form  ^,  which  gives 

dq 
the  specific  heat  at  the  desired  temperature  t,  since  ~^  =  ^ 

from  the  derivation  of  equations  giving  values  for  ^,  as  well 
as  by  definition  of  the  terms  used.  So  that,  if  ether  be 
taken  for  which  (§  139) 


q  =  0.52901/  +  0.0002959/*; 


then 


dq         n  dt 

^  =  Y  ^  I   (0-52901  +  .0005919/)^;, 

which  becomes 

6  =  (0.52901  +  .0005919/)  hyp.  log  7". 


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VAPORS  AS  HEAT'CARRIEKS,     STEAM.  2\f 

144.  Increase  of  the  Entropy  of  the  Vapor.— In  the 
case  cf  a  vapor  which  is  formed  from  a  liquid  with  which  it  is 
in  contact,  the  heat  is  continually  added  at  the  constant  tem- 
perature at  which  the  vapor  stands  or  is  formed.  Hence  the 
weight  X  of  the  original  unit  weight  receives  a  quantity  of 
heat  q\  which  is  represented  by  the  heat  of  vaporization  r, 
which  is  the  difference  between  the  total  heat  \  and  the  heat 
of  the  liquid  q  (§§  138,  139,  and  140).  Hence  it  follows  that 
the  increase  in  entropy  for  the  weight  x  will  be  repre- 
sented by 

xr 

The  entire  increase  in  entropy  will  be  therefore  the  sum  of 

-r- 


as  was  explained  in  §  124. 

The  convenient  approximation  is  also  to  be  remembered 
in  the  absence  of  tables  or  formulae  for  ^,  the  entropy  of  the 
liquid,  whereby  the  specific  heat  is  assumed  to  be  constant; 
so  that 

e,  —  6^  —  c  J  Y  =  ^  hyp.  log  Y-  y 
whence  for  adiabatic  relations,  and  0  —  0,  =  o, 


can  be  written 


-7^  =  -y^  +  c  hyp.  log  -=-, 


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2l8  HEAT  AND   HEAT-ENGINES. 

in  which  x^  is  the  unknown  quantity  for  which  the  equation 
is  to  be  solved. 

145.  Superheated  Steam,  Total  Heat  of. — Superheated 
steam  has  been  already  defined  (§  1 19).  The  total  heat  of 
such  superheated  steam  is  therefore  that  due  to  the  increase 
of  its  temperature  considered  as  a  gas  by  the  addition  of  the 
sensible  degrees  of  temperature  above  that  total  heat  which 
it  had  as  a  saturated  vapor,  as  given  in  §  138.  The  formula 
for  the  total  heat,  when  the  sensible  temperature  of  satura- 
tion at  any  pressure  is  t  and  the  superheat  temperature  is  /, 
becomes  for  Fahrenheit  units: 

\  =  1091.7  H-  o.305(/  -  32)  +  r(/.  -  -  /). 

The  value  of  r,  or  the  specific  heat  of  steam  becomes  at  once 
of  significance. 

146.  Specific  Heat  of  Steam. — It  is  obvious  that  there 
will  be  a  difference  in  the  specific  heat  of  steam  at  constant 
pressure  and  at  constant  volume,  as  is  the  case  with  all 
gaseous  media,  but  furthermore  it  would  be  expected  that 
there  would  be  a  different  specific  heat  for  constant  pressure 
at  or  near  the  saturation-point  from  that  prevailing  when  the 
steam  is  superheated  to  a  degree  permitting  considerable 
cooling  before  condensation  to  liquid  began. 

Regnault's  accepted  value  for  the  specific  heat  of  super- 
heated steam  at  constant  pressure'is 

c^  =  0.4805, 

which  is  the  mean  of  three  determinations,  giving 

0.481 1 1, 
0.47963, 
0.48080. 

The  specific  heat  of  saturated  steam  has  to  be  more  defi- 
nitely defined   to  secure  exactness,  by  stating  that  it  is  the 


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VAPORS  AS  NEAT  CARRIERS,     STEAM.  219 

quantity  of  heat  which  must  be  added  to  one  unit  o  weight 
of  steam,  when  the  temperature  is  raised  one  degree  and  the 
pressure  increased  the  corresponding  amount  while  the  steam 
remains  dry  and  saturated  under  this  change.  It  will  appear, 
therefore,  that  the  specific  heat  of  a  dry  and  saturated  vapor 
is  not  exactly  like  either  of  the  others,  as  the  condition  of 
saturation  imposed  compels  a  change  of  both  pressure  and 
volume  to  maintain  the  imposed  equilibrium.  The  accepted 
statement  for  the  value  of  the  specific  heat  of  saturated  steam 
has  therefore  the  form 

C  =  0.305  -  ^. 

147.  Negative  Specific  Heat  of  Saturated  Steam.— 
If  the  foregoing  equation  be  solved  for  C,  by  means  of  the 
relations  r  =  X  —  ^,  and  the  values  for  \  and  q  already  given 
(§§  138  and  139)  for  several  temperatures,  it  will  result  that 
within  usual  limits  of  practice  the  specific  heat  C  comes  out 
negative.     For  example : 

At  0°  C.  or  32°  Fahr.,  C  =  —  1.911 
**  50  **  **  100  ''  C  =  —  1. 461 
**  100  **  **  212  *'  C  =  —  1. 131 
•'  150  ''  ''  300  '*  (7  =  —  0.879 
**  200    **    **  392       ''       C=— 0.676 

It  will  be  apparent  that  the  value  for  C  is  approaching  a 
point  of  inversion  at  which  it  will  be  zero  and  beyond  which 
it  will  become  positive,  as  for  many  of  the  other  heat  media, 
such  as  ether.  This  point,  however,  is  beyond  present  ex- 
perimental knowledge.  The  negative  value  within  experi- 
ence means  that  when  temperature  and  pressure  are  increased 
together,  the  steam  will  become  superheated  unless  heat  is 
abstracted  by  doing  work.  Or,  in  other  words,  a  sudden 
expansion  or  drop  of  pressure,  if  accompanied  also  with  a 


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220  HEAT  AND    HEAT-ENGINES. 

drop  of  temperature,  causes  a  part  of  the  steam  to  be  con- 
densed. The  heat  freed  by  the  condensation  of  that  weight 
which  is  condensed  serves  to  keep  the  uncondensed  part  in 
the  required  state-of  saturation  under  the  changed  conditions. 
This  was  shown  experimentally  by  Him  (Bulletin  de  la  So- 
ci^t6  Industrielle  de  Mulhouse,  tome  133).  This  is  quite 
different  from  the  condition  discussed  in  §  131,  in  which  the 
temperature  was  assumed  to  be  maintained  at  the  point  be- 
longing to  the  higher  pressure,  while  the  pressure  fell.  The 
negative  specific  heat  of  steam  acts  in  an  unjacketed  and 
conducting  cylinder  to  increase  the  cylinder  condensation, 
since  the  pressure  is  falling  and  heat  is  being  withdrawn  by 
radiation  outwardly,  while  the  piston-work  is  being  done  at 
the  expense  of  the  heat  brought  into  the  cyUnder. 

148.  Specific  Heat  of  Superheated  Steam  at  Constant 
Volume. — The  specific  heat  of  superheated  steam  at  constant 
volume  can  be  calculated  by  means  of  a  ratio  between  the 
two  specific  heats,  assumed  by  Zeuner  to  be  f  or  1.333, 
whence  for  various  pressures  in  pounds  per  square  inch 

5  50  100  200  300 

C,  =  0.351         0.348         0.346         0.344         0.341 

or  is  apparent  as  a  variable. 

149.  Specific  Volume  of  Superheated  Steam. — The  vol- 
ume  of  superheated  steam  in  metric  equivalents  and  centi- 
grade degrees  as  given  in  the  following  table  presents  the 
results  of  experiments  by  Hirn.  The  comparison  column  is 
deduced  from  an  equation  expressed  in  kilograms  per  square 
meter  for  the  volume  belonging  to  any  pressure  and  temper- 
ature Ty  which  has  the  form  in 

Metric  units pv  =  51.3  7^—  188/*; 

and  in  English    **      ...  /t/ =  93.57^— 971/i. 

When  the  same  equation  is  applied  near  the  limit  or  near 
the  condition  of  saturation  it  seems  to  apply  fairly  well. 


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VAPORS   AS  HEAT-CARRIERS,     STEAM. 
SPECIFIC    VOLUME   OF   SUPERHEATED    STEAM. 


221 


Cubic  Meters 

per  Kilogram. 

Pressure 

Temperature 
Centigrade. 

in  Atmosphere. 

Hirn's  Experiments. 

Calculated  Values. 

II3.5 

1-74 

1.75 

141 

1.85 

1.87 

200 

0.697 

0.699 

165 

0.4822 

0.476 

200 

0.522 

0.520 

246 

0.5752 

0.577 

162.5 

0.3758 

0.376 

205 

0.414 

0.418 

150.  Specific  Volume  of  Saturated  Steam. — The  vol- 
ume occupied  by  a  unit  weight  of  saturated  steam  has 
already  been  given  in  the  steam-tables  presented  in  §  136. 
It  will  be  of  significance  to  refer  to  experiments  to  determine 
these  values.  Those  of  Fairbairn  and  Tate  in  England  {Pkil- 
osophical  Transactions^  vol.  150,  p.  185,  i860)  are  among  the 
most  complete.  Fig.  52  represents  a  diagram  to  illustrate 
their  method.  A  and  B  are  globular  vessels 
containing  slightly  varying  weights  of  water. 
They  are  connected  by  a  tube  containing  mer- 
cury, and  the  whole  apparatus  is  immersed  in 
a  bath  whereby  any  desired  temperature  may 
be  given  to  the  globular  vessels  and  their  con- 
tents. As  long  as  any  water  is  in  either 
globe  the  vapor  in  each  will  have  the  same  tension,  and  the 
mercury  will  stand  even  in  the  two  legs.  There  will  be  a 
temperature,  however,  at  which  the  water  in  that  vessel 
which  has  originally  the  least  weight  of  water  in  it  will  be- 
come altogether  vapor,  in  a  dry  and  saturated  state,  and,  if 
this  point  can  be  accurately  observed,  the  density  can  be 
found  from  the  known  weight  and  observed  volume.  Be- 
yond this  point  of  dryness  and  saturation  the  steam  in  a  state 
•of  complete  vaporization  becomes  superheated  by  addition 


'd 

^y^ 

r 

Fig.  52. 


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222  HEAT  AND   BEAT-ENGINES. 

of  heat,  and  the  mercury  will  rise  in  the  dry  leg.  The  pres- 
sure for  saturated  steam  at  any  temperature  is  greater  than 
for  superheated  steam  at  that  same  temperature.  The  diffi- 
culty and  uncertainty  in  the  experiment  is  due  to  the  chances 
of  error  and  uncertainty  in  fixing  on  the  period  of  complete 
vaporization  and  the  corresponding  temperature. 

The  Tate  and  Fairbairn  formula  which  they  deduced  to 
represent  their  yrork  is  of  the  form 

^       ^p  4-0.72 

The  term  V  is  the  volume  of  steam  compared  to  that  of  the 
water  which  produced  it,  and  P  is  the  pressure  in  inches  of 
mercury, 

This  transformed  to  cubic  feet  per  pound,  and  with  /  in 
pounds  per  square  inch,  becomes 

r,  =  o.o,6[.s.6.  +  j^i5^]. 

Zeuner*s  empirical  formula  is 

in  which  a  =  0.6061   and  —  =  0.9393.    D  is  in  kilograms  per 

cubic  meter,  and  /  is  in  atmospheres. 

151.  Condensation  in  Adiabatic  Expansion  of  Steam. — 

It  will  be  apparent  in  an  adiabatic  expansion  in  which  by 
definition  the  external  work  is  being  done  at  the  expense  of 
the  intrinsic  heat  energy  of  the  steam,  that  with  the  use  of 
superheated  steam  a  certain  amount  of  expansion  will  occur 
before  the  steam  becomes  saturated,  and  that  if  the  expan- 
sion be  carried  further  the  steam  will  become  moist  by  con- 
densation of  a  part  of  it.  The  equations  of  §  144  when  ap- 
plied to  an  actual  case  with  the  proper  data  will  make  this 
clear.     Let  a  unit  weight  of  steam  {x^  =  i)  be  taken  at  100 


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VAPOXS  AS  HEAT^CARRIERS.     STEAM.  22$ 

pounds  pressure  above  vacuum  and  let  it  be  superheated  to  a 
temperature  of  400**  F. :  then  let  it  be  expanded  adiabatically 
down  to  atmospheric  pressure.     Then  in  the  formula 

^  +  «>.  +  0.4805  hyp.  log  ^'  =  ^*  +  e^ ; 

all  data  are  known  or  to  be  taken  from  tables  except  ;r,,  the 
final  state  of  steam  in  the  same  unit  of  weight.  When> 
therefore,- 

e^  =  0.4733  ;  /,  =  327.6 ;  r,  =  884 ; 

d,  =  0.3143 ;       /,  =  213.9;       ^  =  965.1 ; 

the  equation  becomes 
884     .  .         o      ,_        ,      860.7       965. 1;r,  . 

+  0.4733  +  0.4805  hyp.  log  "^  =  ~^— r  +  0.3143^ 


788.3^    ^^^^^^^^^-'*^"  ^788.3        673.7 

and  there  will  result 

;r,  =  0.923, 

or  a  little  less  than  8  per  cent  of  the  steam  has  become  water^ 
in  the  process  of  expansion,  in  spite  of  the  initial  superheat. 

If  instead  of  T,,  or  the  absolute  superheat  temperature, 
the  temperature  of  saturation  had  been  used,  the  formula 
and  calculation  would  show  the  amount  of  condensation  to  be 
expected  from  steam  which  is  simply  dry.  See  also  Chapter 
XIV,  §  200  et  seq. 

152.  Evaporation  from  a  Feed-water  Temperature.— 
The  formulae  for  total  heat  of  steam  (§  138)  give  the  total 
heat  counted  from  freezing-point  of  water.  When  the  feed- 
water  which  is  pumped  into  the  boiler  of  a  steam-engine  is  at 
some  higher  temperature  than  this,  it  is  apparent  that  the 
coal  burned  in  the  boiler-furnace  does  not  have  to  supply  as 
much  heat  per  pound  of  water  evaporated  as  the  formula 
would  indicate.     The  feed-water  being  assumed  at  t'  F.,  the 


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224  HEAT  AND   HEAT-ENGINES, 

total  heat  required  to  make  steam  at  /  degrees  temperature 
becomes  for  each  pound  of  water  evaporated 

Q,  =  1091.7  +  0.305  (/  -  32)  -  c{t'  -  32), 

or  (if  the  specific  be  called  unity  between  t  and  32°  F.,  in- 
stead of  using  its  more  exact  value) 

Q;  =  109 1.7  +  0.305  it  ~  32)  -  {t'  -  32). 

153.  Evaporation  from  and  at  212°  F. — A  very  conven- 
lent,  practical,  and  useful  deduction  is  made  from  the  formulae 
for  total  heat  of  steam  (§§  138-144)  to  compare  the  evapora- 
tive performances  of  steam-boilers  working  under  different 
pressures.  It  is  apparent  that  more  heat  goes  into  each 
pound  of  water  at  the  higher  pressures.  Hence  it  has  been 
agreed  to  reduce  all  conditions  of  feed-water  temperature  and 
evaporative  temperature  and  pressure  to  the  condition  of  a 
feed-water  temperature  of  212®,  and  an  evaporation  of  the 
water  at  that  temperature  into  steam  at  atmospheric  pres- 
sure, with  a  temperature  of  212°.  This  has  been  shortened 
into  the  compact  expression,  ''  Evaporation  from  and  at 
2I2^'' 

The  pressure  of  one  atmosphere  is  14.7  pounds  per  square 
inch,  and  at  212°  F.,  which  is  the  corresponding  boiling  tem- 
perature, the  heat  necessary  to  make  water  at  that  tempera- 
ture into  steam  at  that  pressure  is 

965.7  =  966  B.T.U. 

If,  then,  from  the  preceding  paragraph,  the  total  heat  Q  re- 
quired to  vaporize  a  weight  of  water  W  be  observed  from  a 
test,  in  which  the  feed-water  was  introduced  at  f  and  the 
evaporation  took  place  into  steam  at  /,  the  total  heat  which 
went  into  the  evaporated  water  was  the  product 

QW. 


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VAPORS  AS  HEAT'CARRIERS.     STEAM,  22$ 

If  the  evaporation  had  taken  place  from  and  at  212**,  Q 
would  have  been  966  for  each  pound,  so  that 

966;ir 

would  have  been  the  equivalent  heat  absorption  if  x  is  the 
corresponding  weight  of  water  evaporated  at  that  atmospheric 
pressure.      Equating  these, 

QW 


QW -=.  966X    or   ;r  = 


966' 


gives  the  pounds  of  water  which  would  have  been  evaporated 
from  and  at  212''.  This  may  be  either  the  total  equivalent 
evaporation,  or  the  equivalent  evaporation  per  pound  of  coal, 
or  per  horse-power  per  hour,  according  to  the  unit  used 
for  W. 

154.  Rankine's  Factor  of  Evaporation. — Rankine  com- 
puted a  table  giving  values  for  a  factor, 

^      966' 

wherewith  to  multiply  the  quantity  W  Xo  produce  the  de- 
sired weight  X  (Rankine,  '*  Steam-engine  and  other  Prime 
Movers,"  pp.  255,  256).     His  equation  for  F  is 

r^_  ,    ,    0.3(^1 -212°) +  (212-/,) 
■^  966 

in  which  /,  is  the  temperature  of  the  feed-water,  and  t^  the 
temperature  at  which  vaporization  actually  took  place. 

155.  Theoretical  Evaporation  of  Water  per  Pound  of 
Fuel. — The  formula  for  total  heat  of  steam  under  various 
conditions  renders  it  possible  to  predict  the  limits  of  evapora- 
tive capacity  with  any  fuel  whose  calorific  power  is  known  or 
assumed.  The  pounds  of  water  evaporated  per  pound  of  fuel 
burned  will  be  the  same  as  the  quotient  found  by  dividing 
the  total  heat  at  that  temperature  into  the  calorific  power 


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226  HEAT  AND  HEAT-ENGINES, 

(§§  22,  58,  59).  For  example,  while  with  pure  carbon,  with 
a  calorific  power  of  14,500  heat-units,  the  evaporation  from 
a  feed- water  temperature  at  212**  will  be 

ii_5oo  _ 
966    "-  ^^ 

pounds  of  water  per  pound  of  carbon,  as  was  already  shown  in 
§  59,  at  higher  pressures,  or  with  cooler  feed-water  tempera- 
tures, the  value  of  the  divisor  increases  while  the  dividend  re- 
mains constant,  and  hence  the  quotient  grows  smaller.  The 
effect  of  this  is  to  make  the  maximum  theoretical  evaporation 
per  pound  of  fuel  burned  less  as  the  pressures  increase  at 
which  the  steam  is  formed. 

156.  Output  of  a  Steam-boiler  in  Heat-units.  —  The 
product  of  the  poundsof  water  evaporated  by  a  boiler  into  the 
total  heat  of  the  steam  at  that  pressure,  as  determined  from 
the  foregoing  formulae,  gives  the  heat-units  which  that  boiler 
is  delivering.  These  may  be  expressed  in  any  unit,  per  hour, 
or  per  boiler  horse-power,  or  per  day,  or  per  1000  pounds  of 
steam  delivered  to  engine,  or  in  any  form.  The  accepted 
boiler  horse-power  unit  of  30  pounds  of  water  evaporated  into 
steam  at  70  pounds  pressure  from  a  feed-water  temperature 
of  100°  is  equivalent  to  an  evaporation  of  34,488  pounds  of 
water  from  and  at  212''.     The  product, 

34.488  X  965.7  =  33305  heat-units, 

is  the  heat-units  per  boiler  horse-power  from  and  at  212°,  ac- 
cording to  the  standard  of  1885  of  the  American  Society  of 
Mechanical  Engineers.  Any  other  similar  computation  can 
be  made  from  the  observed  results  of  a  boiler-test. 

157.  Efficiency  of  a  Steam-boiler. — The  efficiency  of  a 
steam-boiler  as  an  appliance  for  getting  the  heat-units  avail- 
able in  the  fuel  into  the  heat-carrier  or  medium  whereby  they 
are  to  be  utilized  would  appear  to  be  the  relation  between 
the  heat-units  in  the  output  as  compared  with  the  total  heat- 


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VAPORS  AS  HEAT-CAKRIEKS,     S7EAM.  22/ 

units  charged  into  the  furnace.  (See  §  59.)  That  is,  if  the 
efficiency  were  unity,  or  one  hundred  per  cent.,  each  pound 
of  fuel  should  evaporate  a  weight  of  water  IV  which,  multi- 
plied by  its  total  heat  in  heat-units,  should  give  a  product 
equal  to  its  calorific  power;  or, 

calorific  power  =  H'  X  Q- 

This  is  the  statement  of  §  155  reversed.  The  actu?l 
evaporation,  however,  is  not  W  but  a  smaller  weight  \V\ 
raised  to  the  same  total  heat,  Q.     Hence  for  any  boiler, 

^  .  _«  ^^"  X  2  _  ^^  _  actual  output  in  heat-units 

^  ~    IV  y,  Q  '^  W  "  calorific  power  of  the  fuel 

taken  per  hour,  or  per  horse-power,  or  per  pound,  as  may  be 
convenient. 

A  comparison  of  actual  and  theoretical  output  in  tests  of 
modern  economical  boilers  will  show  that  it  may  claim  to  be 
a  fairly  efficient  apparatus  for  its  purpose. 


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CHAPTER  XII. 

WORK   DONE   BY   ELASTIC   HEAT   MEDIA   IN   HEAT- 
ENGINES.      CYLINDER   DESIGN. 

l6o.  Introductory. — In  the  foregoing  chapters  the  sub- 
ject of  heat  has  been  discussed  first  from  the  standpoint  of  its 
generation  or  liberation  froni  a  fuel  or  combustible;  and,  sec- 
ondly, with  respect  to  the  effects  which  heat  produces  upon  a 
suitable  medium  to  convey  the  energy  of  that  heat  to  the 
organ  or  motor  which  is  to  utilize  it.  This  chapter  will  dis- 
cuss the  action  of  such  heat-medium  exerting  an  effort  by 
reason  of  the  elastic  tension  which  has  been  imparted  to  it  by 
heat  to  produce  motion  of  a  suitable  piston  in  a  cylinder  and 
overcome  a  resistance  expressed  in  pounds  exerted  through 
a  space  expressed  in  feet. 

Attention  was  called  to  the  general  truth  in  Chapter  II,  § 
7,  that  a  work  in  foot-pounds  could  be  represented  by  an  area 
equivalent  to  that  of  a  rectangle  whose  height  or  altitude 
was  proportional  to  pounds  on  any  accepted  scale  and  whose 
length  or  base  was  proportional  to  feet.  The  product  of  the 
base  and  altitude  would  therefore  be  a  product  expressed  in 
foot-pounds.  It  will  further  be  recalled  that  for  a  piston- 
engine  which  has  a  piston-area  A  and  a  length  Z,  the  work  in 
any  time  in  which  yV  strokes  are  made  in  such  cylinder  while 
a  pressure  P  is  exerted  over  the  area  A  will  be  a  product  in 
foot-pounds  represented  by 


W=rA  X  LN, 


228 


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ELASTIC  HEAT  MEDIA    IN  HEAT-ENGINES,  229 

which  becomes  expressed  in  horse-power  per  minute  by  mak- 
ing N  represent  the  number  of  traverses  of  the  piston  per 
minute,  and  dividing  both  members  by  33,000,  or 

33000 

It  becomes  necessary  now,  however,  to  take  up  this  work-for- 
mula in  more  exact  detail  for  a  fuller  discussion.  The  ther- 
mal lines  discussed  in  §§  1 19-125  now  have  a  significance. 

161.  Work  Done  with  Constant  Pressure  in  the  Cylin- 
der.— Since  the  product  AL  is  equivalent  to  the  volume  of 
the  cylinder  filled  once,  and  ALN  is  the  volume  filled  during 

N  traverses  or  —  revolutions  if  the  engine  is  double-acting, 

it  becomes  apparent  that  AL  becomes  V  for  one  traverse, 
and  ALN  is  V  for  A^  traverses.  It  is  possible,  therefore,  to 
write 

W=PLA  =PV 

for  one  traverse,  provided  it  be  clearly  kept  in  mind  that  P 

and  A  must  be  kept  in  the  same  unit.     This  is  most  easily 

done  by  expressing  P  in  pounds  per  square  foot,  and  A   in 

square  feet.     It  is  just  as  true  to  use  pressure  in  pounds  per 

P 
square  inch  /,  which  is  equal  to  — ,  provided  the  area  a  is 

in  square  inches,  and  a  =  144A.     Then 

144  ^ 

The  length  L  must  remain  in  feet,  in  any  case,  which  makes 
this  latter  method  liable  to  confuse.     But  it  is  in  the  form 

Work  =  PV 

that  the  formulae  applicable  to  heat-engines  have  so  far  ap- 
peared. 


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230 


HEAT  AND   HEAT-ENGINES, 


The  resistance  against  which  the  heat-motor  works  is  sup- 
posed to  be  a  uniform  effort,  expressed  in  pounds  to  be  over- 
come through  the  given  path.  The  discussion  of  the  fly- 
wheel as  a  regulator  or  accumulator  to  compensate  and  con- 
trol irregularities  of  the  resistance  is  aside  from  the  present 
purpose.  The  resistance  will  be  assumed  to  be  able  to  be 
kept  constant. 

Such  resistance  can  therefore  be  represented  by  a  rectan- 
gle, ABCD^(F\g.  53),  in  which  the  horizontal  is  the  space  s, 
through  which  the  resistance  is  overcome  in  one  traverse  of 
the  motor-piston,  and  the  vertical  or  height  is  proportional 
to  the  intensity /of  that  resistance  in  pounds.    In  order  that 


1 

h 

■ 

D 

4- 

c 

0 

6TR0KE 

V 

p 

/ 

I 

/' 

1 

1 

c' 

0 

< V i- 

V 

Fia.53. 


Fig.  54. 


this  constant  resistance  may  be  overcome,  the  cylinder  of  the 
motor  must  generate  an  equal  product  or  area  in  which  the 
horizontal  shall  be  the  volume  filled  by  the  elastic  heat- 
medium,  and  the  vertical  is  proportional  to  the  pressure  P. 
That  is,  the  work  in  foot-pounds  W  ^  fs  =  ABCD  of  Fig. 
53  must  be  equal  to  the  area  PV  ^  A'B'C'D'  in  Fig.  54. 

It  is  to  be  observed  that  there  is  an  infinite  number  of 
rectangles  or  other  figures  which  have  the  area  PV  =  fs.  The 
two  need  not  have  the  same  altitude  or  base,  provided  only 
their  areas  are  the  same.  This  represents  the  simplest  case 
which  occurs  in  tank-pumping  with  small  pumps  without  fly- 


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ELASTIC  HEAT  MEDIA   IN  HEAT-ENGINES,  23 1 

ivheel,  where  the  parts  are  so  light  as  to  permit  their  inertia 
to  be  neglected,  and  where  no  excess  of  energy  is  required 
from  the  motor  to  cause  the  engine  to  pass  its  centres  at  the 
ends  of  each  stroke  so  as  to  reverse  the  motion.  The  effort 
of  the  elastic  medium  is  a  constant  effort  of  the  same  inten- 
sity and  the  volume  generated  is  that  which  exists  at  the  end 
of  the  stroke.  Instead  of  using  the  stroke  as  the  unit,  the 
work  of  a  minute  might  have  been  chosen  involving  iV strokes. 
Instead  of  either  of  these,  the  volume  might  have  been  made 
that  occupied  by  a  pound  weight  of  the  medium  at  the  con- 
stant pressure  P^  and  the  corresponding  value  oi  fs  calculated 
back  from  the  value  of  the  corresponding  PV.  In  any  case 
one  or  the  other  of  the  two  factors  must  be  assumed,  and  the 
value  of  the  other  calculated  to  meet  the  case. 

162.  Constant  Pressure-work  with  Air  or  Permanent 
Gases. — The  condition  presented  by  the  rectangular  area  for 
PV  is  not  considered  a  desirable  or  economical  one.  The 
difficulty  is  caused  by  the  fact  that  at  the  completion  of  the 
working-stroke  the  contents  of  the  cylinder  must  be  voided 
to  permit  the  piston  to  return  to  its  original  position  against 
-the  least  possible  internal  resistance  in  the  cylinder  itself. 
Hence  a  volume  of  medium  Fat  a  pressure  or  tension  -Pwould 
be  wasted  at  each  stroke.  In  the  case  of  air,  if  it  be  assumed 
that  no  temperature  changes  occur,  and  the  work  represented 
"by  PV^SiS  put  into  the  working  medium  by  the  doing  upon  it 
of  an  external  work  by  a  compressor  which  is  equal  to  that 
same  PV,  then  the  compressed  air  acts  exactly  like  incom- 
pressible water  or  like  a  solid  mass  to  transmit  the  work  of 
the  compressing  motor  to  the  air-motor  cylinder.  A  certain 
weight  or  volume  of  air  is  displaced  mechanically,  and  in  the 
strictest  sense  the  transmission  is  not  a  heat-engine  transac- 
tion at  all.  Usually,  however,  temperature  changes  do 
come  in. 

The  work  represented  in  bringing  up  its  tension  from  at- 
mospheric pressure  to  its  working  tension  is  thrown  away  at 


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232  HEAT  AND   HEAT-ENGINES. 

the  exhaust,  because  the  potential  energy  is  not  exerted 
which  it  might  have  given  out  in  expanding  down  to  atmos- 
pheric pressure  again.  The  drop  in  pressure  takes  place  out- 
side of  the  cylinder.  The  heat  expended  in  raising  the  me- 
dium to  the  higher  pressure  will  be  a  matter  of  later  discus- 
sion. 

163.  Constant  Pressure-work  with  Steam. — In  the  case 
in  which  a  steam-cylinder  receives  steam  through  a  pipe  from 
a  boiler  during  the  entire  stroke  of  the  piston,  the  engine  is 
said  to  work  without  expansion,  or  non-expansively  (Fig.  i). 
This  is  true  in  the  sense  that  the  terminal  pressure  and  tem- 
perature of  the  steam  at  the  moment  when  exhaust  begins  are 
the  same  as  at  the  beginning,  and  all  the  heat  and  potential 
energy  in  the  weight  of  steam  which  fills  the  final  volume  of 
the  cylinder  is  voided  during  the  exhaust.  What  occurs  in 
this  case  is  an  expansion  in  the  boiler  and  not  in  the  engine. 
The  fire  or  source  of  heat  has  to  furnish  the  amount  of  heat 
represented  by  the  total  heat  of  steam  at  the  pressure  /,  at 
which  it  works  in  the  cylinder  for  each  pound  of  steam  repre- 
sented in  the  terminal  volume  v^.  The  data  of  §§  136  and 
138  enable  this  calculation  to  be  made.  The  rejection  of  sa 
much  potential  energy  at  the  end  of  the  working-stroke, 
which  has  been  imparted  to  the  medium  by  the  heat  of  the 
fire,  and  which  might  be  utilized  for  the  doing  of  external 
work  in  the  engine,  make  this  method  of  working  less  econom- 
ical and  efficient  than  methods  now  to  be  discussed. 

164.  Work  Done  by  an  Elastic  Heat-carrier  Expand- 
ing in  a  Cylinder.  Cut-off  or  Degree  of  Expansion.— 
It  has  already  been  made  apparent  (§  112  et  seq..  Chapter 
X)  that  the  elastic  tension  of  a  heat  medium  is  a  function  of 
its  temperature  or  is  dependent  upon  it.  The  necessity  for 
disposing  of  the  working-volume  of  the  medium  at  the  end 
of  the  stroke,  and  its  rejection  from  the  heat-engine  proper, 
would  at  once  suggest  the  advisability  (if  it  were  possible  to 
secure  this  result)  of  making  the  elastic  heat-carrier  surrender 


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ELASTIC  HEAT  MEDIA   IN  HEAT-ENGINES.  2J3 

all  the  heat  energy  which  could  be  gotten  froiii  it  before  it 
leaves  the  cylinder.  This  implies  the  maximum  lowering  of 
Its  temperature  and  pressure,  which  is  wise  to  demand,  within 
the  cylinder  itself^  and  after  the  disconnection  of  the  required 
weight  of  medium  from  its  source  of  heat.  Hence  the  prin- 
ciple is  availed  of  which  is  expressed  mathematically  by  the 
equation, 

Px^i  =/^  =  RT 

for  isothermal  expansion;  or  the  expression, 

p^v^  =  pv"^  =  constant 

for  an  adiabatic  expansion.  As  applied  in  a  practical  way, 
this  means  that  if  the  elastic  heat-carrier  be  admitted  from 
the  heating-appliance  to  fill  a  small  volume  t/,,and  then  that 
volume  is  increased  up  to  the  final  volume  represented  by  the 
entire  piston-displacement  in  one  stroke  (or  v)^  the  final  or 
terminal  pressure  will  be  as  much  lower  than  the  initial  pres- 
sure as  the  final  volume  was  greater  than  that  filled  by  the 
medium  while  it  was  flowing  into  the  cylinder  from  the  out- 
side reservoir  of  pressure.  With  the  non-condensable  media, 
it  is  therefore  desirable  that  the  terminal  pressure  should  be 
that  of  the  atmosphere  surrounding  the  cylinder  if  the  ex- 
haust takes  place  in  the  open  air,  unless  some  practical  con- 
siderations should  give  another  consideration  greater  weight, 
which  is  hereafter  to  be  discussed.  In  condensing  engines 
(Chapter  IX)  a  similar  theory  would  demand  that  the  terminal 
pressure  might  be  that  of  the  vessel  into  which  the  exhaust 
takes  place — which  latter  expression  can  be  made  generally 
applicable,  subject  only  to  the  limitations  to  be  hereafter  im- 
posed. The  heat-carrier  thus  carries  out  of  the  cylinder  the 
minimum  amount  of  available  energy. 

This  principle  of  working  the  heat  medium  so  as  to  make 
it  expand  to  a  larger  volume  and  lower  pressure,  and  do 
work  against  the  resistance  in  thus  expanding,  is  secured  in 


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234  HEAT  AND   HEAT-ENGINES, 

practice  by  cutting  off  the  admission  of  the  medium  at  a  des- 
ignated point  in  the  stroke  of  the  piston.  The  point  where 
admission  of  heat-medium  and  heat-units  to  the  working- 
cylinder  ceases  is  called  the  point  of  cut-off,  and  is  expressed 
as  a  fraction  of  the  entire  piston-stroke  as  unity.  In  a  cyl- 
inder of  uniform  section  the  volume  filled  up  to  the  point  of 
cut-off  of  the  admission  will  bear  the  same  relation  to  the 
final  volume  at  the  end  of  the  stroke  as  the  ratio  of  the 
lengths  of  the  stroke  bear  to  each  other.  Volumes  and 
lengths  can  therefore  be  used  indifferently. 

The  final  volume  of  the  elastic  medium  will  be  to  the  vol- 
ume present  when  cut-off  took  place  in  a  ratio  which  is  the 
reciprocal  of  the  fraction  expressing  the  point  of  cut-off. 
That  is,  the  degree  of  expansion,  or  the  ratio  of  expansion, 
will  be  2  for  a  cut-off  at  one  half  stroke,  since  the  final  vol- 
ume will  be  twice  that  present  when  cut-off  occurred.  This 
distinction  must  be  carefully  observed  lest  confusion  occur. 
In  using  cut-off  terms,  the  final  volume  is  the  denominator 
and  the  cut-off  volume  is  the  numerator;  in  handling  the 
ratio  of  expansion  or  the  number  of  expansions  which  is  usu- 
ally designated  by  r  and  is  a  number  greater  than  unity,  the 
final  volume  is  the  numerator  and  the  cut-off  volume  the  de- 
nominator. 

In  handling  expansions  in  non-conducting  cylinders, 
-where  the  working  medium  gets  no  heat  from  outside,  but 
expends  its  own  heat  energy  in  doing  work  with  the  piston, 
its  temperature  may  drop  inconveniently  in  expanding  down 
to  the  pressure  prevailing  in  the  space  into  which  it  exhausts. 
Furthermore,  it  will  be  apparent  that  a  lowering  of  the  final 
pressure  must  be  accompanied  with  a  less  amount  of  forward 
effort  at  the  end  of  the  stroke  than  at  the  beginning,  and  hence 
a  larger  piston-area  is  required  than  for  the  constant  value 
of  the  pressure.  This  means  a  bulkier  and  probably  heavier 
engine,  and  more  fly-wheel  mass  to  compensate  the  irregular 
effort.    It  will  be  seen,  therefore,  that  it  may  not  be  desirable 


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ELASTIC  HEAT  AfEDIA    IN  NEAT-ENGINES, 


235 


to  carry  the  lowering  of  pressure  to  the  practicable  limit  in 
actual  cases.  This  further  opens  the  question  of  the  consid- 
erable potential  energy  rejected  from  a  heat-motor  with  its 
rejected  medium,  because  of  the  impossibility  of  capturing  it 
for  use.  These  will  be  referred  to  later  in  a  different  con- 
nection. 

165.  Work  of  a  pv  Diagram  Represented  by  an  Area. 
— It  has  been  already  said  that  the  work  of  a  piston-engine 
could  be  represented  by  the  area  of  a  diagram  (§  7).  Let 
Fig.  61  represent   such   a  pv   diagram,  in  which  z/,  is   the 


p 

—  1 f- 

--T-T- 

_5_^._ 

10 

A 

1      I 

I1r| 

,    1    j 

0 

\ 

\l 

1       > 
>       i 

!    1   1 

'0 

*—- i;i- 

1 

i^^>^ 
J 

■*" 

"    *2 

^ 

FIG.61. 
volume  filled  at  cut-off  and  v^  is  the  final  volume,  while  the 
vertical  ordinates  reproduce  the  pressures  prevailing  at  each 
point  of  the  piston-stroke.  If  this  is  a  pv  diagram  from  an 
actual  engine  v  while  variable  is  yet  known,  and  the  problem 
resolves  itself  into  finding  a  value  for  the  varying  /  which 
shall  be  a  mean  value  for  that  stroke,  whereby  the  effort  of 
the  medium  can  be  equated  to  the  mean  value  of  the  resist- 
ance during  the  same  period.  The  inequalities  of  the  varying 
value  for  /  in  each  stroke  can  be  provided  for  by  the  fly- 
wheel, and  must  be  so  taken  care  of.  If  the  mean  value  of 
/  is  too  small,  the  engine  will  slow  down  until  the  dimin- 
ished distance  through  which  the  resistance  is  moved  restores 
equilibrium.  If  /  is  too  large  for  the  mean  resistance,  the 
-engine' accelerates  its  speed  until  the  greater  space  per  min- 


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236  HEAT  AND    HEAT-ENGINES. 

ute  for  the  resistance  balances  the  excess  of  effort,  or  the 
internal  resistances  of  the  motor  itself  supply  the  excess  of 
resistance.  It  is  from  the  governor  of  the  engine  that  a 
proper  control  of  the  mean  effort  must  be  expected. 

The  area  of  the  pv  diagram,  as  determined  by  observa- 
tion or  otherwise  as  to  its  bounding  curves,  will  give  a  figure 
expressing  a  number  of  square  inches  or  square  feet.  If  this 
number  be  divided  by  the  measured  length,  the  quotient  will 
be  the  height  of  an  equivalent  rectangle  having  the  same 
length.  This  value  for  the  mean  pressure  (called/  )  can  be 
substituted  in  the  formula, 

„p^KLAN_ 

33000 

in  which  A^  L,  and  -A^  are  taken  from  the  actual  case. 

The  area  of  the  pv  diagram  can  be  found  by  dividing  it 
lengthwise  into  conveniently  short  portions,  and  taking  the 
area  of  each  portion  and  making  a  summation  of  the  frac- 
tional areas.  If  the  number  of  areas  be  made  ten,  their 
bases  being  of  equal  length,  the  sum  of  their  mean  heights 
divided  by  ten  (displacing  the  decimal  point  one  place  to  the 
left),  gives  the  mean  height  of  the  diagram  as  a  whole.  If  a 
planimeter  is  at  hand,  the  area  is  determined  directly  within 
the  error  of  that  instrument. 

To  apply  Simpson's  rule  for  determining  an  area  the  dia- 
gram is  divided  vertically  by  n  ordinates.  The  first  one  is 
called  p^  and  the  last  one  /«.  Then  the  area  A  is  given  by 
the  formula: 

A  =  ^/(-— ^"  +  A  +/,•••  -A-.). 

when  /  is  the  measured  length.  Dividing  this  area  by  the 
length  /,  the  mean  pressure/    results;  or. 


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ELASTIC  HE  A  T  MEDIA    IX  HE  A  T-EXGIXES. 


237 


If  the  expulsion  of  the  working  medium  used  in  the  pre* 
ceding  stroke  exerts  a  negative  pressure  upon  the  piston  on 
its  working  stroke,  then  the  pressure  ordinates  cannot  be 
measured  from  a  zero  line  of  no  pressure.  The  working  dia- 
gram representing  the  effective  pv  area  is  displaced  up- 
ward above  the  horizontal  reference  line  of  zero  pressure 
(Fig.  62).     The  value  of  that  constant  back  pressure/,  must 


1 

1 
1 
•1 

1 
1 

D 

^v.C 

>^ 

1       f. 

0 

<• — ■'—--% — 

1                     V 
1 
>\ 

Fig.  63. 
be  subtracted  from  the  mean  forward  pressure/^,  making  the 
effective  pressure  p^  =  pm  —  A*  O*"  ^^^  subtraction  may  be 
made  by  scaling  the  values  for /^  to/„  from  the  back-pressure 
line  instead  of  the  zero-pressure  line.  The  planimeter  also 
gives  p^  directly. 

It  is  apparent  that  the  steam-engine  indicator  draws  a 
pv  diagram  from  which  the  mean  effective  pressure  usually 
designated  M.E.P.  is  one  of  the  primary  deductions.  A 
calibrated  spring  equilibrating  the  pressure  in  the  cylinder 
against  a  piston  of  known  area  can  be  made  to  compel  a 
pencil  or  tracing-point  to  draw  a  diagram  giving  the  values 
lor p  and/,  at  each  point  of  the  stroke  of  the  engine-piston. 

166.  Work  of  an  Elastic  Heat  Medium  Expanding  Iso- 
thermally. — The  foregoing  discussion  applies  to  ^ny  pv  dia- 
gram bounded  by  any  curves.  If  the  special  case  be  assumed 
of  an  expansion  according  to  the  isothermal  law  in  a  cylinder 
of  highly  conducting  material  through  which  heat  from  outside 


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238 


HE  A  7^  AND    HEAT-ENGINES, 


may  be  supplied  to  the  working  medium  as  it  requires  it  ii> 
expanding,  certain  simple  rules  of  procedure  derived  from  the 
calculus  enable  the  area  of  the  pv  diagram  or  the  mean 
pressure  /„  to  be  foretold  when  the  value  of  the  initial  pres- 

sure  is  given,  and  the  ratio  — . 

In  Fig.  63  the  total  work  represented  by  the  diagram  is 
the  sum  of  the  areas  of  the  rectangle  ABCD  equal  to  /,?',, 
and  the  curved  portion  BEC  bounded  on  its  upper  side  by  an 


equilateral  hyperbola  BE,  if  the  expansion-curve  is  an  iso- 
thermal curve  in  which  p^i\  ^=  p^v^.  The  work  W^  of  the 
rectangular  part  is  obviously  p^v^.  The  work  IV^  of  the 
hyperbolic  part  will  be  expressed  by  the  differential  equation. 


VV,  =    /    pdv  =  p,v,   /    ^, 


since  p^v^  =  pv,  and  p^v^  is  not  a  variable. 

The  integration  of  that  expression  by  the  methods  of  the 
calculus  between  the  limits  v^  and  v^  gives 

W^  =  A^^  l^yp-  log  ^'.  —  A^i  hyp.  log  z/,; 
or 

W^  =  A^'i  hyp.  log  — . 


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ELASTIC  HEAT  MEDIA    IN  HEAT-ENGINES,  229- 

The  total  work  is  the  sum  of  the  two  portions: 

W^t  +  ^.  =  P^^^  +  A^i  hyp.  log  ^ 

=  A^'i(i  +  hyp.  log  r), 

,  .       ,  ...  v^ 

since  the  ratio  of  expansion  r  is  the  same  as  — . 

If  the  foregoing  expression  for  work  is  the  area  of  the 
/fv  diagram,  the  mean  value  for  /,^  will  be  found  by  divid- 
ing through  both  members  by  z/„  the  known  length  of  the 
stroke  or  final  volume  of  the  cylinder.      Hence 

But 

v^       r  * 
Hence,  the  mean  pressure  becomes 

_   ^/^i  +  hyp,  log  r^ 

from  which  the  pressure  to  be  inserted  in  the  horse-power 
formula  can  be  calculated  from  any  assumed  initial  pressure 
in  boiler  or  pressure  reservoir,  when  the  effects  of  clearance 
and  compression  are  not  considered,  and  the  expansion  is 
isothermal.  If  there  is  a  back  pressure/,  it  must  be  sub- 
tracted from  p^  before  the  latter  is  inserted  in  the  horse-power 
formula, 

33000 

because/^  is  the  gross  effective  mean  pressure  counted  from 
lines  of  zero  pressure. 

167.  Work  of  an  Elastic  Heat  Medium  Expanding: 
Adiabatically. — In  the  foregoing  paragraph,  where  the  final 


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240  HEAT  AND   H^AT-ENGINES. 

State  of  the  medium  as  respects  heat  energy  was  the  same  as 
the  initial  state,  by  the  supply  of  the  necessary  heat  to  the 
expanding  medium  through  a  conducting  cylinder  wall  by  a 
hot  jacket  or  otherwise,  the  external  work  was  all  done  by 
the  applied  heat.  This  is  obvious  for  the  admission  stage 
/jZ/j,  and  is  made  clear  for  the  expansion  stage  by  considering 
that  the  final  pressure  and  temperature  are  no  less  than  they 
would  be  if  the  piston  had  been  moved  from  outside  by  some 
force,  whereby  the  medium  expanded  doing  no  work.  Any 
work  done  by  expanding  without  such  addition  of  heat  from 
without  must  be  accompanied  by  a  fall  of  the  heat  energy 
represented  by  the  work  done  during  such  expansion.  If  the 
cylinder  is  a  non-conducting  and  non-absorbing  one  for  heat, 
and  work  is  done  during  expansion,  the  terminal  pressure 
ought  to  be  less  at  the  end  of  such  adiabatic  expansion  than 
when  the  law  pv  -=•  RT  is  true.  Hence  the  equation  of  the 
form 

P.K  =  P.K 

will  be  true,  if  n  has  a  proper  value,  greater  than  unity. 
Rankine  (**  Steam-engine,"  p.  392)  gives  for  the  exponent  a 
value  ^  when  the  initial  pressure  is  not  less  than  one  atmos- 
phere nor  more  than  twelve  atmospheres,  in  a  non-conducting 
cylinder.  For  a  jacketed  engine  with  pressure  between  30 
and  120  pounds  initial  pressure,  and  for  ratios  of  expansion 
between  4  and  16,  he  gives  a  value  of  W  for  the  exponent. 
Zeuner  considers  1.0646  nearer  than  Rankine's  value  of 
I. III. 

The  most  general  form  of  the  work-equation  is  conven- 
iently applied  in  this  case, 

,^    ,    Fadmission"!    ,    Texpansion"] Tback-pressureT 

""  L     work     J        L     work     J        |_         work         J 


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ELASTIC  HEAT  MEDIA    IN  HEAT-ENGINES.  24I 

but  since  /z/*  =  A^i"»  the  integration  of  the  expansion  work 
becomes 

-which  can  be  transformed  into 

«-.=£-![- -(in 

since 

/.«'."  =  A^.(z'.)""'  =  P^K  =  A^'.K)""'; 

whence 

This  factors  into  the  expression 

«  —  I  L         V?',/     J* 
when  /,z/,  be  added  in  the  form  of 

As  before,  the  mean  pressure  is  — ,  or 


w_M.'-^n 


^"  =  1;:  = 


or,  if  r  =  ~  =  ratio  of  expansion,  then 


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242  HEAT  AND   HEAT-ENGINES. 

since 


1=1  .„a  cr=c-r 


and 


vJvY-^         I 


The  expression  for  mean  pressure  can  be  substituted  for 
p^  in  the  horse-power  formula  for  the  work  when  expansion 
is  adiabatic,  and  the  desired  work  per  minute  or  per  stroke 
worked  out  as  before,  when  the  value  for  n  is  assumed  or  is 
known.     When  Rankine's  value  ^  is  used  for  «,  then 

/lO  I  \  lio         Q  \ 

x68.  Adiabatic  Work  in  Terms  of  Pressures. — Since 
Af .-  =  P.K,     then    ^  =  ^ 
whence  by  extracting  the  nth  root 

^.  _  (P^ 

and  by  raising  both  members  to  the  «  —  i  power, 

r  ■=  (r 

Hence  the  equation  for  work  of  expansion  of  the  preceding 
paragraph  becomes 


^>=Mj-i$y-' 


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ELASTIC  HEAT  MEDIA    IN  HEAT-ENGINES.  243 

and  adding  the  admission  work/jZ/^ , 


>-=A.+^[.-(r]. 


which  can  be  factored  into 


'^=/^.[«-(|;n. 


which  is  a  general  expression  for  the  work  of  a  stroke  with 
admission  and  adiabatic  expansion,  and  which  can  also  be 
transformed  to  express  the  work  of  compressing  adiabatically 
and  displacing  into  a  reservoir  in  air-  or  gas-compressors. 

169.  Temperature  Changes  in  Adiabatic  Expansion. — 
Since  in  adiabatic  expansion 


c^) = ©• 


V 

Multiplying  both  sides  by  —',  we  have 


But 


hence 


But  the  previous  paragraph  has  shown 


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244  ffEA  T  AND  HE  A  T-ENGINES. 

hence 


Which  can  be  substituted  in  either  of  the  previous  expres- 
sions, giving 


'^^B-L'-B 


a  convenient  transformation  for  use  in  problems  connected 
with  compression.  While  this  is  of  value  as  presenting  gen- 
eral expressions  for  the  relations  of  temperature  and  pressure 
in  the  pressure-volume  discussion,  a  more  direct  method  is 
convenient.  At  the  state  indicated  by/,  the  inherent  heat 
energy  will  be  the  product  of  the  specific  heat  by  the  ab- 
solute temperature.  This  can  be  expressed  in  foot-pounds 
for  the  volume  v^  by  multiplying  the  product  of  cT^  by  the 
factory  =  778,  and  again  by  the  number  of  pounds  required 
to  fill  the  volume  v^,  which  can  be  called  /.     Or, 

E  =  c  xJ  X  r,  X  /. 

At  the  end  of  the  expansion,  no  heat  having  been  given  out 
or  received,  but  all  heat  energy  having  been  directed  to  per- 
form external  work,  and  the  final  temperature  is  7",,  found 
from  the  preceding  relations  of  volume  or  pressure,  it  will  be 
true  that 

E^^cXjX   T,X  I, 

whence  the  work  in  expansion  becomes  the  difference  in  the 
two  states  of  energy,  or 

E,-E,=  VV,=MT,-T,), 

or  the  outer  work  in  expansion  is  proportional  to  the  differ- 
ence between  the  initial  and  final  absolute  temperatures,  as 
should  have  been  foreseen. 


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ELASTIC  HEA  T  MEDIA   IN  HEA  T^ENGINES.  245 

The  above  relation  also  indicates  how  much  heat  in  units 
must  be  withdrawn  by  artificial  refrigeration  in  compression, 
or  must  be  added  in  expansion  between  limits  of  v^  and  i\  or 
/,  and  /,  if  the  final  temperature  is  to  be  kept  the  same  as 
the  initial  temperature,  as  required  in  isothermal  conditions. 

170.  Conclusions  regarding  Isothermal  and  Adiabatic 
Expansion. — Neither  isothermal  nor  adiabatic  expansion  is 
ever  exactly  realized  in  practice,  by  reason  of  the  conducting, 
absorbing,  and  radiating  effect  of  metallic  walls  of  the  cyh'n- 
der  in  which  actual  work  is  done.  These  interchanges  take 
place  so  rapidly  that  differences  in  piston-speed  affect  the 
action  less  than  might  be  anticipated.  True  isothermal  ex- 
pansion is  not  desired  where  the  heat-carrier  is  a  hot  medium, 
because  at  the  end  of  expansion  the  gas  is  as  hot  as  it  was  at 
the  beginning,  and  this  heat  is  voided  at  the  exhaust  with 
attendant  waste  of  applied  heat.  What  is  desired  is  to  re- 
duce the  inherent  energy  in  the  medium  at  exhaust  to  its  low- 
est practicable  value. 

In  the  foregoing  discussion,  the  volume  v^  at  the  end  of 
admission  from  the  boiler  or  reservoir  of  energy  has  been  the 
quantity  assumed,  and  its  pressure  p^  given  to  it  by  heat  or 
other  source  of  energy.  Both  these  quantities  have  been 
made  arbitrary.  If  it  be  desired  to  assume  the  initial  tempera- 
ture the  initial  volume  z/,  can  be  taken  as  that  of  a  unit  of 
weight  of  the  medium,  and  filling  this  volume  at  a  calculated 
pressure  /,  belonging  to  that  state  of  the  medium.  The  work 
for  /  pounds  of  the  medium  will  be  simply  /  times  greater 
than  that  for  one  pound. 

171.  Design  of  Cylinders  for  Piston-motors. — The  fore- 
going paragraphs  lead  directly  to  the  fundamental  processes 
of  the  design  of  a  cylinder  volume  V  which  will  perform  a 
given  mechanical  work  in  foot-pounds  when  the  mean  effect- 
ive pressure  has  been  ascertained.     In  the  general  formula 

H.P.  =  ?!^ 

33000 


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246  HEAT  AND   HEAT-ENGINES, 

the  value  for  P  (when  usual  assumptions  are  made  as  to  cut- 
off) is  given  for  the  various  media  by  the  preceding  deduc- 
tions. The  horse-power  or  foot-pounds  is  given  as  a  fixed 
element  of  the  problem,  and  the  desired  number  of  traverses 
of  the  piston  is  imposed  as  a  rule  by  the  work  to  be  done. 
Hence  the  remaining  factors  to  be  worked  out  are  the  rela- 
tions of  L  \.o  A  when  their  product  LA  for  one  stroke  is 
known.  The  product  LN  is  called  the  piston-speed,  and  is 
the  aggregate  of  the  piston  travel  in  feet  per  minute.  Val- 
ues for  LN  as  a  product  will  make  a  high-speed  or  a  low- 
speed  engine  according  as 

LN  =  400  to    600  ft.  per  minute low  speed 

LN  =  600  *'     800  *'     *•        "      moderate  speed 

LN  =  800  "    1000  '*  or  over,  per  minute..  .    high  speed. 

When  the  value  for  N  indicates  a  high  or  a  mean  or  a  low 
speed,  the  relation  of  length  to  diameter  of  cylinder  is  likely 
to  be 

Stroke  =  diameter  X  ('i  or  2)  for  low  speed 
"       =        '*         X   li  "  mean    " 

''       =         '*         X   I  *'  high     *' 

Hence  from  the  relation  A  = ,   and  the    assumption 

concerning  LN,  a  value  for  L  and  for  the  cylinder  diameter 
can  be  worked  out  for  a  single-cylinder  engine.  The  cylin- 
der proportions  having  been  fixed  upon,  the  design  of  the 
valve-gear  to  give  the  required  cut-off  and  the  proportions  of 
parts  to  resist  the  dynamic  strains  belong  to  another  branch 
of  engineering  design  apart  from  the  present  purpose.  The 
questions  concerning  clearances  with  their  losses,  and  the 
economics  possible  as  affecting  wise  design,  belong  to  the 
more  advanced  treatment  of  heat-engines  in  subsequent 
chapters. 


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ELASTIC  HEAT  MEDIA    IN  HEAT-ENGINES. 


247 


These  remarks  concerning  design  apply  to  the  single  or 
simple  engine  of  a  typical  design.  But  the  engine  may  be 
compound  or  multiple-expansion;  it  may  be  rotary  instead 
of  reciprocating;  the  heat  medium  may  be  used  in  a  turbine. 
The  mechanical  features  of  these  motors  have  been  more  fully 
treated  elsewhere  than  is  here  possible,  but  some  brief  refer- 
ence is  desirable. 

172.  The  Compound  or  Multiple^expansion  Engine. — 
In  the  compound  engine  the  steam  expands  continuously  after 
admission  is  cut  off  from  the  boiler  in  the  high-pressure 
cylinder.  There  are  three  stages  of  such  expansion  in  the 
triple-expansion  engine,  and  four  stages  in  the  quadruple- 
expansion.  The  number  of  cylinders  is  not  important,  but 
the  number  of  steps  or  stages  is  the  determining  factor. 

The  diagram  of  steam  effort  in  the  Woolf  or  tandem-com- 
pound engine  (Fig.  64)  reveals  the  continuity  of  the  expan- 


Fio.  64. 


sion  in  the  two  cylinders,  and  that  the  driving  steam  of  the 
larger  or  low-pressure  cylinder  is  the  back  pressure  upon  the 
smaller  or  high-pressure  cylinder.  The  greater  area  of  the 
low-pressure  piston,  however,  secures  a  net  forward  effort. 
The  foregoing  formulae  make  it  plain  that  it  is  the  final  vol- 
ume of  the  steam  which  is  significant  as  compared  with  its 
initial  volume,  so  that  the  cylinder  design  compels  a  calcula- 
tion of  the  volume  of  the  low-pressure  cylinder  to  secure  a  re- 
quired horse-power,  and  from  accepted  relations  the  cylinder 
area  of  the  smaller  is  worked  out.     The  other  way  and  more 


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248 


HEA  T  AND   HEA  T-ENGINES. 


usual  is  to  draw  the  P.V.  diagram  for  the  desired  ratio  of  ex- 
pansion, with  the  given  initial  and  terminal  values,  and  then 


Fio.  66. 


Fig.  66. 
divide  the  area  of  that  diagram,  so  that  equal  work  will  be 
done  in  each  of  the  two  or  more  cylinders  (Figs.  65  and  66). 


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ELASTIC  HEAT  MEDIA    IN  HEAT-ENGINES, 


249 


In  the  cross-compound  or  receiver  engine  with  a  cut-off  in 
the  low-pressure  cylinder  there  will  be  an  apparent  discrep- 
ancy or  break  of  continuity  in  the  diagrams  of  effort.  This 
disappears  when  the  length  of  the  high-pressure  diagram  is 
reduced  in  proportion  to  that  of  the  low-pressure  diagram  in 
the  relation  of  the  cylinder-volumes.  That  is,  if  the  cylinders 
are  as  l  :  4  the  length  CD  of  the  high-pressure  diagram  at 
any  pressure  level  is  reduced  to  \  of  that  length  at  the  same 
level  cd  (Fig.  6^).  The  only  loss  of  area  is  from  friction  or 
condensation  or  free  expansion  into  the  receiver.     It  is  the 


loss  between  the  two  diagrams  which  the  reheater  between 
cylinders  aims  to  reduce. 

The  following  table  presents  accepted  practice  with  re- 
spect to  a  selection  of  the  grade  of  expansion  with  fixed 
boiler-pressures : 

When     the    values    for    T    are   those    which    belong     to     a 

pressure  below  80  lbs use  single  engine 

for  pressures  between  80  and  100  lbs.      **  compound  engine 
«            ii              a       130    **     160  **         '*  triple  «' 

**  **         above   170  lbs **    quadruple     ** 

Usual  cylinder-ratios  of  practice,   for   usual  pressures  with 
triple  engines,  are: 


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2 so  HEAT  AND  HEAT-ENGINES. 

Pressures.  Small.  Intermediate.  Large. 

130 I  2.25  5 

140 I  2.40  5.85 

150 I  2.55  6.90 

160 I  2,70  7.25 

170 Quadruple  engine  preferred. 

For  quadruple-expansion  engines  the  usual  ratios  of  cyl- 
inder-areas and  volumes  approximate  i  :  2  :  3.78  :  7.70, 
which  may  be  called  1:2:4:8. 

If  the  principle  be  adopted  that  the  ratios  of  areas  are  to 
be  as  the  fourth  root  of  the  number  of  expansions,  the  ratio 
of  the  first  to  the  fourth  will  be  as  the  cube  of  the  fourth  root. 
The  ratio  will  increase  as  the  initial  pressure  becomes  greater; 
e.g.,  I  :  2.2  :  4.8  :  10.6. 

Mr.  G.I.  Rockwood  has  designed  a  compound  engine  with 
a  cylinder-ratio  of  7  :  I  with  the  view  of  making  heat-range 
equal  in  the  two  cylinders,  whence  the  ratio  of  surfaces  is 
taken  account  of,  as  well  as  the  differences  in  temperature. 

The  subjects  of  the  mechanisms  of  the  compound  engine, 
arrangement  of  cylinders,  compounding  above  atmosphere, 
the  compound  locomotive,  etc.,  will  be  found  discussed  else- 
where, to  which  references  appear  in  the  Appendix. 

173.  Advantages  of  the  Compound  or  Multiple-expan- 
sion Engine. — The  principle  of  securing  expansion  by  the 
continuous  working  of  steam  in  cylinders  of  increasing  volume 
is  to  be  defended  by  reason  of  the  following  advantages: 

I.  The  high  grade  of  expansion  and  the  difference  between 
the  initial  and  final  temperature  in  the  steam  used  is  secured 
with  an  admission  of  steam  into  the  cylinder  through  a  longer 
proportion  of  the  stroke  than  in  the  single  cylinder.  It  has 
been  seen  that  the  efficiency  of  the  fluid  used  increases  with 
the  difference  in  the  initial  and  final  temperatures.  The 
work  of  the  steam  reaches  the  crank  in  angles  more  favorable 
to  produce  rotation. 


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ELASTIC  HEAT  MEDIA    IN  HEAT- ENGINES,  2$ I 

2.  With  the  terminal  temperature  at  exhaust  fixed  by  the 
temperature  possible  with  the  mtans  used  to  condense  the 
steam,  the  compound  principle  enables  higher  pressures  to  be 
used  in  the  boilers  as  initial  pressures  in  the  cylinder.  To 
increase  the  pressures  in  the  boilers  is  to  carry  more  stored 
energy  in  a  given  space ;  to  use  higher  pressures  is  to  enable 
each  cubic  foot  or  pound  of  steam  to  carry  more  energy  into 
the  engine-cylinder,  and  the  given  quantity  of  heat  raises  the 
pressure  of  steam  more  rapidly  after  the  steam  has  become  a 
complete  gas  than  it  does  at  lower  pressures,  when  a  large 
part  of  the  heat  is  absorbed  in  changing  the  molecular  condi- 
tion of  the  water. 

3.  By  receiving  the  high-pressure  steam  from  the  boiler 
first  upon  a  cylinder  of  small  area,  as  in  the  compound  en- 
gine, the  strain  upon  the  mechanism  at  the  joints  and  moving 
members  is  less  than  if  that  same  pressure  had  to  be  received 
at  the  beginning  of  a  stroke  in  a  cylinder,  and  against  a  pis- 
ton of  a  large  diameter.  Less  loss  from  friction  also  follows 
during  the  less  effective  angles  of^the  stroke. 

4.  From  the  longer  period  of  admission  discussed  in  num- 
ber one  above,  it  follows  that  a  more  advantageous  arrange- 
ment for  admitting  and  cutting  off  the  steam  becomes  possi- 
ble. With  the  single  cylinder  and  early  cut-off  in  it,  the 
openings  to  admit  steam  would  have  to  be  closed  so  early 
that  it  would  be  difficult  to  admit  steam  through  wide  and 
generous  ports  or  passages.  Such  single-cylinder  valve-gear 
with  narrow  areas  for  steam  would  introduce  the  difficulty 
known  as  wire-drawing  of  the  steam.  This  is  a  phenomenon 
present  when  the  pressure  of  steam  is  reduced  by  compelling 
it  to  pass  through  a  narrow  or  constricted  opening. 

5.  With  high-pressure  steam  it  is  difficult,  both  by  reason 
of  changes  of  shape  due  to  heat  and  by  reason  of  the  pres- 
sure itself,  to  make  the  valves  controlling  the  admission  of 
steam  so  that  they  shall  be  and  remain  tight.  In  the  com- 
pound engine  the  steam  which  leaks  past  the  valve  of  the  first 


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252  HEAT  AND   HEAT-ENGINES. 

or  high-pressure  cylinder  does  not  leak  into  the  air  or  con- 
denser, but  into  a  later  cylinder  in  the  chain  in  which  it 
expands  and  does  work. 

6.  If  by  reason  of  doing  work  in  expanding  there  is  a- 
transformation  of  heat  into  work  which  must  be  compensated 
by  a  condensation  of  the  steam  in  the  first  cylinder,  that 
water  reheated  and  expanding  at  the  lower  temperature  does 
work  in  the  later  cylinder  of  the  chain  instead  of  escaping 
unutilized  through  the  exhaust. 

7.  In  those  forms  of  the  compound  engine  in  which  the 
work  of  the  several  cylinders  reaches  the  crank-shaft  each 
through  its  own  crank-pin,  there  is  the  advantage  of  such  dis- 
tribution, for  this  avoids  the  concentration  for  large  engines 
of  great  energy  on  small  areas,  and  enables  designers  to  avoid 
either  excessive  lengths  or  inconvenient  diameters  for  their 
crank-pins.  When  the  crank-pin  becomes  of  inconvenient 
diameter  with  respect  to  the  length  of  the  crank,  the  angle 
during  which  the  pressure  of  steam  is  available  to  produce 
rotation  of  the  crank  is  diminished. 

8.  The  turning  effort  is  equalized  when  the  compound 
engine  is  arranged  to  have  its  cranks  quartering.  This 
diminishes  the  weight  of  the  fly-wheel. 

9.  The  compound  engine  gives  an  opportunity  to  im» 
prove  the  quality  of  the  steam  during  the  process  of  expan- 
sion when  it  is  possible  to  use  a  reheater. 

ID.  The  clearance- volumes  of  the  small-diameter  cylinder 
carry  less  steam  by  weight  than  if  the  steam  had  to  fill  the 
clearance- volume  of  the  large  cylinder.  The  steam  in  these 
clearance-volumes  is  also  used  expansively  in  the  later  cylin- 
der, instead  of  being  rejected,  as  would  be  the  case  in  the 
single  cylinder. 

11.  The  hottest  steam  is  used  in  the  cylinder  of  the  small- 
est volume,  causing  a  diminished  loss  from  radiation  and  con- 
densation due  to  cool  external  air. 

12.  In  the  compound  locomotive  the  less  terminal  pres- 


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ELASTIC  HEAT  MEDIA    IN  HEAT-ENGINES.  253 

sure  gives  less  violence  to  the  escape  of  the  exhaust  which 
induces  the  draft  through  the  fire-box.  The  fire  is  pulled 
about  less. 

13.  The  greatest  advantage  incident  to  the  use  of  the 
principle  of  continuous  expansion  in  several  cylinders  is  that 
thereby  the  range  of  temperature  between  the  initial  and  final 
states  of  that  cylinder  is  less  than  it  would  have  to  be  if  the 
expansion  were  in  the  one  cylinder  only.  The  law  of  trans- 
fer of  heat  from  one  body  to  another  is  that  the  transfer  is 
rapid  in  proportion  as  the  difference  in  temperature  is  greater. 
The  less  the  temperature  between  the  incoming  and  outgoing 
steam  in  any  cylinder,  the  less  condensation  occurs  when  the 
hot  steam  enters.  This  is  a  particularly  favorable  condition 
for  the  large  and  low-pressure  cylinder,  whose  ends  are  alter- 
nately open  to  the  comparatively  low  temperature  of  steam 
as  it  is  escaping  into  the  condenser.  It  is  of  great  advantage 
that  the  high-temperature  steam  fresh  from  the  boiler  should 
not  have  to  meet  the  relatively  cool  metal  and  large  surface 
of  this  low-pressure  cylinder. 

174.  Disadvantages  of  the  Compound  Engine  — When 
it  is  recalled  that  the  low-pressure  cylinder  is  the  fundamental 
unit,  and  determines  the  working  capacity  of  the  compound 
engine,  it  is  apparent  that  by  introducing  the  other  cylinders 
in  the  multiple-expansion  type  certain  disadvantages  are  intro- 
duced.    These  are: 

1.  The  cost  of  the  cylinders  other  than  the  low.  This 
may  mean  in  tandem  engines  the  cost  of  piston  and  cylinder 
with  additional  rod,  but  in  cross-compound  and  fore-and-aft 
engines  it  means  an  additional  cost  of  practically  another 
engine  with  crank,  connecting-rod,  cross-head,  and  the  like. 

2.  The  weight  and  bulk  of  the  additional  cylinder  adding 
to  foundations  and  taking  up  valuable  space. 

3.  The  friction-loss  due  to  the  work  absorbed  by  this 
extra  cylinder  in  operating  its  mechanism,  valve,  and  the 
like. 


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254  HEAT  AND   HEAT-ENGINES. 

4.  The  loss  by  radiation  of  heat  from  the  surface  of  the 
extra  cylinder  and  valve-chest,  which  are  surfaces  exposed 
to  the  air. 

5.  The  loss  of  work  due  to  the  difficulties  represented  by 
lost  area  in  the  work-diagram  from  friction,  free  expansion, 
condensation,  and  the  like.  The  single-engine  diagram,  get- 
ting the  same  grade  of  expansion  in  the  same  cylinder,  would 
not  experience  this. 

6.  The  difficulty  connected  with  regulating  the  power  of 
the  engine  when  the  work  varies  widely,  and  the  first  cylinder 
has  measured  oil  a  volume  of  steam  adapted  to  a  resistance 
different  from  that  upon  the  engine  when  that  volume  of 
steam  reaches  the  later  cylinders.  This  is  the  difficulty  of 
regulating  the  multiple-expansion  engine,  except  by  regu- 
lating devices  operating  upon  each  cylinder  independently. 

7.  There  has  been  considerable  trouble  in  compound  en- 
gines from  the  accumulation  of  water  in  the  low-pressure  cyl- 
inders, particularly  when  compounding  above  the  atmosphere 
and  using  wet  steam.  The  wide  range  of  expansion,  the  low- 
ered terminal  pressure,  and  the  large  diameter  of  the  low- 
pressure  cylinder  have  made  this  difficulty  a  very  trouble- 
some one  in  locomotive  practice. 

8.  In  compound  locomotives,  the  terminal  pressure  may 
not  be  high  enough  to  give  intensity  to  the  draft  in  the  stack 
sufficient  to  keep  the  engine  steaming  freely. 

It  is  very  obvious  that  the  weight  to  be  attached  to  the 
above  objections  is  not  considered  by  most  designers  to  be 
great  enough  to  overbalance  the  advantages  which  follow 
from  the  principle  of  compounding. 

175.  Design  of  the  Rotary  Engine. — In  the  rotary  en- 
gine, a  series  of  pistons  or  vanes  are  attached  radially  upon 
crank-arms  so  as  to  receive  the  pressure  of  the  steam  directly 
to  produce  rotation.  It  is  so  difficult  to  secure  expansive 
working  by  allowing  the  steam  admitted  to  the  cylinder  to 
lower  its  pressure  while  doing  work,  that  it  is  not  usually 


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ELASTIC  HEAT  MEDIA    IN  HEAT-ENGINES. 


255 


attempted,  and  the  foregoing  formulae  are  not  applicable. 
The  pressure  from  the  boiler  acts  upon  the  effective  area  of 
the  vane,  and  moves  it  through  a  space  in  feet  (Fig.  68). 
The  product  is  the  foot-pounds  exerted  while  that  vane  was 
in  action.  For  the  mechanisms  and  for  the  advantages 
and   disadvantages  of   the  rotary  engine,  see  the  reference 


in  the  Appendix.  A  difference  between  the  initial  and  final 
volumes  of  the  steam  in  the  machine  itself  is  only  to  be 
easily  secured  by  compounding,  or  the  use  of  engines  in  series. 
176.  The  Steam  Turbine. — The  third  type  of  motor 
which  is  used  to  avail  of  the  pressure  energy  of  an  elastic 
heat  medium  is  the  steam  turbine.  It  is  a  transfer  to  the 
field  of  the  elastic  fluids  of  the  idea  long  familiar  in  water- 


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256  HEAT  AND  HEAT•E^GlNES. 

motors  which  use  an  incompressible  medium.  The  turbine 
uses  the  impact  of  a  weight  of  fluid  having  a  velocity  due  to 
head  or  equivalent  pressure,  and  after  the  impulse  has  been 
utilized,  a  further  propelling  effect  is  sought  from  the  reac- 
tion of  the  current  of  the  fluid. 

The  low  density  of  steam  as  compared  with  water  makes 
it  difficult  to  secure  a  high  value  for  the  unit  of  effort  upon 
the  bucket  of  the  steam  turbine;  the  best  results  along  this 
line  are  secured  by  using  a  considerable  number  of  jets  of 
steam.  On  the  other  hand,  if  it  be  conceded  (as  can  be 
proved)  that  the  best  result  is  obtained  when  the  velocity  of 
the  jet  is  twice  that  of  the  surface  receiving  its  impulse,  or 
when  the  circumference  of  the  wheel  is  moving  tangentially 
with  half  the  velocity  of  the  steam  at  the  nozzle,  the  wheel 
has  to  have  so  high  a  velocity  that  it  is  not  easy  to  resist  the 
centrifugal  effort  of  the  outer  elements  of  the  wheel  itself. 
For  example,  if  the  steam  issue  from  the  nozzle  at  a  pressure 
of  140  pounds,  it  has  a  velocity  of  upwards  of  2000  feet  per 
second.  This  follows  because  v  =  V2^/i  and  A  =  (140  X 
144)  X  0.3148,  the  latter  being  the  weight  of  a  cubic  foot  of 
steam  at  that  pressure.  Solving  when  A  =  64,000  feet,  v 
becomes  2030  feet  per  second. 

This  linear  velocity  at  the  circumference  compels  a  rota- 
tive speed  of  many  thousand  revolutions  per  minute  for  the 
turbine  wheel  proper,  which  has  to  be  of  small  diameter  to 
withstand  the  centrifugal  strain,  and  therefore  a  reducing  train 
to  bring  the  speed  to  limits  which  are  convenient  and  usual. 
On  the  other  hand,  where  high  rotative  speed  is  no  disadvan- 
tage, as  in  driving  of  dynamo-armatures  or  specially  designed 
propeller-wheels,  the  turbine  is  the  most  compact  and  light- 
est of  motors. 

The  mechanical  principle  underlying  the  motors  of  this 
class  is  that  the  energy  imparted  to  the  wheel  will  be  the 
difference  between  the  moments  of  the  living  force  of  the 
mass  of  the  fluid  upon  entering  and  leaving  the  wheel,  mul- 


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ELASTIC  HEAT  MEDIA   IN  HEAT-ENGINES.  257 

tiplied  by  the  angular  velocity  of  the  wheel.  That  is,  if  x  be 
the  tangential  velocity  of  the  jet,  and  u  be  the  less  tangen- 
tial velocity  of  the  buckets,  the  work  per  second  will  be 

Work  per  second  =  M{x  —  «)«, 

when  iW  =  —  is  the  mass  passing  the  nozzles  in  one  second, 

and  u  =  cor.  If  the  steam  left  the  wheel  without  velocity 
relatively  to  the  direction  of  its  effort,  the  work  per  second 
per  pound  would  be: 

Work  per  second  per  pound  =  — , 

when  the  velocity  of  the  rim  is  known.  If  the  weight  in 
pounds  of  steam  is  known  which  flows  per  second  {w)  and  the 
work  per  second  per  pound  is 

then  the  horse-power  per  minute  becomes 

zvU  X  60 


H.P.  = 


33000 


The  outward-flow  turbine  (Dow  type)  permits  the  range  of 
pressure  to  occur  within  the  arm,  so  that  at  the  issue-point 
the  steam  has  expanded  to  atmospheric  pressure  or  nearly  so, 
leaving  only  energy  and  velocity  enough  to  free  itself  from 
the  wheel.  The  same  is  secured  in  Parsons  and  Curtis  tur- 
bines by  the  principle  of  compounding,  whereby  successive 
increase  in  volume  results  in  the  lowering  of  pressure.  In 
the  De  Laval  turbine  the  expansion  occurs  in  the  nozzle  itself 
by  the  changes  in  its  cross-section. 

Figs.  69a:,  69^,  and  70  show  typical  sections  of  steam-tur- 
bines   selected   from    outward-flow    and   tangential    impulse 


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HKA  T  AND  HEA  T-ENGINES. 


Fig.  G96. 


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ELASTIC  HEAT  MEDIA   IN  HEAT-ENGINES. 


259 


types.  The  high  speeds  compel  the  greatest  care  in  balancing 
and  in  the  construction  of  the  bucket  detail.  Where  it  can 
be  done,  the  plan  of  mounting  the  axis  of  the  turbine  verti- 


cally avoids  the  disturbance  of  balance  from  its  own  weight. 
Excellent  results  have  been  secured  by  the  use  of  an  annular 
jet  around  a  fine  central  needle  in  a  small  nozzle. 


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CHAPTER    XIII. 
MECHANICAL  COMPRESSION  OF  HEAT  MEDIA. 

l8o.  Introductory. — It  will  be  at  once  apparent  that  in 
the  case  of  permanent  gases  or  heat  media  within  the  usual 
limits  of  pressures,  it  is  easily  possible  to  invert  the  formu- 
lae for  expansion  and  so  express  the  changes  when  a  heat 
medium  has  outer  work  exerted  upon  it  to  produce  those 
changes  in  its  heat  condition  which  must  follow  its  subjection 
to  such  external  force.  When  such  changes  are  studied 
upon  the  pressure-volume  plane  the  diagram  of  pressures  is 
traced  in  reverse  direction,  or  contrary  to  that  of  the  hands  of 
the  clock  in  the  previous  right-hand  diagrams.  When  this  is 
done  with  air  or  gas  as  a  medium,  the  machine  is  called  an 
air-  or  a  gas-compressor.  The  compressor  is  a  heat  force- 
pump,  raising  a  weight  of  air  to  a  higher  heat  condition  by 
converting  external  work  into  heat.  The  blowing  engine 
differs  from  the  compressor  only  by  having  a  low  ratio  be- 
tween final  and  initial  pressures  of  the  medium,  and  usually 
also  by  being  adapted  to  handle  large  volumes  of  air. 

i8i.  The  Air-compressor,  with  Pressures  Given. — The 
air-compressor  problem  in  practice  usually  requires  that  air 
shall  be  taken  into  the  cylinder  at  a  pressure  (/,)  of  the 
atmosphere  or  nearly,  and  that  a  volume  per  stroke  (z/,)  of  air 
at  this  pressure  shall  be  compressed  to  a  higher  pressure  (/,). 
This  will  be  accomplished  by  reducing  its  volume  to  (2',)  cor- 
responding to  that  higher  pressure,  when  the  valves  leading 
to  a  receiver  will  be  opened  by  the  pressure  in  the  cylinder, 

260 


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MECHANICAL   COMPRESSION  OF  HEAT  MEDIA.        261 

and  the  compressed  air  without  increase  of  pressure  or  tem- 
perature will  be  fofced  out  into  the  receiver.  If  the  air  un- 
dergoing compression  is  cooled  by  water-jacketing  or  by  injec- 
tion of  water,  the  compression  may  be  isothermal.  As  a 
rule,  however,  by  reason  of  the  short  time  allowed  for  the 
compression  and  the  slowness  of  transfer  in  air,  the  compres- 
sion is  practically  adiabatic,  and  the  air  is  warm  or  hot  as  ic 
leaves  the  compressor.  If  the  air  is  only  compressed  to  re- 
ceiver pressure,  at  the  end  of  the  piston  traverse,  the  valves 
will  not  open  to  discharge  the  air,  and  consequently  on  the 
return  traverse  the  compressed  air  in  clearances  will  simply 
expand  down  to  atmospheric  pressure  (^,)  like  a  spring  and 
no  fresh  charge  will  be  taken  in.  It  will  be  apparent,  there- 
fore, that  clearance  volumes  are  of  significant  detriment  in  air 
compressing,  and  the  higher  the  pressure  above  atmosphere, 
the  worse  the  loss  which  they  occasion. 

The  formulae  of  §  167  are  therefore  directly  applicable, 
provided  the  direction  of  the  process  be  reversed,  in  the  dia- 
gram representing  the  cycle.  The  total  work  of  one  stroke 
will  be  made  up  of: 

Yv     L-  —  i  compression  )    i    j  displacement )  _   ( inlet  back- 
^^     ""   (         work        )         I         work         )         (    pressure 

W=  W,  +  W^  ^  Wi 

W,=  jpdv 

n  —  iLV,/  J 

which  can  be  transformed  as  in  §  168  to 


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262  HEAT  AND   HEAT-ENGINES. 

The  work  of  displacement 

by  using  the  same  methods  as  in  the  foregoing  expansion  dis- 
cussion, since 

A 
A 


0.         \J    ' 


V 

by  multiplying  both  members  by  —  we  have 


whence 


A^.=A^.^)"   =a4|;)". 
The  compressing  cycle  work  is  therefore 

which  factors  into 

»'=^[(r-']- 

This  has  been  made  intentionally  to  differ  from  the  form 
of  the  statement  for  expansion  work  (§  167),  inasmuch  as  in 
expansion  the  back-pressure  line  does  not  necessarily  coincide 
with  the  end  of  the  expansion  line,  and  to  introduce  another 
pressure  value  not  related  to  the  rest  of  the  factors  would  be 
to  complicate  the  computations.  In  compression,  however, 
the  initial  pressure  is  the  same  as  the  terminal  pressure  for 
the  intake  stroke. 


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MECHANICAL    COMPRESSION  OF  HEAT  MEDIA.        263 

182.  The  Air-compressor  with  Volumes  given. — If  the 

volume  of  compressed  air  should  be  given,  or  the  volume  at 
atmospheric  pressure,  the  relations  between  pressures,  vol- 
umes, and  temperatures  given  in  §§  167  and  168  enable  easy 
substitutions  to  be  made.     In  adiabatic  changes 

in  which  r  expresses  the  relation  between  the  less  and  greater 
pressures,  and  the  greater  and  the  less  volume.  The  relation 
shows  how  the  temperatures  absolute  will  change  as  external 
work  is  done  upon  the  air,  and  also  how  much  heat  must  be 
abstracted  if  the  compression  is  to  be  kept  isothermal  and  the 
air  to  be  at  the  same  temperature  in  the  receiver  as  in  the 
outer  air.  The  table  on  page  264  gives  data  of  interest  as 
to  the  rise  in  temperature  for  air. 

183.  Value  of  the  Factor  n  in  Air-compressing:. — The 
exponent  n  of  an  adiabatic  expansion  and  compression  of  air 
or  other  non-condensable  gases  will  be  the  ratio  between  the 
specific  heat  of  the  gas  at  constant  volume  and  the  specific 
heat  at  constant  pressure;  i.e. : 

For  air,  when  C^  =  .238  and  C^  =  .168 

238 

The  heat  required  to  raise  a  unit  weight  one  degree  at  con- 
stant pressure  will  be  obviously  the  greater  since  the  expand- 
ing air  is  overcoming  the  outer  pressure  on  it  as  it  increases 
in  energy  but  does  not  increase  in  pressure.  The  difference 
C^  —  C,  will  denote  the  amount  of  heat  corresponding  to 
overcoming  the  pressure/,  when  a  volume  ^,  of  air  at  zero 
degrees  is  heated  one  degree. 


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264 


HEAT  AND   HEAT-ENGINES, 


One  hundred  volumes  of  dry  air  at  mean  atmospheric  pressure  of  14.7 
pounds  per  square  inch  and  a  Fahrenheit  temperature  of  60*  (15.5  C.)when 
compressed  without  withdrawal  of  heat  will  have  the  temperatures  centi- 
grade given  in  column  2  of  the  following  table,  and  the  volumes  given  in 
column  3  for  that  pressure.  If  the  compression  is  isothermal  so  that  the 
temperature  is  kept  at  60"  F.  or  15.5  C,  the  volumes  will  be  as  in  column  5. 
(Thurston,  Journ,  Frank.  Inst.,  1884.) 


Pressure 

Temperature 

Volume  of 

Temperature 

Volume  if 

Absolute, 

Centigrrade 

Temperature 
and  Pressure 

Temperature  had 

Pounds  per 

at  end  of 

V  ciiir  cnnciL 
Corresponding. 

remained  constant 

Square  Inch. 

Compression. 

Preceding. 

at  ,5.5**  C. 

' 

2 

3 

4 

5 

14-7 
15 

15.5 
17.26 

100. 0 

60 

• 

98.58 

63 

98.00 

20 

42.60 

80.36 

108 

73- 50 

25 

64.76 

68.59 

149 

58.80 

30 

82.10 

60.27 

180 

49.00 

35 

98.38 

54-01 

208 

42.00 

40 

113.86 

49.13 

237 

36.75 

45 

126.54 

45.18 

259 

32.67 

50 

138.96 

41.93 

282 

29.40 

55 

150.53 

39-19 

303 

26.73 

60 

161.38 

36.84 

322 

24.50 

65 

171. 61 

34.80 

340 

22.62 

70 

181.29 

33.02 

357 

21.00 

75 

190.49 

31.44 

375 

19.60 

80 

199.26 

30.03 

391 

18. 3S 

85 

207.66 

28.77 

405 

17.29 

90 

214.71 

27.62 

418 

16.33 

95 

223.25 

26.58 

434 

15.47 

100 

230.91 

25.63 

447 

14.70 

125 

264.66 

21.88 

508 

11.76 

150 

293.91 

19.22 

561 

9.80 

175 

319.87 

17.23 

608 

8.40 

200 

34331 

15.67 

649 

7.35 

225 

364.71 

14.41 

687 

6.53 

250 

411.57 

13.38 

772 

5.88 

300 

420.34 

11-75 

788 

4.90 

400 

480. 76 

9.58 

896 

3.90 

500 

531.21 

8.17 

986 

.       2.94 

600 

574.93 

7.18 

1065 

2.45 

700 

603.74 

6.44 

1117 

2.10 

800 

648 . 80 

5.86 

1200 

1.84 

900 

680.86 

5-39 

1256 

1.63 

1000 

710.49 

5.00 

1310 

1-47 

•    2000 

929.67 

3.06 

1706 

0.74 

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MECHANICAL   COMPRESSION  OF  HEAT  MEDIA.        265 

But  it  has  been  already  seen  (§§  107  and  115)  that 

or  that 

p,v,  =  RT,. 

Hence  it  follows  (see  §116)  that 

JiC,  -  Q=  R. 

From  which,  if  the  other  quantities  have  been  observed,  the 
value  of  the  mechanical  equivalent  can  be  calculated  in  ad- 
vance of  experiment.  When  densities  are  known,  for  any 
standard  temperature,  R  can  be  calculated  for  any  gas,  since 


because  the  weight  of  a  unit  cubic  volume  is  by  definition  its 
specific  gravity.     (See  §  107). 

This  enables  a  usual  transformation  of  the  equation  for 
work  to  be  made.     For  since 

Cf-  C,  =  CXn  —  i), 
R 


"""^JC," 


hence  (§  167) 


«'=^^-(-  -w-^ 


when  there  is  no  work  of  admission. 

184.  Mean  Pressure  in  the  Compressing-cylinder. — If 
the  work  of  the  compressing-cylinder  be  given  by  a/,z/i  prod- 
uct, which  can  be  represented  by  an  area,  the  mean  pressure 
will  be  the  height  of  a  rectangle  whose  base  is  the  final  vol- 


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266  HEA  T  AND   HEA  T-ENGINES. 

ume.     Hence  the  mean  pressure  will  result  if  the  equation 
for  W  be  divided  by  v^.     This  makes  (§  i8o) 

Mean  effective  pressure  =  —^ —    f— J      —  i    • 

If  the  compressor  is  a  steam-machine,  the  mean  effective 
pressure  in  the  steam-cylinder  must  be  enough  greater  than 
this  to  overcome  the  frictional  resistances  at  bearings, 
guides,  stuffing-boxes,  etc.,  and  to  overcome  the  friction  in 
the  cylinders  from  packing-rings,  valves,  and  the  like,  and 
the  fly-wheel  must  be  able  to  equalize  effort  and  resistance  by 
its  stored  energy  when  these  are  unequal  at  different  parts  of 
the  stroke. 

185.  Isothermal  Compression. — The  formula  for  isother- 
mal expansion  (§  166)  and  for  mean  pressure  for  such  expan- 
sion are  the  same  for  compression,  with  proper  changes  in 
the  letters  for  volumes  and  pressures.     The  formula  becomes 

jr  =  /,z;,  +  /  pdv  =p,v^  +  p,v^  Nap.  log  ^ 

=  A^i[i  +  Nap.  log^J, 

and  the  mean  pressure  as  before  is  found  by  dividing  by  the 
length  or  volume  v^ ;  or 


M 


E.P.  ==/,[i  +  Nap.log!i]. 


When  this  is  compared  with  the  work  and  M.E.P.  in  adi- 
abatic  compression,  it  will  be  found  that  isothermal  compres- 
sion requires  less  work  than  adiabatic  compression  between 
the  same  pressures,  but  a  less  volume  is  displaced  into  the 
receiver  because  of  the  reduction  of  volume  resulting  from 
the  abstraction  of  the  heat  of  the  compression,  which  is  made 
to  disappear  by  the  cooling  and  is  lost.  That  is,  if  Fig.  75 
represents  by  its  curve  of  compression  ia  the  path  of  the 


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MECHANICAL    COMPRESSION  OF  HEAT  MEDIA.       267 

pressure-volume  relation  in  adiabatic  compression,  and  by  its 
curve  is  the  path  of  isothermal  compression,  there  is  a  waste 
of  power  in  adiabatic  compression  represented  by  the  shaded 
area  isa  as  compared  with  isothermal,  when  both  compres- 
sions start  from  atmospheric  pressure  and  temperature  at  c.  If 
the  air  cools  down  from  the  higher  temperature  belonging  to 
the  adiabatic  point  a  to  the  atmospheric  pressure  in  pipes  and 
reservoirs  so  as  to  have  a  volume  represented  by  es  instead 


Fig.  75. 


of  ea^  the  adiabatic  compression  will  suffer  a  further  loss  when 
the  air  comes  to  expand  from  the  volume  es  back  to  atmos« 
pheric  pressure  in  a  proper  air-engine  (Chapter  XVIII).  The 
expansion,  if  adiabatic  and  starting  from  j,  will  end  at  a  point 
d^  while,  if  isothermal,  would  return  to  i.  Hence  the  area 
between  the  bounding  curves  sd  and  ai  will  represent  the 
waste  of  power  if  the  compression  were  adiabatic  as  well  as 
the  expansion.  If  the  compression  were  isothermal,  the  loss 
would  be  only  the  area  isd.  If  the  expansion  could  be  also 
isothermal,  there  would  be  no  loss  in  the  reversible  process 
outside  of  pipe  friction  (see  further,  Chapter  XVIII). 

186.  Effect  of  Clearance  in  Compressing-cylinders. — It 
has  been  already  said  (§  181)  that  any  air  remaining  behind  in 
a  compressing-cylinder,  between  piston-head  and  valves,  will 
expand  on  the  return  or  inlet  stroke,  preventing  early  opening 
of  the  inlet  valves  or  any  flow  of  air  into  the  cylinder,  until 


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268 


HEAT  AND   HEAT-ENGINES. 


the  pressure  of  that  imprisoned  air  falls  below  that  outside 
which  acts  on  the  inlet  valves  to  open  them.  The  effect  of 
this  expanding  air  is  to  help  the  working  stroke  at  the  start, 
by  acting  as  a  cushion  or  spring,  but  the  harmful  effect  is  to 
increase  the  size  of  cylinder  required  for  a  certain  net  output 
of  air.  The  expansion  of  this  imprisoned  air  is  safely  called 
adiabatic,  and  the  work  which  it  does  (if  it  is  worth  while  to 
find  it)  is  to  be  found  for  the  weight  or  volume  as  given  in 
the  expansion  value  for  W^(§§  167  and  168).  The  increase 
in  the  size  of  cylinder  required  is  to  be  found  by  plotting  the 
curve  of  such  expansion  work  on  a  diagram  (Fig.  J^)^  and  in- 
creasing the  volume  by  that  percentage  of  itself  which  is  given 


Fig.  76. 

by  the  ratio  of  the  entire  length  of  the  diagram  between  ver- 
ticals €C  to  the  length  cd  of  the  diagram  between  the  termi- 
nals of  the  adiabatics. 

The  mean  effective  pressure  is  of  course  reduced  by  the 
effect  of  the  clearance  volume  of  air.  This  will  be  in  the  pro- 
portion of  the  effective  length  between  the  feet  of  the  adia- 
batics to  the  total  length  between  perpendiculars.  Other- 
wise, the  formula  for  mean  effective  pressure  may  be  applied 
directly  in  calculating  the  work  to  be  done  in  horse-power  if 
the  actual  volume  of  air  be  used,  taken  after  the  inlet-valves 
have  opened,  instead  of  the  full  piston-displacement. 


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MECHANICAL   COMPRESSION  OF  HEAT  MEDIA.       269 

187.  Volume  of  the  Compressing-cylinder. — If  the  prob- 
lem be  given  to  design  a  cylinder  to  give  F,  cubic  feet  of  air 
at  a  pressure  of  /,  pounds  per  square  inch  (or  per  square 
foot)  after  compression,  it  will  first  be  necessary  to. find  the 
corresponding  absolute  temperature  T^  corresponding  to  that 
pressure,  from  the  foregoing  equations.  Then  the  volume 
V^  at  atmospheric  pressure  and  temperature  can  be  found 
from  the  relation 

PjKl    -.Mi 

7;  -   r,  • 

Then  if  clearance  effect  be  neglected,  and  the  piston  makes 
2n  traverses  per  minute  for  n  revolutions  in  that  same  time, 
the  cylinder  volume  v^  will  be 

V.  z=z  —^  cubic  feet. 
*        2// 

If  there  be  a  clearance  expressed  in  terms  of  piston-displace- 
ment by  the  fraction  — ,  the  air  in  the  clearance  volume  ex- 

^  c 

panding  down  from  /,  to  /,  will  occupy  a  volume  which 
will  be 


K4)-" 


of  that  piston-displacement.  The  denominator  271  should  be 
therefore  multiplied  by  the  factor 

of  itself  to  allow  for  this  clearance  loss.  Furthermore,  the 
inlet-valves  do  not  open  until  the  pressure  in  the  cylinder  is 
less  than  p^  and  friction  through  them  keeps  it  less  than  p^ 
on  the  aspirating  stroke;  and  similarly,   the  delivery-valves 


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270  HEAT  AND    HEAT-ENGINES, 

do  not  open  until  /,  is  exceeded,  and  their  friction  makes 
the  pressure  of  displacement  in  the  cylinder  greater  than  /,. 
These  losses  compel  the  real  volume  to  exceed  the  calculated 
volume  by  an  amount  for  which  experience  is  the  only  guide. 
188.  Cooling;  of  Compressing^-cylinder. — The  relation 
between  pressures  and  absolute  temperatures  in  compressing 


enables  the  rise  or  range  of  temperature  to  be  calculated 
when  the  pressures  are  given.  Hence  if  it  be  desired  to  cool 
the  compressing-cylinder  by  water-jacketing  or  to  cool  the  air 
by  injection  of  water,  the  pounds  of  water  required  are  easily 
calculated.  If  t^  is  the  range  of  temperature  for  the  air,  and 
/„  is  the  range  to  be  permitted  to  the  water,  then  the  law  of 
transfer  gives 

I  X  c;  X  /a  =  ^  X  I  X  /« 

for  each  pound  of  air,  when  w  is  the  desired  weight  of  water 
with  a  specific  heat  of  unity. 

Water-jacketing  does  not  cool  the  air  much,  since  air  is 
cooled  by  contact  only,  and  this  is  not  easily  managed  unless 
the  air  is  in  thin  films.  Injection  of  water  is  effective  for 
cooling  the  air,  but  in  many  cases  the  presence  of  water-mist 
in  the  compressed  air  is  an  objection  on  account  of  its  freez- 
ing when  the  air  is  used  expansively  in  the  compressed-air 
rr.otor.  If  the  air  be  assumed  to  be  saturated  with  all  the 
steam-vapor  it  can  carry,  the  effect  of  the  steam-vapor  is 
probably  inappreciable  on  the  work  of  the  air.  The  expo- 
nent of  the  equation  may  be  slightly  affected,  but  this  is  all. 

189.  Compressing  in  Two  or  More  Stages.  Compound 
Compressors. — It  early  suggested  itself  to  designers  of  com- 
pressors that  if  the  compound  principle  were  applied  to  com- 
pressing they  would  reap  certain  advantages  belonging  to 
the  principle  as  applied  to  the  steam-engine.     The  air  taken 


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MECHANICAL    COMPRESSION  OF  HE  A  T  MEDIA. 


271 


at  lower  pressure  and  larger  volume  into  a  large  cylinder  and 
delivered  from  it  to  a  smaller  one  would  allow  an  inter- 
cooler  between  the  two  cylinders  to  be  advantageously  ai;- 
ranged  to  cool  the  air  and  diminish  the  volume  of  the  small 
cylinder,  while  the  entire  volume  of  the  small  cylinder  was 
available  for  the  second  stage  of  the  compression,  instead  of 
forcing  this  into  that  part  of  the  stroke  of  the  one  cylinder  at 
which  the  diminishing  crank-angle  reduced  the  piston  to  a 
slower  velocity.  The  intercooler,  however,  has  a  manifest 
advantage,  because  it  usually  happens  that  a  storage  of  air  in 
reservoirs  occurs  in  which  the  temperature  of  the  air  drops 
down  to  or  near  that  of  the  incoming  atmospheric  air.  Here 
the  work  of  compression  can  be  reduced  by  the  division  into 
two  stages,  by  making  it  approach  to  isothermal  compres- 
sion. The  air  is  taken  in  at/,  and  is  compressed  in  the  first 
cylinder  to//,  and  in  the  reservoir  at//  it  is  cooled  back  to 
7",  or  nearly  so,  at  which  it  entered  the  first  cylinder.  The 
second  cylinder  draws  the  air  at  a  pressure  //  and  com- 
presses it  to  the  final/,.  This  is  represented  graphically  for 
a  three-stage  compression  by  Fig.  TJ.     By  the  first  cooling 


F1Q.77. 


the  volume  is  diminished  from  the  adiabatic  point  x  to  the 
isothermal  point  i.  The  second  compression  adiabatic  in  the 
second  cylinder  would  bring  the  pressure  and  volume  \,o  y\ 
by  the  second  intercooler  it  is  reduced  in  temperature,  and 


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272  HEAT  AND   HEAT-ENGINES, 

therefore  in  volume,  to  /.  The  final  compression  carries  the 
pressure  up  to  the  volume-line  through  z^  whereas  k  would 
have  been  the  isothermal  point.  Hence  the  loss  drops  to 
that  represented  by  the  hatched  area  instead  of  being  the  full 
area  outside  of  the  isothermal  curve  cijk. 

What  is  desired  in  two-stage  compression  is  to  make  such 
a  division  of  the  compressing  work  as  shall  make  it  a  mini- 
mum. If  the  first  stage  compress  from/,  to//  and  the  work 
be  called  W^^  the  equation  of  §  i8i  is 

for  one  pound  of  air,  neglecting  clearance  loss. 
The  work  of  compressing  from  //  to  /,  is 

But  if  the  air  be  cooled  back  to  the  temperature  7",  in  the  in- 
tercooler  between  the  cylinders,  this  last  work  becomes 

Hence  the  total  work  in  the  two  cylinders  is  their  sum ;  or, 
This  value  for  W^will  be  a  minimum  when 

is  a  .ninimum.     When  /,  and  /,  are  known,  this  expression 

X       b 
IS  of  the  form  — I ,  which  can  be  differentiated,  and  when 


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MECHANICAL    COMPRESSION  OF  HEAT  MEDIA.       2/3 

the  first  differential  coefficient  is  put  equal  to  zero,  the  value 
for  X  corresponding  to  such  minimum  =  ^ ab.  Hence  the 
minimum  value  for  the  work  occurs  when 

//  =  ^>7a. 

When  the  air  is  supplied  to  both  cylinders  at  the  temperature 
7",  their  respective  volumes  should  be  inversely  as  the  abso- 
lute values  of  the  pressures /^  and//. 

When  high  pressure  is  sought,  a  similar  reasoning  would 
point  to  using  three  stages  or  four.  The  smaller  diameter  of 
the  higher  pressure  cylinders  enables  greater  strength  to  be 
secured  with  less  proportionate  increase  in  weight,  besides 
the  diminution  of  the  motor  work,  resulting  from  cooling  the 
air  in  transit.  The  intercooler  is  usually  a  receiver  with  a 
coil  of  pipe  within  it,  around  which  the  air  passes. 

190.  Fluid  Compressors. — By  combining  the  use  of  a 
displacing-piston  with  the  use  of  a  displacing  fluid  in  the 
compressing-cylinder,  or  by  using  a  fluid  alone  on  which  the 
air  or  gas  undergoing  compression  was  without  physical  or 
chemical  effect,  designers  have  been  able  to  diminish  the  evil 
effects  of  clearance.  The  liquid  used  may  be  water  or  oil. 
It  fills  all  dead  space  behind  the  piston  up  to  the  valves, 
which  are  placed  above  the  liquid,  and  therefore  the  expul- 
sion or  displacement  of  air  is  practically  complete.  The 
pumps  must  not  operate  at  too  high  a  speed  with  these  fluid 
pistons,  which  must  not  be  allowed  to  churn  or  spatter.  If 
water  is  used,  it  grows  warm  and  begins  to  form  vapor,  and 
requires  renewal. 

191.  Conclusions  and  Remarks. — It  will  have  been 
made  apparent  that  in  compressing  air,  as  the  volumes  dimin- 
ish, the  pressures  increase  more  rapidly.  Air  at  very  high 
tension,  therefore,  is  not  heated  so  hot  in  proportion  to  the 
stored  energy  in  it  as  at  the  lower  pressures.  It  is  the  loss  of 
the  heat  of  compression  in  receivers,  pipes,  conduits,  and  the 
like  which  withdraws  energy  from  compressed  air  after  it  is 


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274 


HEA  T  AND   IIEA  T-ENGINES, 

Jll,  lUj 


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MECHANICAL    COMPJiESSION  OF  HEAT  MEDIA.        275 

stored  in  it  by  the  compressing  process,  which  forces  conti- 
pressed  air  to  lower  effectiveness  as  a  medium  of  transmitting 
energy,  unless  the  air  is  heated  again  just  before  using, 
which  can  be  cheaply  done.  The  cooler  the  intaken  air,  the 
greater  the  weight  per  cubic  foot  and  the  greater  the  mass  or 
weight  of  air  handled  by  a  machine  of  a  given  size.  Fur- 
ther, the  greater  energy  is  a  given  machine  capable  of  im- 
parting to  the  air.  At  high  mountain  altitudes  the  efficiency 
of  a  compressor  is  less  than  at  sea-level.  If  the  air  can  be 
used  directly  as  compressed,  the  heat  energy  stored  in  it  is 
of  more  moment  than  the  pressure  without  the  heat.  If  the 
air  is  not  used  expansively  in  the  air-motor,  energy  stored 
in  it  is  wasted  at  the  exhaust.  If  the  air  is  used  expansively, 
its  condition  as  to  heat  is  lowered,  and  the  energy  expended 
in  doing  useful  work.  If  pressure  is  raised  without  heat-rise, 
then  in  working  expansively  its  heat  standard  is  lowered 
below  the  normal,  and  it  has  to  be  regenerated. 

The  operation  of  the  air-engine,  or  compressed-air  motor, 
and  the  storage  losses,  will  be  discussed  in  Chapter  XVIII. 
Fig.  78  will  serve  as  a  type  for  two-stage  tandem  steam  air- 
compressors. 


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CHAPTER   XIV. 
TEMPERATURE-ENTROPY  DIAGRAMS  FOR  HEAT-ENGINES. 

195.  Introductory. — It  will  have  been  observed  that  the 
formulae  and  diagrams  of  the  foregoing  chapters  have  been 
diagrams  of  work  in  terms  of  co-related  pressures  and  vol- 
umes, and  similar  to  the  diagram  traced  by  the  pencil  of-  the 
steam-engine  indicator. 

It  has  long  been  a  conception  of  the  master  thinkers  on 
the  mutual  relations  of  pressure,  volume,  and  temperature  for 
any  medium,  that  these  factors  might  be  regarded  as  the  co- 
ordinates, taken  with  respect  to  three  rectangular  co-ordinate 
axes,  of  points  upon  a  surface,  which  they  have  called  the 
thermodynamic  surface  for  any  medium  undergoing  such 
changes  of  pressure,  volume,  and  temperature  as  were  repre- 
sented analytically  by  the  equations  of  the  mathematical 
treatment.  If  the  axis  of  x  be  the  line  representing  volumes, 
and  the  axis  of  ^  represent  pressures,  the  axis  of  b  will  be  the 
axis  of  temperatures.  The  pv  diagram  is  therefore  drawn 
on  a  surface  parallel  to  the  plane  fixed  by  the  axes  of  /  and 
v^  either  with  disregard  of  temperatures  or  with  the  tem- 
perature assumed  constant.  The  distance  from  the  plane 
through  the  axes  of  /  and  v  is  the  value  of  the  temperature 
at  the  pressure  assumed  for  the  initial  or  final  pressure.  In 
all  the  foregoing  discussion  the  variations  of  temperature 
have  been  deduced  analytically  from  the  /z;  variations  at 
assumed  points.  It  would  be  an  interesting  deduction  if  it 
should  result  that  the  exponent  of  an  expansion  curve  should 
prove  to  be  the  consequence  of  the  distortion  of  the/z/  sur- 

276 


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TEMPERATURE'ENTROPY  DIAGRAMS,  2/7 

face  when  temperature  alters  with  variations  of  pressure  and 
volume.  The  projection  oi  pv  surfaces  will  be  by  lines  paral- 
lel to  the  temperature  axis. 

The  projection  parallel  to  the  volume  axis  on  the  plane 
through  the  t  and  v  axes  of  the  pv  diagram  when  the  latter 
is  distorted  as  required  by  the  temperature  change  in  adia- 
batic  expansion  or  compression  gives  lines  or  areas  on  the// 
surface,  which,  however,  are  of  no  practical  service.  The 
actual  cycle  of  a  heat-motor  always  demands  the  addition  to 
the  working  substance  or  heat  medium  of  a  quantity  of  heat 
energy  which  may  or  may  not  take  the  form  of  increased  tem- 
perature. The  pvt  thermodynamic  surface  is  adapted  prima- 
rily for  the  study  of  phenomena  involving  no  change  of  energy 
from  without,  but  only  transformations  in  which  the  unit 
weight  has  the  same  intrinsic  total  energy  but  undergoes  only 
variation  in  the  factors.  What  is  desired  is  a  scheme  of 
graphical  representation,  whereby  the  expense  of  heat  in  the 
form  of  temperature  or  other  form  of  heat  energy  can  be  rep- 
resented by  an  area,  the  product  of  two  factors,  which  shall 
be  so  connected  to  the  pv  diagram  that  the  heat  expendi- 
ture or  return  which  accompanies  the  cycle  of  a  piston-motor 
can  be  readily  examined,  or  the  heat  work  of  different 
motors  and  media  examined  and  compared,  even  as  the  pres- 
sure work  is  studied  for  design  when  a  capacity  in  foot- 
pounds is  desired.  In  gas-engines,  or  such  as  have  the  heat- 
energy  liberated  by  combustion  in  the  motor-cylinder  di- 
rectly, the  temperature  phenomena  are  more  significant  than 
the  phenomena  of  the  indicator-card  in  studying  efficiencies. 
While  it  is  also  true  that  certain  areas  of  work  expressed  in 
foot-pounds  by  the  pv  diagram  can  be  translated  into  heat- 
units  by  the  division  by  /  =  778,  the  foot-pounds  cor- 
responding to  one  heat-unit,  this  can  only  be  done  with  iso- 
thermal expansion  of  the  permanent  or  true  gases  and  is  not 
exact  for  isothermal  work  of  vapors  or  mixtures. 

196.  The  Temperature-entropy  Diag^ram. — It  will  be 


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278  HEAT  AND   HEAT-ENGINES. 

recalled,  however,  from  the  discussion  oi  thermal  lines  and 
the  significance  of  the  entropy,  that  when  a  heat  medium  is 
undergoing  the  operations  usual  to  such  media  under  the 
isothermal  conditions,  with  pv  a  constant  product,  and  the 
temperature  T  is  not  allowed  to  vary  when  the  pressure  or 
volume  vary  inversely  together,  there  is  a  quantity  which 
should  vary  when  increased  heat  energy  is  imparted.  If  this 
quantity  be  called  the  entropy  (§  124),  and  a  quantity  of 
heat  in  units  be  added  which  would  raise  the  absolute 
temperature  through  7",  —  Z",  degrees,  the  total  inciease  in 
entropy  for  the  quantity  of  heat  energy  added  will  be  ex- 
pressed by 

Jt,    T' 

Hence  when  a  quantity  Q  of  heat-units  is  being  added  to  the 
medium  at  a  temperature  Ty  the  energy  which  is  being  added 
can  be  expressed  by  the  product 

Heat  energy  added  =  T<t>. 

In  this  the  temperature  is  that  at  which  the  medium  is  receiv- 
ing the  energy  but  growing  no  hotter  under  the  process  as  it 
is  conducted  at  the  fixed  temperature  of  that  source  of  heat 
which  is  supplying  heat  energy ;  and  the  entropy  is  that  which 
belongs  to  the  body  after  the  increase  of  entropy  ceases.  It 
is  the  final  or  maximum  state  of  the  entropy,  at  the  point  of 
highest  heat  energy  then  under  consideration. 

A  diagram,  therefore,  on  which  the  absolute  tempera- 
tures shall  be  the  vertical  ordinates  and  the  entropy  factor 
shall  be  the  horizontal  abscissae  will  have  an  area  enclosed 
between  the  bounding  co-ordinates  and  the  curves  embody- 
ing their  relations  at  intermediate  points,  which  will  present 
graphically  to  the  eye  at  once  the  magnitude  of  the  heat 


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TEMPERA  TUKE-ENTROP  Y  DIAGRAMS.  2/9 

energy  supplied  under  difTering  conditions  and  with  different 
heat  media. 

When  it  is  remembered  that  the  adiabatic  change  of  vol- 
ume is  that  in  which  no  change  in  entropy  occurs,  or  the 
entropy  is  constant,  it  will  appear  that  the  changes  in  heat 
energy  in  adiabatic  expansion  or  compression  find  conven* 
ient  analogies  in  the  descent  of  a  weight  of  water  W 
through  a  height  measured  from  the  sea-level  of  absolute 
zero  down  to  a  second  level  lower  than  the  first,  but  still 
having  a  value  greater  than  zero  (cf.  §  124).  The  available 
energy  of  the  weight  is  thus 

W{Jt^  —  h^  =  available  foot-pounds. 

By  analogy,  if  the  constant  entropy  during  adiabatic  ex- 
pansion descend  from  an  initial  height  7",  to  a  final  height  7", 
on  the  absolute  scale, 

0(7"^  —  ZJ  =  available  energy  in  heat-units, 

if  a  pound  of  the  medium  is  under  consideration. 

Interesting  extensions  of  this  will  be  noted  hereafter.  It 
is  further  to  be  noted  that  the  same  ignorance  as  to  the  real 
meaning  of  weight  or  the  attraction  of  the  earth  for  bodies  to 
it  prevails  for  W  in  the  hydraulic  analogy  as  exists  for  the 
quantity  0  in  the  heat  energy  diagrams. 

197.  Temperature-entropy  Diagram  for  an  Ideal  Heat- 
engine. — An  ideal  heat-engine,  as  will  be  shown  in  a  succeed- 
ing chapter,  is  one  in  which  a  given  mass  or  weight  of  a  heat 
medium  is  acted  upon  by  heat  to  produce  work,  and  returns 
after  the  completion  of  one  cycle  of  operations  to  its  initial 
state,  the  heat  being  supplied  at  a  given  constant  temperature, 
and  withdrawn  or  rejected  at  another  constant  temperature. 
The  difference  between  the  two  quantities  measures  the  work 
done   in  a  perfect  engine.     The  heat  is  therefore  necessarily 


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28o 


ffEA  T  AND   HEA  T-ENGINES. 


supplied  and  withdrawn  under  the  isothermal  law  for  constant 
temperature,  with  change  in  entropy;  the  expenditure  of 
energy  on  expansion  is  most  effectively  done  by  adiabatic 
expansion,  and  the  rise  to  initial  state  of  entropy  is  also  to  be 
done  without  change  of  such  entropy,  or  by  a  second  adia- 
batic. The  pv  diagram  will  therefore  show  a  pair  of  adia- 
batic curves  (Fig.  79)  connected  at  their  extremities  by  a  pair 
of  isothermals.  To  express  this  set  of  relations  on  the  tem- 
perature-entropy   diagram,   with    T  ordinates   and    entropy 


P1G.79. 


FiG.SO. 


abscissae,  the  isothermal  line  of  increasing  energy  starts  from 
the  upper  end  of  the  T  ordinate  corresponding  to  the  temper- 
ature (Fig.  80).  The  top  horizontal  line  1,2,  has  a  length 
representing  the  increase  of  entropy  during  that  isothermal 
process.  At  2  the  adiabatic  must  begin.  The  expansion 
along  an  adiabatic  is  accompanied  by  no  change  in  entropy, 
but  by  a  drop  in  absolute  temperature  to  the  point  3  corre- 
sponding to  7",.  At  3  the  withdrawal  of  heat  and  a  lowering 
of  entropy  occurs  till  the  point  4  is  reached,  where  the  adia- 
batic begins,  with  constant  entropy  and  increase  of  tempera- 
ture from  7*,  back  to  7",,  closing  the  cycle.  The  heat  which 
could  not  be  utilized  but  was  rejected  is  the  area  of  the  lower 
unshaded  rectangle  represented  by  71,(0,  —  0,),  a  quantity 
which  is  obviously  reduced  as   T^  is  made  smaller,  and  be- 


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TEMFEJiATUJ^E'EXri^OPY  DJAGJ^AMS.  28 1 

comes  zero  when  T^  is  zero.     The  relation  between  the  entire 
energy  supplied  or  received  by  the  medium 

area  1256=  ^,(0.  -  0.), 
and  the  work  done 

area  1234  =  (7;  -  7;X0.  -  0j. 
will  be  the  efficiency  of  the  cycle,  or 

Efficiency  =  (^."^.XA-/.)  =  ZW;  ^  ,  _  ^ 

a  result  to  be  otherwise  deduced  hereafter. 

If  the  passage  from  I  to  2  take  place  at  100  pounds  pres- 
sure of  steam  absolute,  corresponding  to  a  latent  heat  of  882 
thermal  units,  and  an  absolute  temperature  of  7S8  degrees, 
then  the  entropy  counted  from  32°,  or  freezing-point  of  water, 
should  be 

882 

788  ='-'^7, 

for  one  pound  of  such  water,  and  gives  the  length  of  the  line 

0.  —  0,« 

If  the  unit  of  heat  medium  was  a  permanent  gas,  then  the 
heat  added  during  an  expansion  from  t\  to  z\  will  be  the 
same  as  the  work  of  such  isothermal  expansion,  which  was 
found  (§  166)  to  be  in  foot-pounds 

w,  =  p,v.  Nap.  log  ^ 

=  p^z\  Nap.  log  r 
=  //?rNap.  logr. 

If  this  value  in  foot-pounds  be  divided  by  /,  it  becomes  heat* 
units,  and  if  the  increase  in  energy  be  divided  by  T',  at  which 


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282  HE  A  T  AND   HEA  T-ENGINES, 

that  increase  took  place,  the  quotient  is  the  final  value  for  0; 
or  (§  124), 

(f>  =  R  Nap.  log  r. 

It  is  a  matter  of  indifference  at  what  distance  from  the 
point  6  the  origin  or  zero  of  entropy  be  taken;  or,  in  other 
words,  what  value  of  J",  be  taken  as  a  datum.  Temperature 
will  of  course  be  taken  from  absolute  zero,  if  the  value  of 
heat  rejected  has  any  significance.  Usually,  however,  it  will 
be  only  the  differences  in  temperature  and  in  entropy  which 
are  required. 

198.  Deductions  from  the  Temperature-entropy  Dia- 
g^ram. — The  use  of  the  temperature-entropy  diagram  permits 
a  direct  and  obvious  deduction  of  certain  facts  and  princi- 
ples, also  deducible  from  the/z/  equations  but  less  simply. 

-  (i)  When  heat  passes  from  one  body  to  another,  the  en- 
tropy of  the  system  is  increased.  This  follows  because  heat 
passes  downward  only  from  a  warmer  to  a  colder  body  (never 
automatically  the  other  way);  and  if  the  heat-area  trans- 
ferred from  the  hotter  and  equal  to  the  heat-area  received  by 
the  lower  have  a  higher  and  longer  temperature-ordinate,  the 
other  area  with  lower  and  shorter  temperature-ordinate  must 
have  a  greater  entropy  value  to  give  equality  of  area. 

-  (2)  Clausius  announced  the  generalization  that  the  entropy 
of  the  world  tends  to  a  maximum.  This  follows  from  the 
previous  principle,  since  all  transfers  are  downward  unless 
mechanical  force  is  introduced  at  the  expenditure  of  heat  to 
make  them  otherwise. 

"^  (3)  The  entropy  imparted  by  adding  heat  so  as  to  change 
the  state  of  the  heat  medium  from  that  belonging  to  one 
adiabatic  to  that  belonging  to  another  adiabatic  is  the  same 
by  whatever  path  the  passage  takes  place.  The  diagram  shows 
that  the  distance  between  the  two  parallel  lines  representing 
the  adiabatics  is  everywhere  the  same  (cf.  §  124). 

(4)  The  heat  absorbed  or  given  out  by  a  heat  medium  in 
passing  from  one  state  to  another  is  given  by  the  area  between 


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TEMPERATURE-ENTROPY  DIAGRAMS.  283 

the  curve  which  represents  the  change  of  state  and  two  adia- 
batics,  one  drawn  through  each  extremity  of  this  curve. 

(5)  If  a  series  of  equidistant  isothcrmals  be  drawn  be- 
tween two  adiabatics,  they  will  cut  off  equal  areas;  or  isother- 
mals  equidistant  in  temperature  divide  the  heat  into  equal 
parts. 

(6)  If  two  bodies  differ  sufficiently  in  heat  energy,  a  part 
of  that  excess  of  energy  in  the  hotter  body  can  be  trans- 
formed into  mechanical  work  by  a  proper  heat-engine,  and 
the  remainder  transferred  to  the  cooler  body.  The  test  that 
all  available  heat  energy  has  been  transferred  is  that  the 
entropy  of  the  system  has  not  been  increased  by  a  mere 
transfer  as  given  in  (i).  If  there  has  been  such  a  transfer, 
the  lost  work  is  proportional  to  that  increase  in  entropy. 

(7)  The  temperature  condition  of  a  medium  which  is  to 
operate  adiabatically  in  a  heat-engine  is  a  measure  of  its  avail- 
ability, since  the  lower  temperature  limit  is  fixed  by  that  of 
the  coldest  available  body:  The  area  of  the  diagram  in- 
creases as  7",  increases,  when  7*,  is  fixed  by  the  temperature 
of  water  available  for  condensation.      Hence: 

(8)  Where  a  given  heat-energy  is  under  consideration,  in- 
crease of  entropy  is  concurrent  with  a  loss  of  availability  of 
that  energy. 

(9)  If  the  conditions  of  the  preceding  paragraph  (197)  be 
applied  to  one  pound  of  steam,  within  very  small  variations 
of  pressure,  and  consequently  a  small  corresponding  range  of 
temperature,  the  height  of  the  figure  on  the/z/  plane  becomes 
also  very  small,  or  may  differ  from  a  rectangle  by  only  an 
inappreciable  quantity.  If  the  symbol  v  denote  the  volume 
of  the  one  pound  of  steam,  the  area  on  the  pv  diagram  will 
be  (/,  —  p^v.  The  area  on  the  7"0  diagram  will  be 
(T'j  —  7\)0,  the  temperatures  belonging  to  the  pressures  of 
the /z/ diagram.      Hence 

f A  -  P>  =  (^1  -  7;M     or     0  =  vfy^^y 


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284  HEAT  AND   HEAT-ENGINES. 

giving,  when  the  relation  of  pressures  and  temperatures  are 
given  by  a  table,  a  method  for  calculating  the  value  of  0. 

(lo)  Since  the  heat  energy  which  disappears  on  making  a 
liquid  at  a  necessary  temperature  and  pressure  into  a  gas  at 
that  pressure  and  temperature  is  an  isothermal  absorption  of 
heat,  the  so-called  latent  heat  can  be  expressed  by  the  equa- 
tion L  =  T<f>y  since  the  entropy  is  the  quotient  of  the  applied 
heat  divided  by  the  temperature  at  which  it  was  applied. 
Hence  from  section  (9) 


199.  Entropy-temperature  Diagram  Applied  to  a  Per- 
fect Steam-engine,  with  Complete  Expansion. — The  per- 
fect engine  and  the  diagram  of  §  197  assumed  the  water 
to  be  at  the  boiling-point,  so  that  in  forming  steam  at  the 
temperature  T^  there  was  only  the  latent  heat  to  be  added. 
The  more  usual  case  is  that  at  which  the  water  is  condensed 
after  expansion  to  a  temperature  7",  by  an  isothermal  process, 
and  is  returned  as  water  at  that  temperature  to  the  boiler  as 
the  source  of  heat.  The  water  therefore  requires  to  be  heated 
from  7!,  to  7,  as  feed-water  and  then  to  be  made  steam  and 
to  receive  entropy  at  the  higher  temperature. 

For  any  temperature  T,  the  entropy  counted  from  an 
assumed  origin  at  T^  will  be 


Entropy 


_  fdH 


which,  if  the  specific  h^at  of  water  be  considered  as  constant 
and  equal  to  unity  (§  143)  for  the  limits  in  question,  trans- 
forms into  the  equation 


~A  T  - 


Entropy  =   /     ^?  =  Hyp.  log  T  —  Hyp.  log  T,. 


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TEMPERATURE-ENTROPY  DIAGRAMS. 


285 


the  temperature  T  being  for  any  state  intermediate  between 
T^  and  7!,  The  first  element  of  the  diagram  will  therefore 
be  a  logarithmic  curve  through  the  points  a  and  e  (Fig.  81) 


Fia.81. 

which  have  for  their  temperature-ordinate  T^  and  T",,  respect- 
ively, and  for  their  horizontal  abscissae 

0.  =  Hyp.  log  7;  -  Hyp.  log  7;, 
and  for  ^, 

0,  =  Hyp.  log  T,  -  Hyp.  log  T,. 

This  will  give  the  distance 

wx  =:  <t>e  —  <t>a  =  Hyp.  log  T,  —  Hyp.  log  T,. 

It  is  not  significant  where  the  origin  of  entropy  be  taken, 

although  in  the  figure  the  usual  convention  is  observed,  of 

calling  the  entropy  of  water  at  32°  F.,  zero.     The  weight  of 

one  pound  of  water  is  the  mass  of  heat  medium  in  question; 

7",  corresponds  to  103''  F.,  or  the  temperature  at  one  pound 

absolute  pressure,   and    7",   corresponds  to  373°   F.,  or  the 

temperature  corresponding  to   180  pounds   absolute.      T^   is 

therefore  834  and    7",  =  562.     At  the  point  e  steam  forms 

L 
isothermally,  and  the  length  </"=  -^c,  if  the  entire  pound  of 


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286  HEAT  AND   HEAT-ENGINES. 

water  passes  into  steam.     If  a  percentage  x  only  becomes 

xL 
steam,  the  length  will  not  be  ef^  but  will  equal  -^^  less  than 

that  belonging  to  complete  vaporization.  At  /  the  cut-off 
takes  place,  and  adiabatic  expansion  without  change  of 
entropy  reduces  the  temperature  down  to  7",,  when  the  ex- 
haust opens  and  the  entropy  is  reduced  by  the  isothermal 
condensation  process,  at  7*,  constant,  which  brings  the  cycle 
to  the  starting-point. 

Examining  now  the  heat  interchanges: 

Area  waex  =  heat  taken  in  to  heat  feed-water  to  boiling-point ; 
**     xefy  =  heat  taken  in  during  evaporation; 
**     wacy  =  heat  rejected  at  exhaust; 
**     ae/ca  =  work  done. 

The  rectangle  xe/y  is  the  analogue  to  the  area  in  the  previous 

paragraph,  where  the  proportion  of  utilized  heat  to  the  heat 

T  —  T 
applied  was  given  by  the  ratio  — '—7^ — *,     The  area  to  the  left 

of  this  rectangle  is  the  heat  taken  in  during  warming  of  the 
cool  feed-water,  and  the  utilized  part  abe  bears  a  less  ratio 
to  the  whole  heat  supplied,  or  the  heat  is  used  less  efficiently. 
This  is  because  the  heat  is  not  supplied  at  a  constant  temper- 
ature Ty,  but  at  a  temperature  gradually  changing  from  the 
lower  to  the  higher  value.  That  is,  while  this  engine  does 
more  work  and  receives  more  heat  than  the  engine  of  the  pre- 
vious paragraph,  the  work  it  does  requires  an  amount  of  heat 
more  than  larger  in  proportion. 

200.  Amount  of  Condensation  in  Adiabatic  Expansion. 
— The  temperature-entropy  diagram  can  easily  be  extended 
so  as  to  give  graphically  the  proportion  of  steam  and  water  in 
an  adiabatic  process  of  expansion  at  any  stage.  If  a  curve  c/ 
be  drawn  from  c  (Fig.  82),  whose  points  are  found  by  drawing 
horizontals  (isothermals)  from  the  logarithmic  curve  ai,  each 


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TEMPERATURE-ENTROPY  DIAGRAMS. 


287 


such  horizontal  being  equal  to  the  value  of  •=,  for  that  partic- 
ular value  of  7",  a  curve  will  result  concave  outward,  because 
the  entropy  will  increase  as  evaporation  takes  place  at  a  lower 

value  for  T.     Hence  if  af  be  equal  to  ~ ,  and  the  steam  were 

entirely  dry  when  it  had  cooled  by  expansion  down  to  7",, 
the  heat  disposed   of  during  condensation  would  have  been 


A» 


9  » 


Fia.82. 


qfaw.  But  it  was  less  than  this  actually,  or  the  area  pdaw. 
Hence  there  must  have  been  some  part  of  the  unit  weight  of 
water  already  condensed  before  the  temperature  7,  was 
reached,  or  the  length 


— -  =  ;ir,     the  percentage  of  steam, 


and 


^  t=  I  —  ;r,     the  percentage  of  water. 
af 

Similarly,  any  horizontal  line  -=.  between  the  curves  ab  and 

^/will  be  divided  by  the  adiabatic  cd  into  segments  giving 
the  proportion  of  steam  at  that  temperature.     For  example, 

at  the  point  /,  ;r  =  t;- 


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288  HEAT  AND   HEAT-ENGINES, 

On  the  compression  curve  of  the  pv  cycle,  it  will  be 
apparent  that  the  condensation  should  be  stopped  at  a  point 
€  on  the  line  fa  if  by  compression  of  the  heat  medium  it  is 
to  be  brought  to  the  temperature  7",  as  water  ready  to  evap- 
orate. In  other  words,  if  adiabatic  compression  is  to  be  used 
to  restore  the  medium  to  the  condition  2"^,  the  process  must 

begin  when  — >  represents  a  proportion  of  steam  still  uncon- 

densed,  and  at  any  point  of  the  adiabatic  compression  eb  the 

•    U 

dryness  is^. 

Finally,  if  the  entire  pound  of  steam  is  not  dry  vapor 
when  the  expansion  begins,  but  only  a  proportion  x.  Let 
the  point  g  give  the  proportion*  of  complete  vaporization 
which  has  taken  place,  so  that 

^  \ 

f>g 

X  =  -^ 

The  perpendicular  through  g  now  gives  the  line  of  complete 
vapor  adiabatic  expansion,  and  the  segments  to  the  right  as 

before  are  water.     At  the  exhaust  period,  x  =  ->,  and  the 

proportion  of  water  is  -^. 

201.  Temperature-entropy  Diagram  when  the  Expan- 
sion is  Incomplete. — If  the  steam  or  heat  medium  expands 
down  to  the  temperature  and  pressure  represented  by  the  ex- 
haust at  T",,  it  must  follow  that  at  the  end  of  the  piston- 
traverse  there  is  little  or  no  forward  effort  acting  upon  it. 
This  tends  towards  irregular  motion,  which  must  be  counter- 
acted by  stored  kinetic  energy  in  fly-wheel  or  the  reciprocat- 
ing masses  of  the  mechanism,  or  else  the  effort  must  be  main- 


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TEMPERATURE-ENTROPY  DIAGRAMS.  289 

tained  by  causing  the  motor-pressure  to  drop  to  7",  only  after 
the  stroke  has  been  completed.  This  is  a  practical  condition 
which  prevails  very  widely,  and  will  result  in  changing  the 
heat-diagram  by  a  loss  of  availability  along  the  lower  line. 
In  Fig.  83  let  the  expansion  take  place  from  the  point  of 

cut-off  c  adiabatically  until  a  tem-        hry^,yy^yyy.^^^'^..yy^^^^'...y.y.^s 
perature  is  reached  at  the  end  of       ^         ^  1\ 

the  piston-traverse    corresponding    yMC^I^^^^ 
to   the   point   c'  in   the  figure,   at 
which    pressure   and    temperature 
(above  7",)  the  exhaust  opens  and  J^g.83. 

available  heat  is  swept  out  by  a  non-adiabatic  expansion  and 
condensation,  resulting  in  a  fall  both  in  entropy  and  temper- 
ature until  the  line  af  is  reached  proper  for  7,,  whence  the 
return  stroke  da  brings  the  substance  back  to  the  starting- 
point. 

The  curve  from  c'  to  d  represents  the  change  at  the  end 
of  the  stroke,  before  the  piston  reverses  its  motion,  and  is  a 
curve  of  constant  volume,  while  varying  in  pressure  and  tem- 
perature from  the  withdrawal  of  heat  energy  by  condensation 
from  contact  with  some  cooler  body.  It  is  described  by 
points.  Any  point  on  it  will  be  found  at  the  intersection  of 
the  temperature  ordinate  for  T  with  the  line  drawn  from  the 
curve  ab^  which  has  a  length  representing  the  percentage  of 
steam  in  the  mixture  at  that  temperature.  The  length  le  is 
to  be  to  the  length  Ik  as  the  original  volume  ;irF'(in  which 
V  is  the  volume  of  one  pound  of  saturated  steam  at  the 
temperature  corresponding  to  the  point  c\  but  which  must 

have  moisture  in  it  represented  by  ^'«,  so  that  x  =  — I  is  to 

*^  ^  mn  I 

the  volume  belonging  to  the  assumed  temperature  T.  Or, 
in  other  words, 

le\  IkwxV  \V,     or     le^'^lk. 


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290  HEA  T  AND   HEA  T-ENGINES. 

The  loss  of  available  energy  as  compared  with  complete  ex- 
pansion is  the  area  bounded  by  the  lines  c'g  and  dg  and  the 
curve  c'eg.  In  the  scale  used  in  Fig.  83,  the  drop  in  temper- 
ature represented  by  the  line  cc'  is  from  the  pressure  of  180 
pounds  to  3  pounds  pressure. 

202.  Temperature-entropy  Diagram  when  there  is  na 
Expansion. — If  the  steam  follows  at  full  pressure  to  the  end 
of  the  piston-traverse,  and  is  there  released  at  full  pressure  to 
exhaust  without  any  adiabatic  expansion,  there  is  no  length 


.  FiG.84. 

cc'  in  the  diagram,  but  the  curve  of  constant  volume  of  satu- 
rated steam  as  temperature  is  lowered  starts  from  the  corner 
c  (Fig.  84).  Points  on  the  curve  are  found  as  before,  since 
xV ■=^  F„  and  hence 

lex  Ik:':   V:   V,,     or     le  =.  ^-Ik. 

The  area  of  lost  work  is  the  area  cgd,  which  is  greater  than 
in  the  preceding  case,  the  conditions  being  assumed  the  same, 
or  T^  as  834°  and  7",  as  603°  absolute.  The  line  da^  as  be- 
fore, shows  the  change  in  state  or  the  condensation  occurring 
as  the  piston  returns. 

203.  Temperature-entropy  Diagram  when  Steam  is 
Superheated. — If  the  specific  heat  of  steam  undergoing  a  pro- 
cess of  heating  beyond  the  saturation  point  be  represented  by 
the  factor  0.480  (§  146),  then  the  entropy  will  be  increased 
after  the  point  c  is  reached  by  an  amount  which  will  exceed 
that  at  7",  by  the  quantity 

0,  =  0.480  /     —  =  0.480  (Hyp.  log  T  -  Hyp.  log  T,\ 


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TEMPERATURE-ENTROPY  DIAGRAMS,  29 1 

The  effect  of  this  upon  the  diagram  is  to  add  a  curve  plotted 
by  points  as  given  for  a  series  of  values  of  T'  up  to  the  max- 
imum temperature  used.  The  curve  3-7  is  such  a  logarithmic 
curve  (Fig.  85),  and  the  point  7  indicates 
that  maximum  temperature.  At  this 
point,  if  adiabatic  expansion  sets  in,  the 
line  7-4  is  described  with  complete  expan- 
sion. The  heat  taken  in  is  increased  by 
3798,  while  the  work  done  is  increased 
by  5  3  7  4  as  the  result  of  the  superheating. 
It  will  appear  that  even  if  the  superheat- 
ing be  considerable  (200°  in  the  scale 
selected)    the    proportionate    increase    is  Fiq.85. 

small,  as  compared  with  the  total  expenditure.  In  other 
words,  so  much  of  the  heat  is  taken  in  at  the  temperature  of 
saturation  that  the  subsequent  raising  of  temperature,  even 
to  a  considerable  degree,  offers  small  theoretical  advantage. 
It  offers  a  practical  advantage,  however,  as  will  be  shown 
hereafter  (§  229.  See  also  §  232).  The  temperature  may 
drop  in  expanding  down  to  a  point  on  3—4,  where  the  adiabatic 
line  would  cross  the  saturation  curve  before  condensation 
begins.  Up  to  this  point  the  steam  has  been  superheated. 
If  the  steam  were  to  be  dry  at  the  end  of  expansion  down 
to  T^  then  the  curve  3-7  would  have  to  be  prolonged  until 
it  met  the  temperature  ordinate  through  4. 

204.  Plotting  of  Entropy-temperature  Curves  for  Water 
and  Steam. — For  the  convenient  use  of  the  entropy-temper- 
ature diagram,  the  logarithmic  curves  for  the  relation  of  tem- 
perature to  entropy  may  be  conveniently  plotted  on  cross-sec- 
tion paper,  and  on  the  scale  preferred  for  the  heat  diagrams, 
and  then  used  directly  between  the  desired  limits  in  drawing 
in  the  curves  of  heating  of  water  and  in  the  heating  of  the 
steam-gas.  As  drawn  in  Fig.  86,  the  horizontal  distance 
between  the  two  curves  gives  the  change  in  entropy  which 
takes  place  when  water  at  any  temperature  is  changing  into 


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292 


HEAT  AND   HEAT-ENGINES. 


steam  at  the  same  temperature  ^^j.     The  numerical  values 

start  at  zero  at  32°  F.,  and  are  for  one  pound  weight.  The 
specific  heat  of  water  increases  as  the  temperatures  increase, 
it  will  be  remembered  (§  139). 


•00 


780 

I'" 

2  TOO 
•-•fO 


410 


— 

— 

— 

— 

^ 

— 

- 

= 

F 

/ 

t 

/ 

T 

/ 

~T 

]j 

— 

— 

.1 

— 

... 

... 

— 

- 

... 

B-.             I\* 

( 

L        S 

— 

i 

— 

1          i  \ 

^ ]-«v^ 

f 

!                    1  •/    \ 

j^i 

—  1                    "      W 

^ 

|_ 

1 

T 

> 

> 

/ 

r  " 

t 

:;^  ■ 

/ 

' 

r 

/. 

y 

^ 

rt 

rr 

T5 

rr 

0 

TT 

7T 

\n 

T- 

i"i'a-i!n  r\\'\  •-rrdrr.     trti 

ENTROPY 

Fig.  86. 
This  pair  of  curves  is  also  of  great  convenience  in  drawing 
in  the  curve  of  saturation  for  an  adiabatic  expansion  in  terms 
of  pressure  and  volume.  If  the  curve  BCD  (Fig.  87)  repre- 
sent a  curve  plotted  from  the  tables  for  saturated  steam,  let 
it  be  required  to  draw  the  adiabatic  through  B.  Let  C  be 
any  point  on  the  saturation  curve  whose  pressure  is  given, 
and  for  which  tables  give  the  corresponding  temperature. 
From  the  point  b  on  the  entropy  curve  drop  a  perpendicular 
(a  line  of  constant  entropy)  to  meet  the  line/c-  drawn  through 
the  temperature  point  corresponding  to  C,     This  will  give  the 


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TEMPERA  TURE'ENTROP Y  DIA GRA MS. 


293 


point  (f  n  Then  the  point  C  on  the  adiabatic  curve  will  lie  at 
a  distance  NC  from  the  line  of  no  volume  given  by  the 
relation : 

NC  \  NC  w  p^  :  pc. 

Other  points  are  similarly  found.  If  the  initial  volume  in 
cubic  feet  were  the  result  of  vaporization  of  less  than  one 

M E      B 


pound  of  water,  or  the  percentage  of  steam  was  less  than  100 

at  the  beginning,  then  the  curve  of  vaporization  of  such  a 

^  ^    ME  ^  ^    EB 

mixture,  as  represented  by  -j^  per  cent  of  steam  and   ^fn 

percentage  of  water  could  be  found  by  dividing  the  space  ob 
in  Fig.  86  in  that  proportion,  and  using  the  ratio  given  by 
the  line  ec" .  Points  on  the  adiabatic  through  E  would  be 
found  by  making 

NC"  :  NC::  pc''  :  pc. 

This  same  diagram  can  be  used  to  find  the  curve  c/  in  the 
foregoing  sections. 

It  will  be  apparent  from  the  slope  of  the  entropy  curves 
that  for  each  range  of  temperature  there  is  a  certain  adiabatic 
for  which  the  initial  and  final  figures  are  the  same.  If  the 
steam  contains  more  than  50  per  cent  of  water  within  the 
range  given,  it  will  become  drier  by  expansion ;  if  less  than 
this,  it  will  become  wetter. 


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294  HEAT  AND   HEAT-ENGINES. 

205.  Transfer  of  the  Indicator-diagram  to  the  Tem- 
perature-entropy Diagram. — The  foregoing  paragraphs  have 
made  clear  the  methods  to  be  used  with  any  actual  case  in 
transferring  the  pv  points  on  the  curve  traced  by  a  steam- 
engine  indicator-pencil  to  the  temperature-entropy  diagram- 
plane.  The  theoretical  diagram  is  first  drawn,  giving  the  ideal 
condition  of  complete  vaporization,  with  the  expansion  curve 
that  of  saturation,  and  with  cut-off  located  with  respect  to  the 
line  of  zero-volume,  thus  neglecting  clearance.  The  corre- 
sponding ideal  temperature-entropy  diagram  is  then  drawn, 
with  values  for  T^  and  7",  corresponding  to  the  given  pres- 
sures, and  the  entropy  values  laid  off  according  to  the  ob- 
served data  as  taken  from  tables.  The  actual  engine-diagram 
will  lie  within  the  theoretical  one  in  both  cases,  by  reason  of 
the  losses  in  pressure  and  temperature  caused  by  the  neces- 
sity of  operating  engines  in  air  cooler  than  the  medium,  and 
for  other  causes  to  be  discussed  in  a  following  chapter. 
Hence  it  is  the  problem  to  locate  points  within  the  theoret- 
ical pv  diagram  at  the  corresponding  points  within  the  theo- 
retical te  diagram.  The  vertical  distances  above  the  zero  of 
temperature  on  the  te  diagram  are  taken  from  steam  tables 
which  gjve  the  temperature  corresponding  to  the  pressure 
on  the  pv  curve,  To  locate  the  upper  end  of  these  pres- 
sure-temperature ordinates  on  the  entropy  scale,  the  principle 
is  used  that  corresponding  points  in  each  actual  diagram 
divide  the  horizontal  lines  of  the  theroretical  diagrams  in 
the  same  proportion.  That  is,  if  X  in  Fig.  88  be  a  point 
in  the  actual  indicator-diagram,  a  horizontal  AB  is  drawn 
through  X  on  the  pv  theoretical  diagram,  and  also  a  line  ab 
through  the  point  on  the  te  diagram  which  is  at  the  distance 
from  the  line  of  zero  temperature  required  for  the  pressure 
corresponding  to  X  on  the  other.  Then  divide  ab  in  the 
same  proportion  as  the  point  X  divides  the  line  AB^  which 
determines  the  desired  point  x.  It  will  be  apparent  that  if 
the  volume  of  the  liquid  be  not  considered,  the  percentage  of 


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TEMPERA  TURE'ENTROP  Y  DIA GRAMS, 


295 


liquid  evaporated  when  X  denotes  its  condition  will  be  in  the 
same  ratio  to  ABy  denoting  complete  evaporation,  as  the  heat 
required  for  this  evaporation  will  be  to  the  heat  required  for 
such  complete  evaporation.     Or, 

AX :  AB  ::  ax  :  ad. 

This  can  also  be  worked  out  from  entropy  tables  or  from  the 
diagram  of  §  204.  All  the  points  of  the  indicator-diagram 
can  thus  be  located,  and  an  area  enclosed  representing  the 
heat  energy  attaching  to  the  work  in  foot-pounds  of  each 
pound  of  steam  used,  and  its  departures  from  the  ideal  con- 


./      \. 

r 

-             a/l -f-A. 

3 

— ^ 

1 

/  ■        \ 

4 

A 

/ 

« 

V 

\ 

\^^^ 

1 

"^--•.^^4 

i 

1 

V 

Fig.   88. 


sumption  measure  the  efficiency  of  its  operation.  Detailed 
examples  will  be  referred  to  hereafter  when  certain  other 
points  have  been  discussed.  Its  exact  application  involves 
that  certain  desirable  refinements  should  be  made  more  clear. 


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CHAPTER   XV. 
THE   IDEAL  CYCLE   HEAT-ENGINE. 

210.  Introductory. — In  the  discussions  of  the  preceding" 
chapters  certain  principles  have  been  assumed  by  implication^ 
to  which  it  is  desirable  to  refer  now  more  in  detail. 

It  has  been  made  obvious  by  the  heat  diagrams  of  the 
preceding  chapter  that  heat  energy  is  made  available  for  me- 
chanical work  by  the  existence  of  a  difference  in  heat  level 
between  bodies.  Just  as  no  work  could  be  done  by  water- 
power  if  all  water  were  at  a  dead-level  of  the  seas,  so  no  me- 
chanical effect  could  be  produce<^,  however  great  the  amount 
of  actual  heat  energy,  if  all  bodies  were  at  a  dead-level  of 
temperature.  Hence  it  is  desirable  to  separate  T^  and  7",  by 
as  great  an  interval  as  possible,  in  heat-engines. 

Secondly,  the  lowest  available  temperature  will  be  fixed 
by  the  temperature  pertaining  to  that  climate  or  latitude 
which  attaches  to  the  best  cooling  medium  there.  This  is 
usually  water,  by  reason  of  its  high  specific  heat,  and  it  rarely 
can  be  counted  as  having  for  the  year  round  a  temperature 
as  low  as  50°  F.  in  the  temperate  zone.  Hence,  it  will  be 
impossible  to  convert  the  whole  of  any  heat  supply  into  work, 
because  the  temperature  7",  thus  fixed  is  so  far  above  the  ab- 
solute zero  of  temperatures  that  a  considerable  quantity  of 
heat  must  always  be  unavailable,  and  will  be  swept  out  by 
the  exhaust. 

Thirdly,  if  the  highest  temperature  be  a  temperature  7",, 
and  the  lowest  practicable  temperature  be  7„  it  is  obvious 
that  any  heat  taken  in  below  7,  will  have  less  availability  for 

296 


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THE  IDEAL    CYCLE  HEAT-ENGINE.  297 

conversion  into  work  than  if  it  had  beerr  taken  in  at  2",,  or 
will  be  less  effective.  Similarly,  it  M'ill  entail  a  loss  if  any 
heat  is  rejected  above  a  temperature  which  corresponds  to  7\. 

Fourthly,  complete  expansion  will  be  more  efficient  than 
incomplete  expansion,  and  should  be  so  managed  that  there 
are  no  losses  from  eddies  or  internal  movement  in  the 
medium  such  as  will  occur  with  a  free  expansion  or  one  which 
is  imperfectly  resisted  by  the  external  resistance  being  over- 
come. 

It  was  upon  the  basis  of  these  assumptions  and  deduc- 
tions that  Sadi  Carnot  in  1824  proposed  the  classic  concep- 
tion of  a  heat-engine  whose  heat  medium  should  traverse  a 
succession  of  pv  relations  between  two  fixed  limits  of  tem- 
perature, and  return  to  its  initial  state  after  each  traverse. 
The  complete  path  he  called  a  cycle.  He  applied  it  first  to  a 
permanent  gas,  used  as  a  heat  medium.  The  Carnot  cycle, 
and  the  first  and  second  laws  of  thermodynamics,  need  to  be 
noted. 

211.  The  First  Law  of  Thermodynamics. — The  science 
of  thermodynamics  means  by  definition  the  science  of  heat 
energy.  Its  first  and  fundamental  law  has  already  been 
enunciated  (§  9),  that  heat  and  mechanical  energy  are  mutu- 
ally convertible;  and  that  heat  requires  for  its  production  the 
expenditure  of  a  definite  number  of  units  of  work,  or  by  the 
expenditure  of  heat  a  definite  number  of  units  of  work  can 
be  done.  It  is  obvious  that  back  of  this  law  lies  the  funda- 
mental conception  of  the  conservation  of  energy,  which  may 
be  stated:  **  Energy  cannot  be  created  nor  can  it  be  annihi- 
lated  by  any  physical  processes  which  the  mind  can  con- 
ceive.*' 

212.  The  Second  Law  of  Thermodynamics. — What  is 
known  as  the  second  law  of  thermodynamics  has  been  vari- 
ously enunciated  by  the  great  masters  who  have  studied  it. 
The  axiom  of  Clausius  may  be  treated  as  a  first  section  of  the 
second  law:  *'Heat  cannot  pass  of  itself  from  a  colder  body 


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298  HE  A  T  AND   HEA  T-ENGINES. 

to  a  hotter  one,"  meaning  that  of  two  bodies,  that  to  which 
heat  energy  passes  is  always  the  colder  one,  unless  mechan- 
ical energy  comes  in  from  without.  This  is  otherwise  ex- 
pressed by  saying  that  **  A  self-acting  machine  cannot  convey 
heat  from  one  body  to  another  at  a  higher  temperature," 

Rankine's  statement  of  the  second  law  may  be  combined 
with  the  foregoing:  **  If  the  absolute  temperature  of  any  uni- 
formly hot  substance  be  divided  into  any  number  of  equal 
parts,  the  effect  of  each  of  those  parts  in  causing  mechanical 
work  is  equal."  That  is,  provided  the  work  of  transfer  is 
done  in  the  most  efficient  way,  the  equal  intervals  into  which 
any  range  of  temperature  may  be  divided  are  equally  effective 
when  heat  is  allowed  to  pass  through  all  the  intervals  from 
the  top  to  the  bottom  of  the  range.  This  is  graphically  ob- 
vious from  the  temperature-entropy  diagram  of  Fig.  80.  It 
assumes,  therefore,  in  it  the  conception  of  the  absolute  scale, 
and  that  Carnot's  cycle  is  used  in  effecting  the  transfers  of 
heat  into  work. 

213.  Carnot's  Cycle. — Carnot*s  cycle  is  the  realization  of 
the  expansion,  compression,  and  heating  and  cooling  of  a 
perfect  gas  under  conditions  which  §  197  has  shown  to  be 
those  of  maximum  efficiency.  The  heating  and  cooling  must 
be  done  at  a  constant  temperature,  and  therefore  these  changes 
of  pressure  and  volume  in  the  working  cylinder  must  be  by 
the  isothermal  law  to  secure  maximum  effect.  The  expansion 
must  be  done  without  additional  heat  supply  and  without 
loss  externally;  it  must  therefore  be  adiabatic.  The  com- 
pression similarly  must  be  without  change  in  entropy,  but 
only  cause  a  change  from  the  temperature  7",  back  to  T^\  the 
compression  must  therefore  be  adiabatic.  The  conditions, 
therefore,  imposed  by  the  Carnot  cycle  are  those  presented  in 
Fig.  89.  The  cylinder  and  piston  must  have  no  heat  capacity, 
nor  friction.  The  bottom  of  the  cylinder  is  a  perfect  con- 
ductor. The  element  -^  is  a  heat-source  of  great  capacity  at 
a  temperature  T",,  and  the  element  dT  is  a  condenser  of  great 


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THE  IDEAL    CYCLE  HEAT-ENGINE, 


299 


capacity  maintained  at  7*,.  Both  the  source  of  heat  and  the 
cold  body  aie  so  capacious  that  no  change  in  T^  or  T^  can 
occur  while  the  pound  of  gas  behind  the  piston  is  heated  by 
contact  with  the  heater,  and  cooled  by  contact  with  C.  B  is 
a  non-conducting  cylinder-cover,  for  use  when  the  perfect  gas 
is  expanding  adiabatically  and  without  influence  of  heat  and 


cl^i 


FiG.89. 


cold.     The  relations  of  pressure-volume  for  the  various  stages 

are  given  by  the  subscripts  on  the    diagram.     The  specific 

heat  at  constant  pressure  will  be  denoted  by  Cp  and  the  ratio 

V 
between  the  initial  and  final  volumes  -y^,  which  must  be  the 

yd 

same  as  the  ratio  tf,  will  be  denoted  by  the  factor  r,  or  the 

ratio  of  the  expansion. 

There  will  be  four  steps  or  stages.  The  student-reader 
is  advised  to  compare  the  procedure  given  in  §§  197-198: 

(a)  Apply  the  heater  A.  The  piston  rises;  the  unit 
weight  of  gas  expands  isothermally  at  T^.  The  heat  energy 
taken  in  is 

H,  =  CT,  hyp.  log  r, 
which  all  goes  to  increase  entropy. 


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300  HEAT  AND  HEAT-ENGINES. 

{b)  Heater  A  is  removed,  cover  B  is  applied,  and  the  pis- 
ton moves  out  at  the  expense  of  its  temperature,  without 
change  of  entropy,  until  the  temperature  falls  to  7",  by  such 
expansion  against  external  resistance. 

{c)  Take  away,  cover  B  and  apply  cool  body  or  condenser 
C  at  T^.  No  change  will  take  place,  because  the  expansion 
is  complete,  unless  the  piston  be  pushed  back.  But  if  the 
piston  is  retracted  the  smallest  tendency  to  an  increase  of 
temperature  above  T^  is  at  once  met  by  a  flow  of  energy  into 
the  condenser.  The  gas  loses  entropy  down  to  the  stage 
represented  by  7\,  and  the  amount  rejected  to  the  condenser 
will  be  the  difference  between  the  entropy  as  T^  and  T^  or 

//,  =  CT^  byp-  log  ^• 
{d)  Remove  the  condenser  C  and  replace  B  when  the 
point  d  is  reached.  The  determination  of  this  point  has 
already  been  touched  upon  and  found  graphically  (§  199)- 
The  piston  is  now  still  further  forced  in  and  back  until  the  gas 
has  its  initial  volume  F^,  and  if  the  point  d  was  rightly  chosen 
it  has  also  the  temperature  7*,  at  which  it  started  because  the 
compression  has  been  adiabatic,  and  the  cycle  has  been  com- 
pleted. For  the  relations  of  Fi  and  V^  to  produce  the  desired 
final  temperature  7,,  refer  to  §  168,  which  will  give 

T,       IVY-'  7-,  _  IV,\-' 

according  as  the  location  ol  t  or  d  is  desired. 

It  will  appear,  therefore,  that  the  Camot  cycle  gives  an 
external  work  in  foot-pounds  which  will  be  778  times  the 
difference  between  the  heat  rejected  and  the  heat  received, 
or,  for  the  complete  cvcle. 

Work  =  77^C{T,  -  T.)  hyp.  log  r. 

which  is  778  times  the  area  included  in  tht  diagram  of  curves 
(Fig.  89),  all  transfers  having  been  made  at  maximum  effi- 
ciency. 


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THE  IDEAL   CYCLE  HEAT-ENGINE,  3OI 

214.  Carnot's  Cycle  Reversed. — In  the  foregoing  con- 
ception, the  curves  have  been  described  by  starting  at  a  and 
following  round  the  cycle  clockwise,  as  it  were.  P,  however, 
the  start  be  made  from  a  and  the  curves  described  in  the  re- 
verse order,  the  condition  tf  affairs  is  that  in  which  mechan- 
ical energy  is  converted  into  heat,  or  Carnot's  cycle  is  re- 
versed.    What  happens  then  will  be: 

{e)  The  cover  B  being  in  place,  the  piston  is  drawn  to  the 
right  till  the  point  d  is  reached.  The  adiabatic  ad  is  traced, 
and  the  gas  cools  down  to  7*,. 

(y*)  Cover  B  is  removed,  and  condenser  C  is  applied. 
The  piston  is  drawn  out  still  further  to  the  right,  but  as  the 
gas  is  in  contact  with  C  at  the  temperature  7",  it  cannot  fall 
below  that  temperature  in  expanding,  and  heat  flows  from 
the  condenser  according  to  the  isothermal  law,  to  the  amount 

//,  =  C,rhyp.  logr. 

(^)  The  point  c  being  reached,  the  condenser  is  detached, 
the  non-conducting  cover  B  is  replaced,  and  by  external 
mechanical  energy  the  piston  is  forced  back  to  b.  The  com- 
pression being  adiabatic,  the  temperature  rises  to  7,  without 
rejection  of  heat  in  the  process. 

(A)  Further  compression  back  to  initial  volume  with  cover 
B  removed,  and  the  heater  A  applied.  Heat  flows  into  A 
because  the  compression  must  be  isothermal,  the  curve  ba  is 
described  and  the  heat  which  passes  into  A  will  be 

H^  =  C,T  hyp.  log  r. 

It  will  appear  from  a  comparison  of  H^  and  H^  and  of  H^ 
and  //,  that  these  are  equal,  or  the  same  amount  has  been 
put  back  into  A  by  the  reversed  process  as  was  taken  out  in 
the  direct  cycle,  and  the  same  amount  was  taken  out  of  C  in 
the  reverse  process  which  was  rejected  into  it  on  the  direct 
cycle. 

A  cycle  capable  of  being  operated  in  either  direction  is 
called  a  reversible  cycle. 


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302  HEAT  AND   HEAT-ENGINES. 

215.  Carnot's  Criterion  of  Reversibility.— It  is  not  diffi- 
cult to  show  that  the  efficiency  of  the  reversible  engine  is  a 
maximum.  Let  it  be  conceived  that  there  are  two  heat- 
engines  working  between  the  same  limits  7",  and  T",,  one  non- 
reversible operating  by  the  direct  cycle,  to  be  designated  by 
Dy  and  the  other  a  reversible  engine  operating  on  the  reverse 
cycle  R,  Suppose  both  to  be  capable  of  being  connected  to 
the  same  heater  A  and  the  same  condenser  C  and  to  with- 
draw and  apply  heat  as  they  operate.  Let  them  be  sup- 
posed equally  frictionless,  and  that  they  are  connected  to- 
gether so  that  D  drives  R^  as  a  steam-engine  drives  an  air* 
compressor,  without  loss.  Then  if  the  two  machines  were 
equally  efficient,  the  heat  withdrawn  from  A  to  drive  D  would 
be  restored  by  the  pumping  action  of  R,  and  the  heat  added 
to  C  by  Z^  would  be  withdrawn  by  R.  The  result  would  be 
an  indefinite  continuance  of  the  action,  without  addition  of 
outside  heat  or  mechanical  energy.  If,  however,  R  is  more 
efficient  than  D^  and  puts  back  into  A  more  heat  than  D  has 
withdrawn  from  it  in  order  to  drive  R,  then  it  will  follow  that 
the  cold  body  from  which  R  derives  its  heat  is  transferring 
heat  to  a  warmer  body,  which  is  contrary  to  all  experience, 
and  to  the  enunciation  of  that  experience  in  the  second  law 
of  thermodynamics.  But  D  is  any  engine  working  between 
the  same  limits  of  7",  and  7",.  Hence  no  engine  can  be  more 
efficient  than  the  reversible  one.  But  may  not  the  direct 
engine  D  be  less  efficient  than  the  reversible  engine?  This  is 
met  by  assuming  both  engines  to  be  reversible,  and  following 
the  same  reasoning.  It  is  similarly  proved  that  neither  can 
be  more  efficient  than  the  other;  whence: 

(i)  The  reversible  heat-engine  has  the  maximum  effi- 
ciency when  the  limits  7,  and  7  are  given. 

(2)  All  reversible  heat-engines  working  between  the  same 
limits  of  temperatures  are  equally  efficient;  that  is,  the  effi- 
ciency in  the  thermodynamic  sense  is  independent  of  the  heat 
medium. 

This  second  form  of  enunciation  h^s  been   preferred  by 


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THE  IDEAL   CYCLE  HEAT-ENGINE.  303 

some  for  one  of  the  statements  of  the  second  law  of  ther- 
modynamics. 

216.  Efficiency  in  the  Carnot  Cycle. — Remembering  that 
the  efficiency  of  any  machine  is  the  ratio  which  the  total  avail- 
able work  bears  to  the  work  actually  realized,  the  efficiency 
of  a  Carnot  engine  will  be: 

Heat  utilized  _  C(  T,  —  T^  hyp,  log  r  _  T,  —  T^  _     _  T, 
Heat  applied  C3,  hyp.  log  r  T^  T^' 

But  the  foregoing  discussion  has  shown  that  no  reversible 
heat-engine  can  be  more  efficient  than  another  working 
between  the  same  temperature  limits.  Hence  the  above 
expression  for  efficiency  is  that  of  maximum  possible  effi- 
ciency, or  is  the  measure  of  perfect  efficiency  for  all  engines 
receiving  and  rejecting  heat  under  the  conditions  assumed  by 
Carnot. 

Most  heat-engines,  with  the  exception  of  the  gas-engine, 
operate  under  this  assumption.  In  the  steam-engine,  for 
instance,  the  capacity  of  the  cylinder  up  to  cut-off  is  filled  by 
vaporization  at  a  constant  pressure  and  temperature,  and  the 
condensation  or  exhaust  is  at  a  lower  constant  pressure  and 
temperature;  the  expansion  and  compression  are  adiabatic^ 
as  assumed  by  the  Carnot  requirements.  The  difficulty  is, 
however,  that  the  actual  engine  does  not  and  cannot  reach  the 
ideal  efficiency  for  reasons  to  be  made  apparent  in  the  next 
chapter,  which  are  concerned  with  the  actual  construction  of 
the  steam-engine  and  are  not  capable  of  being  reduced  to  non- 
experimental  statements. 

It  will  be  observed  in  discussing  the  conclusion: 

Efficiency  =  -^ — ?  =  i  —  y. 

(1)  The  efficiency  increases  with  higher  temperatures  (and 
pressures)  for  the  heat  medium  as  it  enters. 

(2)  The  lower  temperature  being  fixed  by  available  cooling 
bodies  for  condensers,  the  efficiency  can  never  reach  unity 
while  7i  has  to  be  so  large.    Figs    90  and  91  show  a  plotting 


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304 


ffEAT  AND  HEAT-ENGINES. 


.SO 

\1 

"" 

^ 

^" 

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■"■ 

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L- 

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rat 

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J, 

L« 

Pj  -  20   40    60   80   100   120   140   160   ^80   200   2»   ^40   aeO   280 

Oarnot  Oycle.    Non-oondensinq  Steam  Engine  Oyoli 

P.  =15 

Fia.  90. 


.so 

' 

. 

"" 

^" 

"" 

"■ 

■" 

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r~ 

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.45 

JIO 

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I^-  20  _  40    60   80   100   120   140   100   ISO   200   230   240   260   290   800 

Oarnot  OvoLCi    Oondensinq  Steam  Engine  Oyole 
Pi  =  8 

Fig.  91. 


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THE  IDEAL   CYCLE  HEAT-ENGINE.  305 

of  such  efficiencies  with   7",  chosen  as  212**  F.  in  Fig,  90  and 
with  T^  as  125**  for  Fig.  91. 

(3)  The  effect  of  condensing  the  steam  is  to  lower  T^  and 
of  compounding  cylinders  is  to  make  it  easier  to  raise  7",  (§§ 
172-174). 

(4)  The  efficiency  does  not  include  pressure  or  specific 
heat  or  other  physical  properties  of  the  medium,  but  is  de- 
pendent on  temperature  limits  alone. 

(5)  Air  as  a  heat  medium,  allowing  a  higher  value  for  7", 
before  the  pressure  becomes  troublesome,  is  a  more  efficient 
heat  medium  than  steam  where  this  difficulty  occurs.  There 
must  be  some  other  things  than  heat  efficiency  to  consider. 

(6)  The  low  efficiency  of  the  steam-engine  thermally  is  not 
a  reflection  upon  its  effectiveness  as  a  means  of  transforming 
the  available  energy  of  a  fuel  into  mechanical  energy.  The 
mechanical  efficiency  is  not  to  be  confused  with  the  thermal 
efficiency.  This  latter  is  limited  by  the  greatness  of  the  min- 
imum value  for  7*,. 

217.  Rankine  and  Clausius^ Cycles. — The  Carnot  cycle 
for  the  steam-engine  involves  the  condition,  which  is  not 
usually  realizable,  that  the  heat  medium  is  raised  in  temper- 
ature by  compression.  Rankine  introduced  a  cycle  and  elab- 
orated formulae  for  its  efficiency  in  which  the  succession  of 
curves  are  of  an  ideal  indicator-diagram.  The  isothermal  is 
horizontal  for  the  period  of  admission ;  the  expansion  is  either 
an  adiabatic  or  a  saturation  curve;  the  isothermal  for  the 
back-pressure  line  is  either  at  the  level  of  complete  expansion 
or  below  it;  and  finally  the  effect  of  the  water-volume  in 
the  steam  and  any  effect  of  entrapped  steam  used  as  a  cushion 
in  compression  are  neglected.  This  cycle,  like  the  Carnot, 
is  approachable,  but  not  attainable  in  practice.  It  offers  the 
advantage  that  in  the  design  and  test  of  an  actual  engine  it 
may  be  compared  with  an  ideal  one  which  may  be  called  a 
purely  thermodynamic  machine  of  similar  construction  and 
like  limits  of  pressure,  temperature,  and  degree  of  expansion. 


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306  HEA  T  AND  HEA  T-ENGINES. 

A  cycle  by  Clausius  is  the  Carnot  cycle  without  compres- 
sion, but  with  complete  expansion  down  to  the  back-pressure 
line.  It  permits  the  measure  of  the  loss  incurred  when  the 
Rankine  cycle  is  used  without  such  complete  expansion. 

2i8.  Theoretical  Weight  of  Heat  Medium  for  a  given 
Work. — An  interesting  practical  deduction  from  the  Carnot 
equation  for  efficiency  is  easily  made.     Since 

7",  —  ^«  _  Heat  utilized 
7",  Heat  applied' 

the  second  member  can  be  reduced  to  foot-pounds  by  multi- 
plying both  terms  by  778.     Hence 

J",  —  7", Work  utilized  in  foot-pounds 

~T,  778^;  ' 

in  which  Q,  is  the  product  of  the  weight  of  heat  medium  into 
the  heat  which  it  has  absorbed  in  reaching  the  temperature 
7",.  In  the  case  of  steam,  this  heat  will  be  the  heat  of  vapor- 
ization, or  the  latent  heat,  or  the  product  7^,  when  the  feed- 
water  at  the  temperature  corresponding  to  the  pressure  7,  is 
made  into  steam  at  that  pressure.  In  §  139  this  was  desig- 
nated by  r,  and  is  found  by  subtracting  the  heat  of  the  liquid 
{q)  from  the  total  heat  (X).  Hence  it  is  only  necessary  to  sub- 
stitute for  the  work  term  the  number  of  foot-pounds  of  work 
corresponding  to  a  horse-power  per  hour  (60  X  33,000  = 
1,980,000),  and  for  j2i  ^  factor  made  up  of  the  unknown 
weight  of  heat  medium  sought  multiplied  by  its  heat  of  va- 
porization at  the  temperature  7,.  That  is,  if  M  denote  the 
desired  weight  of  heat  medium, 

(2.  =  Mr,. 
Whence 

7;  —  7,  _  1980000 
7,       "   77^Mr,' 


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THE  IDEAL   CYCLE  HEAT-ENGINE. 


307 


whence 


M^ 


-       T,       V  2  54S 


It  IS  interesting  to  note  that  the  weight  of  heat  medium 
decreases  as  the  heat  of  vaporization  increases,  and  that  the 
latter  is  the  measure  of  the  amount  of  work  which  will  be 
done  by  a  unit  of  weight  of  the  medium.  The  factor  2545 
is  interesting  as  presenting  the  number  of  units  of  heat  to  be 
converted  per  hour  into  work  for  each  horse-power, 

A  table  of  efficiencies  and  theoretical  water-consumption 
per  horse-power  may  be  computed  on  proper  assumptions  for 
condensing  and  non-condensing  engines  as  follows  : 

WATER    CONSUMPTION    AND    EFFICIENCY. 


Condensing. 

Non-condensing. 

Gauge  Pressure 

above 

Atmosphere. 
Initial. 

Efficiency. 
7,  -  7-,. 

Pounds  of  Steam 
per  H.  P.  per 

Efficiency. 

Pounds  of  Steam 
per  H.  P.  per 

7i 

Hour. 

Tx 

Hour. 

15 

0.189 

14.3 

0.053 

50.9 

30 

0.215 

12.8 

0.084 

32.8 

60 

0.249 

II. 4 

0.124 

22.9 

100 

0.278 

10.5 

0.157 

18.4 

150 

0.302 

9.8 

0.186 

16.0 

200 

0.320 

9-5 

0.207 

14.6 

300 

0.347 

9.0 

0.238 

131 

The  temperature  7",  is  2 12**  F.  for  non-condensing  engines, 
and  for  the  condensing  engines  it  was  made  115**,  correspond- 
ing to  1.5  pounds  pressure. 

In  engines  using  a  permanent  gas  like  air,  which  has  no 
heat  of  vaporization,  as  in  the  case  of  vapors,  the  factor  r  is 
replaced  by  latent  heat  of  expansion,  which  is  the  product  of 
the  entropy  by  the  temperature. 

The  same  result  can  be  secured  from  the  temperature- 
entropy  diagram  directly.     Assuming  the  diagram  of  Fig.  80, 


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308  HEA  T  AND   HEA  T-ENGINES. 

which  presents  the  Carnot  cycle  of  maximum  efficiency,  it  is 
apparent  that  the  temperature-entropy  area  in  heat-units  can 
be  made  the  area  in  foot-pounds  by  multiplying  both  mem- 
bers by  778.     That  is, 

Area  in  heat-units  =  (02  —  0,)(7',  —  T",). 

Area  of  work  in  foot-pounds  =  778(0,  —  <t>^{T^  —  T^. 

But  the  factor  0,  —  0,  is  the  change  in  entropy  at  7",  in  pass- 

ing  from  water  at    7",  to   steam  at    7,.  w^iich  is   -7^  for  one 

Mr 
pound  of  fluid  and  becomes    ~j~  if  an  unknown  weight  is  to 

do  the  work  imposed  by  giving  a  value  to  the  foot-pounds  of 

the  first  member.      Hence 

Mr 
Water  per  H.P.  per  hour  =  778-^(7;  -  7;). 

-» 1 

Whence 

^=2545- 


^(7-.  -  7-.)' 

as  before. 

In  the  case  of  a  permanent  gas,  the  value  for  (0,  —  0,)  for 
an  isothermal  expansion  was  found  to  be 

R  hyp.  log  r. 

Whence  the  equations  become 

Work  of  one  H.P.  per  hour  =  77MIR  hyp.  log  r(7,  —  T,), 

whence 

M= ^J15 

R  hyp.  log  r{T,-  T,)' 

in  which  r  is  the  ratio  of  the  final  to  the  initial  volumes  in  the 
expansion  process. 


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THE  IDEAL   CYCLE  HEA  T-ENGINE.  309 

219.  Recapitulation. — The  Carnot  cycle  being  the  cycle 
within  which  must  lie  the  performance  of  actual  engines,  and 
to  which  they  should  approximate  as  closely  as  possible  to 
make  the  actual  value  of  M  small  and  to  make  the  ex- 
penditure of  fuel  to  raise  it  to  T^  as  small  as  possible,  it 
becomes  of  interest  to  examine  the  causes  of  difference  be- 
tween the  ideal  and  the  real  engine,  topics  which  form  the 
next  chapter.  But  it  should  not  be  overlooked  as  a  funda- 
mental departure  from  actual  conditions,  that  the  Carnot 
cycle  for  the  steam-engine  demands  three  impossibilities: 

(i)  That  the  body  of  water  in  the  boiler  be  always  at  the 
temperature  7",  no  matter  what  the  exigencies  of  feeding,  or 
what  feed-water  temperature  be  available,  and  that  there  be 
no  drop  of  temperature  in  supplying  the  cylinder. 

(2)  That  all  heat  be  rejected  from  the  cylinder  at  the  lower 
temperature,  7",,  and  not  by  a  process  of  gradual  cooling. 
That  is,  the  steam  in  giving  up  its  heat  shall  be  at  the  tem- 
perature of  the  condenser;  if  it  were,  it  would  not  give  it  up. 

(3)  That  all  heat  delivered  to  the  medium  shall  be  carried 
down  from  T^  to  T^  purely  adiabatically,  without  being  di- 
verted by  radiation  or  contact  or  other  methods  of  transfer, 
in  spite  of  the  conducting  qualities  of  the  structural  materials 
used,  in  spite  of  eddies  in  the  steam  itself,  and  in  spite  of 
possible  free  or  unresisted  expansion,  '*drop**  into  the  lower 
pressure  of  condensing  appliances,  receiver,  and  the  like. 

Finally,  the  thermal  and  not  the  mechanical  character  of 
the  efficiency  equation  needs  to  be  emphasized,  and  its  applica- 
tion only  to  any  one  medium  to  which  it  is  for  the  moment 
applied.  A  study  of  the  temperature-entropy  diagram,  how- 
ever, for  a  Carnot  cycle,  shows  that  when  the  medium 
changes  and  another  is  used  which  has  a  different  entropy 
value  at  T^^  the  efficiency  ratio  changes  in  the  same  propor- 
tion (another  way  of  saying  that  the  thermal  efficiency  de- 
pends on  the  temperature  ratio  alone);  but  the  Carnot  equa- 
tion does  not  say  that  the  same  weight  of  different  media  will 


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3IO  HEAT  AND   HEAT-ENGINES, 

be  required  with  a  same  temperature  range,  nor  that  all 
media  have  to  be  used  at  the  same  range,  nor  that  the  heat 
to  be  expended  to  raise  all  media  to  7",  is  the  same,  nor  the 
extent  of  condensing  appliances  to  cool  these  different  media 
to  r,.  This  belongs  to  a  different  department  of  the  subject, 
and  will  be  treated  in  Chapter  XXI. 


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CHAPTER   XVL 
THE  CYCLE  OF  THE   ACTUAL  STEAM-ENGINE. 

220.  Introductory. — It  has  already  been  said  that  the  ac- 
tual engine  must  depart  from  the  Carnot  ideal  because — 

(i)  Heat  is  not  received  from  the  furnace  at  a  constant 
high  temperature  T',. 

(2)  Heat  is  not  rejected  at  a  constant  lower  tempera- 
ture 7",. 

(3)  All  the  steam-heat  energy  is  not  devoted  to  work. 

221.  Elements  of  Departure  of  the  Actual  Cycle  from 
the  Ideal  Carnot  Cycle. — But  besides  these,  and  belonging 
to  a  class  which  the  engine-designer  can  control  in  part,  are 
other  sources  of  loss  or  ineffectiveness,  to  which  attention 
must  be  called.     Among  these  are: 

(4]  Loss  of  pressure  and  temperature  from  friction  and 
radiation  and  conduction  in  the  steam-pipe  between  the  boiler 
and  the  engine. 

(5)  For  this  cause  T^  at  the  engine  is  not  the  same  as  at 
the  boiler.  The  steam  is  therefore  not  dry,  but  carries  a  mist 
of  watery  particles  resulting  from  condensation,  and  the  en- 
tropy value  is  not  that  belonging  to  dry  steam  at  T^. 

(6)  In  the  engine  itself,  at  throttle-valve,  governor-valve 
(if  any),  and  at  the  ports  of  the  valve  or  valves  by  which  dis- 
tribution of  steam  is  effected  into  and  out  of  the  cylinder,  a 
loss  of  pressure  occurs  by  the  process  known  as  "  wire-draw- 
ing "  from  friction  and  the  work  of  overcoming  it. 

(7)  Condensation,  and  entropy-drop  by  contact  of  the  hot 

311 


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312  HEAT  AND   HEAT-EhTGINES. 

incoming  steam  with  a  cylinder-head  and  one  side  of  the 
piston,  and  the  steam -passages  to  that  end  of  the  cylinder, 
which  have  just  ceased  a  contact  with  steam  at  the  lower 
temperature  T",.  The  exhaust  steam  has  cooled  these  sur- 
faces off  and  swept  out  the  heat  with  itself,  and  initial  con- 
densation covers  these  cooler  surfaces  with  dew.  This  is  an 
entropy-leakage  of  which  theory  can  take  account  with  diffi- 
culty, and  which  yet  afifects  greatly  the  value  of  M  (^  218). 

(8)  Even  if  the  cylinder-walls  and  cover  were  absolutely 
non-conducting  and  non-diathermanous,  a  condensation  of 
steam  will  occur  after  cut-off  and  during  the  process  which  is 
alleged  to  be  adiabatic.  The  conversion  of  heat  into  work 
must  result  under  non-isothermal  conditions  in  the  condensa- 
tion of  a  certain  percentage  of  steam  to  water,  or  (unless  steam- 
jacketed)  the  actual  curve  of  the  indicator-card  will  fall  within 
the  curve  of  saturation  for  steam  as  laid  out  from  tabular 
values  (§  200).  It  happens,  however,  usually,  that  as  this  con- 
densed percentage  of  moisture  lying  on  the  cylinder  bottom 
or  in  the  form  of  dew  on  the  metallic  surfaces  is  reduced  in 
pressure  by  the  increase  in  cylinder  volume  during  expansion, 
the  point  is  reached  at  which  the  equalization  of  temperature 
and  boiling-point  for  water  is  also  reached.  When  this  oc- 
curs, if  the  cylinder-walls  will  furnish  the  necessary  heat  en- 
ergy to  supply  entropy  to  this  water,  it  will  absorb  the  heat 
of  vaporization  r  which  it  requires  at  this  lowered  pressure, 
and  the  steam  formed  will  raise  the  pressure  ordinate  on  the 
indicator-diagram,  and  the  cylinder  metal  has  been  cooled 
still  further.  Here  again  the  theoretical  diagram  gives  no 
hint  of  this  entropy  reaction,  but  the  incoming  steam  has  to 
supply  the  new  heat  called  for  by  an  increase  in  the  loss  dis- 
cussed under  (7).  The  heat  supplied  to  the  steam  by  this 
re-evaporation  of  condensation  is  swept  out  at  exhaust  and  is 
lost. 

(9)  At  the  end  of  expansion  the  exhaust  opens,  and  the 
release  occurs  to  a  condenser  or  to  the  atmosphere.     It  has 


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THE   CYCLE   OF  THE  ACTUAL  STEAM-ENGINE.       313 

been  already  noted  that  in  steam-engines  it  is  not  usual  to  se- 
cure complete  expansion  (§  201)  because  the  forward  effort 
becomes  ineffective  at  the  end  of  the  stroke.  If  the  valve- 
gear  is  automatically  adjusted  by  variation  in  the  load,  with- 
out change  in  steam-pressure,  it  may  easily  happen  that  the 
pressure  at  the  release  is  rarely  or  never  that  of  the  back-pres- 
sure or  exhaust  line.  If  above  that  point,  there  is  the  loss 
from  non-adiabatic  expansion  on  the  temperature-entropy 
diagram  (§  201),  and  the  exhaust  sweeps  heat  out  unutilized. 
If  the  terminal  pressure  at  release  is  less  than  that  represent- 
ing the  back-pressure,  the  expansion  curve  has  crossed  the 
back-pressure  line,  forming  a  loop  at  this  end  of  the  diagram. 
The  fly-wheel  must  therefore  be  making  the  engine  overcome 
its  own  friction,  and  be  doing  a  little  pumping  action  in  the 
cylinder;  while  the  contents  of  the  exhaust-passages  will 
evince  a  tendency  to  reverse  their  outward  direction,  at  a  cost 
of  mechanical  energy,  and  the  expanding  steam  loses  by  free 
or  unresisted  expansion. 

(10)  During  exhaust  the  pressure  attaching  to  the  actual 
7",  of  the  condenser  or  the  atmosphere  may  not  prevail  in  the 
cylinder,  by  reason  of  friction  or  wire-drawing  of  the  exhaust 
outflow  from  valves,  passages,  and  piping  connections. 

(11)  During  exhaust  at  or  near  7",  the  cylinder-walls  and 
piston-head  are  radiating  heat  to  the  exhausting  volume  of 
saturated  steam,  containing  also  perhaps  a  mist  of  water  un- 
evaporated.  This  is  a  different  heat  from  that  which  the 
heat  medium  is  giving  up,  but  which  must  be  supplied  at  the 
next  stroke  by  the  incoming  steam  [see  (7)]. 

(12)  The  exhaust- valve  and  port  probably  close  before  the 
end  of  the  return  stroke,  entrapping  some  steam  and  com- 
pressing it  adiabatically  in  the  main,  raising  its  pressure  and 
temperature  as  the  volume  diminishes.  If  prudently  done, 
the  pressure  may  rise  to  the  initial  pressure.  It  is  usually 
done  by  the  excessive  living  force  of  the  reciprocating  parts 
which  would  otherwise  be  wasted,  and  the  elastic  steam-cush- 


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314  HEAT  AND   HEAT-ENGINES. 

ion  serves  to  lessen  the  flexing  effect  on  the  crank-pin  which . 
would  otherwise  receive  it.  The  heat  due  to  this  compres- 
sion is  regained  for  the  cylinder-walls,  although  under  abso- 
lutely ideal  conditions  the  heat  represented  by  the  energ}'  of 
the  reciprocating  parts  would  not  have  been  wasted  upon 
them  in  the  first  place,  but  should  all  have  been  absorbed  in 
useful  work  on  the  crank-pin.  If  compression  is  carried  too 
far,  a  loop  forms  on  the  top  of  the  compression  curve,  with 
free  expansion  losses,  excess  of  pumping  action,  and  arrest  of 
steam-flow  into  the  cylinder. 

(13)  The  clearance  space  left  between  the  piston  and  the 
cylinder-head  at  each  end,  to  prevent  impact,  to  lessen 
trouble  from  water,  and  to  give  a  volume  in  which  forward 
pressure  may  establish  itself  at  dead-centres,  adds  a  volume 
to  the  actual  piston  displacement  caused  by  the  stroke.  The 
valve-passages  add  a  further  necessary  waste  volume,  which 
must  be  filled  with  steam  at  full  pressure  and  temperature  at 
each  stroke,  and  which  is  exhausted  (less  the  compression  or 
cushion  steam)  without  having  done  as  much  work  as  if  the 
expanding  volume  had  been  smaller.  The  heat  to  make  this 
wasted  volume  of  steam  is  lost. 

(14)  It  is  only  in  condensing  engines  that  the  exhausted 
steam  after  condensation  is  pumped  back  into  the  boiler  at 
7*,.  When  the  engine  exhausts  into  the  atmosphere  whose 
temperature  is  7",  it  is  apparent  that  there  is  a  jolt  in  the  heat 
cycle,  representing  the  difference  usual  between  the  temper- 
ature of  the  exhaust-steam  and  the  temperature  at  which  the 
feed-water  can  be  usually  presented  to  the  boiler.  If  the 
feed-water  is  preheated  by  a  heat-supply  outside  of  the  boiler- 
furnace,  and  other  than  a  wasted  heat,  this  must  be  allowed 
for. 

(15)  The  ideal  cycle  assumes  that  the  unit  weight  of 
medium  is  raised  from  T^  to  T^  by  an  adiabatic  compression. 
In  actual  conditions  there  is  a  gain  in  entropy  in  the  gradual 


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THE    CYCLE   OF  THE  ACTUAL   STEAM-ENGINE.        31$ 

heating  by  the  fire  from  2",  to  7",,  and  a  loss  because  this  gain 
IS  not  all  made  at  7"^. 

(i6)  During  the  cushion-compression  heat  is  transferred  to 
the  medium  by  the  mechanical  work,  and  some  of  this  in- 
crease in  heat  condition  is  transferred  to  the  metal  of  piston- 
head,  cylinder-head,  walls,  and  passages. 

(17)  The  loss  of  heat  represented  by  the  equivalent  of  the 
mechanical  energy  consumed  wastefully  in  the  friction  of  the 
engine  mechanisms,  which  is  caused  by  the  size  and  weights 
of  the  parts,  packing-friction,  valve-friction,  and  the  like, 
which  are  independent  of  the  load  or  work  done. 

(18)  Any  additional  friction  (usually  small  in  amount) 
chargeable  to  the  load  of  the  engine  in  augmenting  its  friction 
when  running  with  no  load. 

The  above  list  enumerates  the  points  in  which  every  actual 
engine  is  likely  to  differ  from  every  other  actual  engine,  and 
the  losses  which  for  this  reason  are  incapable  of  being  in- 
cluded under  a  generalization,  and  are  to  be  experimentally 
determined  for  each  engine  or  each  type  of  engine.  For  this 
reason  they  have  been  called  extra'tkermodynamic  losses,  or 
internal  wastes.  It  is  the  object  of  the  engineer  or  designer 
to  reduce  these  losses  as  far  as  possible  in  new  constructions, 
and  in  making  guarantees  as  to  performance  he  should  be 
able  to  evaluate  their  proportion  to  the  whole  expenditure  of 
energy.  It  will  be  convenient  for  their  further  study  to 
group  the  principal  sources  of  heat  loss  into  the  following 
headings : 

I.   Loss  by  wire-drawing. 
II.      **        **  clearance. 

III.  **        **  condensation,  initial. 

IV.  **        **  **  during  expansion. 
V.      '*        '*  re-evaporation. 

VI.      *'        **  incomplete  expansion. 
VII.      **        '*  unnecessary  back-pressure,  or  imperfect  vacuum. 


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3i6 


HEAT  AND   HEAT-ENGINES. 


The  other  losses  are  usually  met  by  an  allowance  in  cylin- 
der volume  to  overcome  them,  and  by  that  increase  in  cylin- 
der volume  their  effect  is  introduced  into  the  groups  above, 
and  need  not  be  accounted  for  a  second  time.  It  is  safe  to 
say  that  at  the  end  of  the  nineteenth  century  the  thermal 
wastes  are  not  far  from  20  per  cent,  and  the  dynamic  losses 
are  less  than  10  per  cert. 

222.  Progress  in  Steam-engine  Efficiency. — The  early 
historic  engines  of  Savery  and  Newcomen  in  England  suffered 
greatly  from  heat-wastes,  by  reason  of  their  using  the  work* 
ing-cylinder  barrel  as  a  place  within  which  to  condense  the 
steam  after  the  stroke.  James  Watt's  invention  of  the  sepa- 
rate condenser  in  1769  was  a  most  important  step  toward  re- 
ducing condensation.     The  following  diagram,  Fig.  92,  has 


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Pio.   92. 

been  prepared  to  present  to  the  eye  the  improvements  of  the 
last  one  hundred  and  fifty  years,  showing  at  the  left  the  re- 
duction of  thermal  wastes  by  devices  to  be  discussed  pres- 
ently, and  at  the  right  hand  the  corresponding  increase  in 


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THE   CYCLE  OF  THE  ACTUAL   SIEAMENGINE,        317 

performance  per  hundred  pounds  of  pure  carbon  burned. 
This  latter  is  given  in  miUions  of  foot-pounds  of  work  per  100 
pounds  of  pure  carbon. 

The  elements  which  seem  to  have  had  most  influence  in 
this  result  may  be  said  to  be: 

1.  The  separate  condenser. 

2.  The  higher  temperature  and  pressure  limit. 

3.  The  steam-jacket. 

4.  The  multiple-expansion  principle. 

5.  Better  mechanical  construction. 

6.  Higher  piston  speed. 

7.  Increasing  size  of  units. 

223.  Ideal  and  Actual  Efficiency  Compared. — The  ele- 
ments which  affect  actual  efficiency  are  numerous,  and  hence 
care  is  necessary  in  making  comparisons  to  select  fair  figures. 
Certain  of  the  losses,  being  practically  fixed  in  amount  and 
not  dependent  upon  cylinder  volume,  will  be  much  greater  a 
proportion  or  percentage  in  a  small  engine  than  in  a  large 
one,  and  will  be  greater  when  the  large  engine  is  running 
below  its  rated  power  or  at  best  effect.  An  observed  result, 
with  a  200-H.P.  engine  at  100  pounds  boiler-pressure,  with 
a  back-pressure  of  5  pounds  above  vacuum  in  its  condenser, 
gave  results  at  various  ratios  of  expansion  which  are  given  in 
Fig.  93,  on  which  the  Rankine  ideal  water  consumptions  have 
also  been  plotted,  and  a  curve  for  the  friction  and  radiation 
losses. 

The  thermal  units  per  H.'P.  are  taken  as  1000  for  each 
pound  of  water. 

If  pressures  belonging  to  the  temperatures  T^  be  made  to 
varj",  curves  similar  to  those  in  Fig.  94  will  result.  These 
belong  also  to  the  simple  condensing  engine  of  average  size, 
and  larger  engines  will  do  better,  but  small  ones  not  so 
well. 

The  effect  of  increasing  the  ratio  of  expansion  by  the  ex- 
pedient of  expanding  continuously  through  two  or  three  cyl- 


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3i8 


BEAT  AND  HEAT-ENGINES 


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THE   CYCLE  OF  THE  ACTUAL  STEAM-ENGINE.       319 


inders  is  made  apparent  by  Fig.  95.  The  curves  A  are  those 
for  the  smaller  cylinder  of  a  9-  and  16-  and  24-inch  diameter 
triple  engine,  with  36-inch  stroke,  working  as  a  simple  en- 


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gine.  The  curves  B  are  derived  when  the  small  cylinder  and 
intermediate  are  used  to  form  a  compound  engine;  the 
curves  C  represent  the  triple  engine,  with  the  corresponding 
ratios  of  expansion  possible.  The  dotted  lines  give  unjack- 
eted  conditions;  the  full  line  shows  results  with  cylinders 
jacketed. 

The  table  on  page  320  also  gives  water  consumptions  from 
test  and  experiment. 

224.  Methods  of  Reducing  Internal  Condensation. — It 
>vill  be  apparent  that  the  compound  or  multiple-expansion 
engine  should  offer  the  advantage  of  diminished  wastes  from 
condensation,  when  it  is  remembered  that  the  largest  cylinder 
in  the  series  is  the  unit  cylinder,  which  determines  the  horse- 
power of  the  engine  and  must  be  present  whatever  system  of 


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320 


If  EAT  AND   HEAT-ENGINES. 


b 

e 

/ 

€ 

/ 

Type  of  Engine. 

Feed-water  per  Indicated  Horse-power  per  Hour. 

Per 

Non-condensing. 

Condensing. 

Cent 
Gained 
by  Con- 
densing 

Name. 

Probable 
Limits. 

Assumed 
for 

Compari- 
son. 

Probable 
Limits. 

Assumed 
for 

Compari- 
son. 

Simple  high-speed 

Simple  low-speed 

Compound  high-speed. 
Compound  low-speed. . 

Triple  high-speed 

Triole  low-soeed ...... 

Lbs. 
35  to  26 
32  to  24 
30  to  22 

27  to  21 

Lbs. 
33 
29 
26 

* 

24 

Lbs. 
25  to  19 
24  to  18 
24  to  16 
20  to  12X 
23  to  14 
18  to  12% 

Lbs. 
22 
20 
20 
18 

17 
16 

33 
31 
23 
25 
29 

•  The  terms  *'  high-speed  "  and  '*  low-speed,"  it  is  believed,  refer  to  the  number  of  revolu- 
tions per  minute,  and  not  to  the  piston-travel.  Low-speed  engines  are  Corliss  engines  and 
the  like,  wiih  releasing  cut-offs,  and  have  ft  rotative  speed  usually  less  than  xao  revolutions 
per  minute. 

expansion  is  used.  This  is  because  in  the  horse-power  for- 
mula PLAN  refers  to  a  pressure  over  an  area,  or  a  pv 
result,  in  which  the  volume  is  always  the  volume  at  the  end 
of  the  completed  stroke.  What  has  been  done  is  therefore  to 
add  certain  smaller  cylinders  between  the  boiler  and  the  largest 
low-pressure  cylinder,  among  which  the  temperature  range  is 
distributed,  each  taking  a  fraction  of  the  range.  Reactions 
between  the  cylinder-metal  and  the  hot  medium  within  it  are 
active  in  proportion  as  the  difference  in  their  temperatures  is 
large.  By  diminishing  the  temperature  range  in  each,  the 
expansion  in  each  cylinder  approaches  the  adiabatic  law,  and 
heat  is  saved. 

Secondly,  compounding  utilizes  in  part  at  least,  in  the 
later  cylinders,  the  steam  vaporized  by  the  metal  wall  reac- 
tions in  the  early  cylinders.  Some  heat  is  thus  recovered 
which  would  have  been  wasted  in  the  simple  engine. 

Thirdly,  the  succession  of  the  cylinders  permits  a  regen- 
erating of  the  quality  of  the  steam  by  reheating  between  cyl- 
inders. 


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THE   CYCLE  OF  THE  ACTUAL   STEAM-ENGINE.       321 

Fourthly,  the  compound  engine  favors  a  high  value  for  7\ 
and  hence  a  high  range  in  availability,  and  a  high  efficiency 
value  or  a  low  value  for  M  (§  i88)  when  Z,  is  fixed  by  limita- 
tion. 

The  compound  or  multiple-expansion  principle  has  many 
and  other  advantages  (see  §  173).  These  are  sufficient,  how- 
ever, to  more  than  offset  the  losses  caused  by  the  succession 
of  cylinders,  the  losses  in  passing  from  one  to  another,  and, 
where  fuel  cost'  or  the  size  of  the  plant  will  warrant  it,  to 
neutralize  the  increased  cost  of  the  additional  cylinders  and 
mechanism.  For  the  specific  object  of  reducing  condensation 
in  the  steam-cylinder,  the  steam-jacket,  and  the  use  of  super- 
heated steam,  are  to  be  particularly  discussed. 

225.  The  Steam-jacket. — The  steam-jacket  was  first  de- 
vised and  applied  by  James  Watt,  **  to  keep  the  cylinder  as 
hot  as  the  steam  which  enters  it."  Constructively,  it  is  an 
annular  space  surrounding  the  cylinder-barrel  and  chambered 
spaces  in  the  cylinder-heads  into  which  steam  hot  from  the 
boiler  shall  be  kept  actively  circulating.  Such  boiler-steam 
shall  continually  put  back  into  the  metal  of  the  working  barrel 
the  heat  swept  out  at  the  exhaust  from  evaporation  during 
the  expansion  and  from  contact  with  the  relatively  cool  ex- 
haust-steam. It  is  intended,  therefore,  that  internal  initial 
condensation  shall  be  made  less  because  the  working  charge 
of  steam  finds  the  cylinder  hotter  when  it  enters  it  than  when 
such  jacket  is  not  present  nor  in  action.  Furthermore,  dur- 
ing expansion  after  cut-off,  the  barrel-jacket  will  furnish  the 
heat  for  any  re-evaporation,  or  shall  heat  the  cylinder-metal 
again  after  it  has  furnished  the  heat  energy  represented  by 
such  re-evaporation  of  water  either  the  result  of  adiabatic  ex- 
pansion or  present  as  remains  of  initial  condensation.  Evap- 
oration of  water  mechanically  entrained  may  also  occur  to 
cool  the  metal  walls. 

The  structural  difficulties  which  must  be  met  in  casting 
and  using  a  cylinder  with  hollow  walls  (particularly  when  the 


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322  HEA  T  AND   HEA  T-ENGINES. 

length  is  considerable)  have  been  elsewhere  considered 
(**  Power  Plants,"  p.  291,  §  162).  The  unequal  expansion 
is  likely  to  make  one  wall  crack ;  or  if  made  in  separate  cylin- 
ders, the  inner  fitting  as  a  liner  within  the  jacket,  the  expense 
of  fitting  and  the  joint  at  the  end  are  difficulties. 
In  comment  on  the  steam-jacket  it  may  be  said: 
(i)  The  heat  which  the  jacket  supplies  to  the  cylinder- 
metal  is  surrendered  at  the  cost  of  its  own  condensation. 
Hence  the  net  gain  from  jacketing  is  the  algebraic  sum  of  a 
loss  and  a  gain. 

(2)  The  heat-supply  to  prevent  initial  condensation  is 
mainly  from  the  heads,  and  from  the  piston  if  this  latter  is  also 
jacketed,  because  the  barrel  surface  only  becomes  equal  to 
the  head  surface  when  the  piston  has  travelled  a  distance  equal 
to  one  quarter  of  the  cylinder  diameter. 

(3)  After  cut-off  and  during  expansion  the  jacket  would 
appear  to  be  suppl3nng  a  heat-flow  to  the  gradually  cooling 
steam  which  tends  to  transform  the  expansion  curve  from  an 
adiabatic  towards  an  isothermal,  and  furnish  an  entropy 
change  opposed  to  maximum  efficiency  in  Carnot's  cycle. 

(4)  The  hot  live-steam  jacket,  keeping  the  average  temper- 
ature of  the  cylinder  higher  than  when  the  latter  is  not  jack- 
eted, will  increase  the  loss  by  exterior  radiation,  unless  at 
the  same  time  increased  precautions  are  taken  by  use  of  lag- 
ging and  non-conductors  of  heat  to  diminish  this  action  both 
at  heads  and  at  the  barrel. 

(5)  The  effective  action  of  the  steam-jacket  demands  that 
the  walls  of  the  **  liner**  or  barrel  proper  should  be  highly 
conductive  of  heat.  Transfer  of  heat  by  contact  and  conduc- 
tion is  very  rapid,  but  cannot  be  truly  instantaneous.  Hence 
it  would  appear  that  jackets  are  more  effective  when  their 
time  of  action  on  the  working  steam  is  lengthened,  and  when 
the  weight  of  the  working  steam  is  less  in  proportion  to  the 
quantity  of  heat  in  units  present  i-n  the  jacket.  The  first 
statement  is  confirmed  by  the  generally  observed  fact  that  an 


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THE   CYCLE  OF  THE  ACTUAL   STEAM-ENGINE,       323 

engine  of  slow  rotative  speed  derives  more  benefit  from  jacket- 
ing than  quick-acting  engines;  and  the  other  statement  is  con- 
firmed by  the  fact  that  the  greater  the  ratio  of  expansion,  or  the 
earlier  the  cut-off  in  the  single  cylinder  or  in  the  compound, 
the  greater  the  gain  from  jacketing.  The  time  of  most  effect- 
ive action  in  heating  is  that  from  cut-off  on  one  stroke  to  the 
beginning  of  admission  at  the  next.  Hence  long-stroke  en-' 
gines  gain  less  by  jacket  action  than  short-stroke  engines  with 
the  same  ratio  of  expansion. 

(6)  The  gain  from  the  jacket  is  proportionally  less  in  mul- 
tiple-expansion engines  than  in  single-cylinder  engines  in 
which  high  expansion  is  attempted.  This  follows  because 
the  less  the  amount  or  tendency  to  condensing  action  the  less 
good  the  jacket  can  do.  The  divided  temperature  range  in 
the  compound  or  multiple  series  diminishes  the  actual  con- 
densation, and  the  increased  cylinder  surface  increases  loss  of 
heat  in  the  jackets  themselves.  Marine  tests  have  shown  a 
gain  from  jacketing  the  larger  and  cooler  low-pressure  cyh'n- 
der  of  a  compound  engine,  but  no  gain  from  jacketing  the 
high-pressure  cylinder. 

(7)  If  the  condition  of  high  grade  of  expansion  should  hap- 
pen to  concur  with  a  supply  of  steam  initially  wet,  the  jacket 
during  expansion  will  evaporate  more  water  than  was  initially 
condensed  against  the  walls.  Condensation  of  steam  in  the 
jacket  being  a  wasteful  method  of  evaporating  this  water  in 
the  working  barrel,  the  steam-jacket  may  cost  more  than  it 
saves.  In  other  words,  with  dry  steam  the  jacket  saves; 
with  wet  steam,  the  jacket  condensation  may  offset  the  gain; 
when  the  boiler  primes,  the  jacket  is  likely  to  be  a  loss. 

(8)  Hence  if  the  steam  is  superheated,  there  is  no  occa- 
sion for  a  steam-jacket. 

226.  Conditions  and  Action  of  an  Effective  Steam- 
jacket. — Circulation  of  the  hot  steam  from  the  boiler  is  the 
prime  condition  of  effectiveness  in  a  steam-jacket.  As  the 
water  is  condensed  in  the  jackets  it  should  be  removed  by 


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324  HE  A  T  AND   HEA  T-ENGINES. 

traps  or  by  gravity  back  to  the  boiler.  The  plan  of  passing 
the  steam  through  the  jackets  of  a  main  engine  to  operate  the 
cylinder  of  an  auxiliary  engine  like  an  independent  air-pump 
has  much  to  commend  it.  The  plan  of  jacketing  so  that  the 
steam  from  the  jackets  enters  the  valve-chambers  is  also  a 
good  one,  provided  the  supply  to  the  valves  is  kept  thor- 
oughly dry.  Hot  water  in  jackets  is  fatal  to  economy.  The 
conductivity  of  water  for  heat  is  very  low,  and  a  thin  film  of 
water  will  seriously  impair  the  transfer  of  heat  to  the  metal 
behind  it.  In  fact,  this  peculiarity  of  a  water-film  or  dew  on 
the  inside  of  the  cylinder  often  seriously  disturbs  the  normal 
or  anticipated  action  of  the  jacket  from  without.  The  verti- 
cal cylinder  might  be  expected  to  free  itself  of  a  water-film 
better  than  a  horizontal  one.  Jacketing  of  pistons  has  not 
been  found  to  work  well. 

227.  Gain  from  the  Use  of  the  Steam-jacket. — The  gain 
fom  the  use  of  the  steam-jacket  in  economy  of  fuel  is  a  mat- 
ter to  be  experimentally  found  for  each  engine  and  each  set 
of  conditions.  It  may  be  a  quantity  varying  from  zero  to  15 
per  cent,  rarely  reaching  20  per  cent.  The  expenditure  of 
steam  in  the  jackets  is  likely  to  be  over  5  per  cent  in  single 
engines  and  about  10  per  cent  in  compounds,  and  15  per 
cent  or  less  in  triples  if  all  cylinders  are  jacketed.  The  gain 
from  the  use  of  jackets  results  from  the  fact  that  for  every 
pound  condensed  in  the  jackets  some  greater  quantity  is 
saved  in  the  cylinders.  In  the  case  of  initially  poor  engines 
the  net  gain  from  jacketing  may  reach  20  or  25  per  cent. 
With  well- designed  engines,  such  as  are  met  in  marine  prac- 
tice, the  gain  or  economy  is  not  likely  to  exceed  10  per  cent 
of  the  total  feed- water  evaporated.  It  belongs  to  the  finance 
of  the  problem  to  decide  whether  the  cost  of  the  extra  con- 
struction is  justified  by  the  decrease  in  running  cost  which 
follows  from  it. 

The  jacket  results  in  a  notable  convenience  in  starting 


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THE   CYCLE  OF  THE  ACTUAL  STEAM-ENGINE.       325 

engines,  since  the  barrel  and  all  parts  of  the  cylinder  can  be 
warmed  up  in  advance  of  the  actual  starting  of  the  engine. 
This  avoids  annoyance  from  condensation  of  water,  and  from 
any  seizing  of  fitted  parts  by  difference  of  temperature. 

228.  Non-conducting  Cylinders. — It  has  also  been  sought 
by  certain  skilful  designers  to  mitigate  the  evils  of  internal 
condensation  waste  by  making  the  cylinder-wall  to  possess 
such  a  non-diathermanous  character  that  no  reactions  should 
take  place  between  the  steam  and  the  metal.  These  objects 
have  been  aimed  at  either  by  a  lining  within  the  metallic  cyl- 
inder, or  by  treating  the  metallic  surface  exposed  to  steam. 
The  practical  difficulties  of  a  glazed  or  enamelled  surface  have 
arisen  from  the  unequal  coefficients  of  expansion  of  the  body 
of  the  metal  and  the  non-conducting  coating,  whereby  the 
surface  cracks  and  disintegrates.  The  difficulties  caused  by 
abrasion  have  to  be  overcome  in  the  other  system.  These 
ideas,  if  a  successful  method  could  be  found  for  carrying  them 
out,  would  bring  the  actual  engine  up  to  the  ideal  conditions 
so  far  as  internal  wastes  were  concerned. 

229.  Superheating,  to  prevent  Cylindor  Condensation. 
— The  temperature-entropy  diagram  in  §  203  has  made  it  ap- 
parent that  it  was  possible  to  add  heat  to  the  incoming  steam 
to  such  a  degree  that  all  the  cooling  which  it  must  have  to 
undergo  in  expansion  should  not  be  able  to  bring  it  down  to 
the  point  of  saturation,  when  it  is  just  ready  to  condense  to 
a  mist  on  further  cooling.  It  is  obvious  then  that  the  initial 
condensation  upon  entry  into  the  cylinder  can  be  prevented 
by  superheating  to  a  less  degree,  and  the  losses  thus  avoided 
or  reduced.  For  example,  let  it  be  assumed  that  such  initial 
steam  come  in  in  a  saturated  state  with  a  total  heat  of  1250 
thermal  units  per  pound,  and  that  cylinder  condensation  under 
these  conditions  would  cause  a  loss  of  20  per  cent,  or  that 
1250  X  .20  =  250  British  thermal  units  disappeared  into  the 
metal  walls  of  the  cylinder   by   such  condensation.     There 


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326  HEA  T  AND  HEA  T-ENGINES. 

must  therefore  be  brought  in  by  the  steam,  if  its  specific  heat 
be  called  0.480,  an  amount  of  heat  represented  by 

250  =  0.480/°, 

or  the  range  above  the  working  temperature  of  saturation  for 
each  pound  becomes 

,  =  ^=5200  F., 
480       ^ 

which  is  practically  unattainable  for  reasons  shortly  to  be 
treated.  The  same  result  could  have  been  reached  by  the 
graphic  process. 

On  the  other  hand,  moderate  superheating,  of  100**  to  150** 
F.  above  working  pressure,  is  sufficient  to  reduce  initial  con- 
densation greatly,  if  not  to  eliminate  it,  and  when  the  steam 
is  dry  and  the  cylinder-walls  are  hot  at  the  point  of  cut-off 
the  evils  from  condensation  and  evaporation  during  expansion 
are  mitigated.  The  two  sets  of  curves  shown  in  Figs.  96  and 
97,  derived  from  the  Regnault  experiments,  make  it  plain 
that  as  the  temperature  increases  there  is  a  wider  margin  or 
range  for  a  change  of  condition  at  the  upper  ranges  than  at 
the  lower.  Or  in  other  words,  the  similarity  of  the  curves 
shows  how  much  more  cooling  has  to  be  done  at  the  higher 
levels  to  produce  the  same  change  which  at  the  lower  points 
will  occur  so  easily. 

The  exceeding  rapidity  with  which  cooling  takes  place  in 
the  thin  film  of  metal  when  acted  on  from  within  makes  it 
also  particularly  rapid  in  responding  to  the  heat  effect  of  extra- 
hot  steam  coming  in  as  a  superheated  gas  at  admission.  It 
is  for  this  reason  that  superheating  has  an  advantage  over 
jacketing.  The  jacket  supplies  heat  not  only  at  admission, 
but  also  during  the  exhaust  stroke,  when  it  is  wasting  it,  to 
atmosphere  or  to  the  condenser.  Superheating  supplies  heat 
only  where  it  is  required,  if  the  initial  condensation  only  is  to 
be  considered. 


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THE   CYCLE  OF  THE  ACTUAL  STEAM-ENGINE.       327 

The  effects  of  superheating  the  steam  are : 

(i)  To  raise  T^  in  the  efficiency  formula,  without  such  in- 
crease in  /j  as  to  give  rise  to  practical  difficulty.  This  in- 
creases thermal  efficiency. 


LB8.  PRESeuRE  PER  SQ.  IN. 
IR     U     13     IS     11     10 

)      S      T      «      t      1 

B      t 

I      0 

MS* 

^1 

'      1        1 

\a».G 
X205.9' 

i     I 

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200" 

N 

f^-»:  1  1 

196" 
IW 
186» 
180» 
175* 
170» 

\l!>»-«' 

- 

1      1 

N.». 

r  1 

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1        1^ 

IS2.S 

^ 

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,«..,-    1 

1    1    1 

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\l 

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106« 
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v«^ 

Fig.  96. 

(2)  To  diminish  the  density  of  the  steam-gas.  Hence  a 
less  weight  goes  to  an  initial  volume  introduced  into  the  cyl- 
inder with  a  given  period  of  admission. 

(3)  The  steam  has  more  of  the  reluctance  to  part  with  its 
heat  which  is  the  property  of  a  gas  as  distinguished  from  a 
vapor  which  is  ready  to  transfer  its  heat  to  solid  objects  by 


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328 


HEAT  AND   HEAT-ENGINES. 


condensation  upon  them.  Saturated  or  wet  steam  condenses 
freely ;  steam-gas  is  difficult  to  cool  except  by  intimate  contact 
with  all  parts  of  it,  as  is  the  case  with  air  and  other  gases. 

230.  Methods  of  Superheating. — There  are  three  general 
principles  underlying  the  attainment  of  superheat  in  steam. 


LBS. 

PREMURB  PER  8Q.  IN. 

0  180  ISO  no  100  90   80    70   00    M   10    90   SO    10 

t 

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140* 
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WO" 
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m 

Fig.  97. 

The  first  haj  already  been  referred  to  (§  132),  where  two 
masses  of  steam  are  supposed  to  be  separated  by  a  throttling 
orifice,  and  flow  to  take  place  from  the  higher  pressure  into 
the  lower  pressure  volume.  All  the  heat  which  was  in  the 
sream  at  the  higher  pressure  is  in  the  mass  at  the  lower  pres- 
sure, and  this  latter  must  therefore  have  more  heat  than  is  due 


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THE   CYCLE   OF  THE  ACTUAL   STEAM-ENGINE.       329 

to  its  pressure  or  is  superheated  in  consequence.  That  is,  if 
the  difference  7",  —  7",  of  their  total  heats  be  one  degree,  then 

(r.-  7;)o.48o=i, 

or  there  will  be  a  surplus  of  heat  represented  by 

-4-  =  2.08 
.480 

degrees  for  each  thermal  unit  difference  of  their  total  heats  at 
the  different  pressures. 

This  method  of  superheating  by  wire-drawing  occurs  in 
the  throttling  engine,  such  as  the  locomotive,  and  with  throt- 
tling governors  on  stationary  engines.  It  is  not  available, 
however,  when  maximum  output  of  energy  is  required. 

The  second  method  is  by  an  admixture  of  highly  super- 
heated steam  (usually  secured  by  the  third  method)  with  the 
ordinary  or  saturated  steam.  This  method  of  mixture  has 
been  called  **  adheating,"  or  the  "combined  steam"  pro- 
cess; also  Wethered's  system.  The  claimed  advantage  was 
the  control  of  the  degree  of  superheat  by  the  proportions  of 
highly  superheated  steam  to  be  mixed  with  normal  steam  as 
the  load  might  vary. 

The  third  and  most  usual  method  is  the  direct  method  of 
heating  all  the  steam  by  passing  it  through  pipes  or  coils  on 
its  way  from  boiler  to  engine,  such  pipes  being  kept  at  high 
temperature  by  waste-heat  from  the  furnace-gases.  This  re- 
sult is  secured  in  many  ways: 

(i)  Superheating  coils  in  the  flues  or  at  the  base  of  the 
chimney  (Fig.  98). 

(2)  Superheating  in  the  boiler,  by  having  a  part  of  the 
heating  surface  above  the  waters-line,  and  forcing  the  steam 
into  contact  with  such  superheating  surface.  Corliss  and 
Manning  boilers  exhibit  this  method;  also  the  common  up- 
right boiler,  and  the  steam-chimney  of  the  marine  boiler. 


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330 


HEAT  AND   HEAT-ENGINES. 


(3)  Superheating  by  surrounding  the  cylinder  with  flue- 
gases.     This  is  a  verj'  old  plan,  but  troublesome. 


Fig.  03. 

(4)  In  multiple-cylinder  engine-practice  the  use  of  coils 
of  steam  at  high  or  boiler  pressure,  in  receivers  through  which 
the  lower  pressure  steam  passes  on  its  way  from  cylinder  to 
cylinder.     This  is  called  **  reheating." 

•231.  Objections  to  Superheating. — European  engineers 
have  paid  more  attention  to  superheating  the  steam  than 
American  engineers  have.  The  reasons  for  this  have  been 
the  practical  difficulties  in  the  way.     These  are: 

(i)  The  low  specific  heat  of  steam-gas  causes  the  super- 
heating coil  to  become  highly  heated  in  the  furnace-gases. 
Hence  these  coils  oxidize  or  burn  out  and  give  way. 

(2)  The  range  of  temperature  and  expansion  in  superheating 
coils  or  tubes  makes  it  difficult  and  costly  to  keep  joints  tight. 


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THE   CYCLE   OF  THE  ACTUAL   STEAM-ENGINE.       331 

(3)  The  high  temperature  of  the  steam  compels  the  use 
of  metallic  packings  and  non-oxidizable  lubricants,  to  with- 
stand the  heat.  Fibrous  packings  and  non-mineral  lubricants 
are  impossible. 

232.  Gain  or  Economy  by  Superheating. — The  actual 
gain  from  superheating  in  any  case  should  be  a  matter  of  ex- 
perimental determination,  as  in  the  case  of  the  steam-jacket. 
It  is  furthermore  complicated  by  the  cost  of  renewing  the 
direct  superheater  at  frequent  intervals,  and  the  repairs  to  it. 
Neglecting  this  element,  however,  and  speaking  generally,  it 
seems  safe  to  say  that  a  superheat  of  from  15°  to  20°  F.  will 
effect  an  important  gain  in  reducing  wastes,  and  a  superheat 
of  100°  F.  will  practically  extinguish  initial  condensation. 
With  compound  engines  a  superheat  of  100°  produces  an  aver- 
age gain  of  20  per  cent  of  the  fuel  used  with  saturated  steam 
alone.  That  is,  the  algebraic  sum  of  the  gain  and  the  heat 
expended  to  produce  the  superheat  will  always  be  a  positive 
quantity,  because  the  return  will  be  from  twice  to  ten  times 
the  expenditure,  taking  the  average  of  recorded  tests. 

233.  Loss  by  Clearance. — There  must  be  linear  clearance 
between  the  piston  and  the  two  cylinder-heads,  and  a  clear- 
ance volume  in  the  passages  below  the  values  which  control 
inlet  and  exit  of  working  steam.  If  no  compression  is  used 
or  desirable,  a  volume  of  steam  is  taken  from  the  boiler  at 
each  stroke  and  wasted,  and  the  mean  pressure  is  less  than  it 
would  be  if  a  smaller  volume  were  expanding  after  cut-off. 

The  clearance  volume  in  any  actual  case  is  found  from 
drawings,  or  better  by  pouring  in  water  behind  the  piston  on 
its  dead-centre  until  the  clearance  volume  is  filled.  The  ob- 
served weight  or  volume  of  such  water  gives  a  volume  in 
cubic  inches  or  cubic  feet  to  be  added  to  the  real  piston-dis- 
placement for  each  stroke  to  give  the  actual  weight  or  volume 
fed  to  the  cylinder  per  stroke. 

In  representing  the  clearance  on  the  pv  or  indicator  dia- 
gram, it  is  only  necessary  to  prolong  the  diagram  at  its  admis- 


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332 


HEAT  AND   HEAT-ENGINES. 


sion  end  by  a  length  which  shall  give  to  the  admission  area 
the  same  percentage  of  increase  in  area  as  the  clearance  vol- 
ume adds   to  the   piston-displacement.      (See  also  §   i86). 


N 

i 

k                  B 

1              '"^->.\ 

^"^'^ 

L 

K            \M 

A 

Fig.  100. 


That  IS,  if  C  (Fig.  lOo)  denote  the  clearance  volume,  ex- 
pressed as  a  fraction  or  percentage  of  the  piston-displace- 
ment volume,  which  latter  will  be  the  product  of  the  area  A 
into  the  length  of  stroke  Z,  then 


or 


C^/AL, 
C 


/  = 


AL' 


Therefore  a  length  of  diagram  is  to  be  added  to  the  admission 
area  of  the  indicator-card  which  shall  be 


fL  = 


C 
A' 


and  the  line  of  zero  clearance  drawn  through  a  point  outside 

the  line  of  furthest  stroke  as  far  beyond  that  point  as  is  given 

C 
by  the  ratio  -j .     In  the  diagram 


LK=NA=  f{AL),     since 


LK  _C 

KI  ~A' 


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THE  CYCLE  OF  THE  ACTUAL  STEAM-ENGIIfE.       333 

Neglecting  clearance,  with  admission  AB  on  the  P.V.  dia- 
gram, the  apparent  cut-off  is 

AB  _\^ 
KI~r' 

and  the  apparent  ratio  of  expansion  is 

KI 

AB^'' 

But  the  real  admission  volume  is  NB^  and  the  final  vol- 
ume LI\  whence 

1  _NB  _AB+/  _r  ^^ 
T-U-lcn^f-  1+/ 
and 

_  LI  _  i+f  ^r-^/r 
''~NB-i  i+/r' 

r 

so  that  the  increase  of  expenditure  of  fluid  and  hence  of  heat 
becomes 

NB 


AB 


=  1  +A. 


while  the  absolute  mean  pressure  is  less  than  it  would  be  if 
the  clearance  volume  were  not  also  filled  with  expanding 
steam  in  the  proportion 

If  the  values  of  the  clearance  volume  are  not  known  or 
conveniently  measurable,  the  line  of  zero  volume  and  no 
clearance  can  be  drawn  with  close  approximation  from  the 
actual  card,  upon  the  assumption  that  for  a  short  distance 
the  compression  line  departs  so  little  from  an  equilateral  hy- 


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334 


HEAT  AND   HEAT-ENGINES, 


perbola  that  it  may  be  called  one.     Then  if  two  symmetrical 

points  are  chosen  on  the  curve  (Fig,  loi)  and  a  line  drawn 

.  through  them  to  the  line  of  zero  pressures,  which  it  will  cut 


Fig.  101. 

at  some  point  e,  and  prolonged  also  beyond  c^  it  will  cut  the 
line  of  zero  volumes  as  far  beyond  c  as  the  point  e  is  beyond 
d.  Making  cf  =•  de^  the  line  O  V  through  /  is  the  line  of  zero 
volumes,  or  the  line  of  clearance  zero.  This  comes  because, 
by  similar  right-angled  triangles, /z/ =^,z/,,  only  when  O  is 
determined  in  this  way.  A  determination  of  the  location  of 
the  point  O  by  two  points  on  the  expansion  curve  is  less  ac- 
curate because  the  curve  may  diverge  from  the  equilateral 
hyperbola,  and  any  errors  in  such  diagonal  line  are  multiplied 
in  locating  the  point  O. 

234.  Probable  Amounts  of  Clearance. — Small  engines 
may  have  the  linear  clearance  as  low  as  one  eighth  of  an 
inch ;  larger  engines  may  have  as  much  as  one-half  inch.  The 
longer  the  stroke  relatively  to  the  diameter,  the  less  the  per- 
centage of  clearance  represented  by  a  linear  unit  of  clearance. 
Short-stroke  high-rotative-speed  engines  therefore  empty  the 
greatest  clearance  volumes. 

Corliss  valve-gearing  causes  the  least  volume  between 
valves  and  cylinder-bore,  and  the  same  is  true  for  those  de- 
signs which  have  the  valves  in  the  cylinder-heads.     Valves  of 


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THE   CYCLE  OF  THE  ACTUAL   STEAM-ENGINE. 


335 


the  poppet  type  and  piston-valves  compel  a  considerable 
clearance  volume  and  attendant  loss.  A  value  for /as  low  as 
2^  per  cent  is  as  low  as  is  usually  obtained;  it  ought  not  to 
exceed  7  per  cent;  if  it  goes  above  10  per  cent  it  is  ex- 
cessive. 

235.  Clearance  Losses  Diminished  by  Compression. — 
The  effect  of  a  preclosure  of  the  exhaust-valve  before  the  end 
of  the  exhaust-stroke  is  to  entrap  steam  between  the  piston 
and  the  cylinder-head,  and  to  raise  its  pressure  by  compress- 
ing it  into  the  clearance  volume,  which  it  may  fill  completely. 
The  work  of  such  compression  is  a  negative  work  so  far  as  the 
useful  work  of  the  engine  is  concerned,  and  is  done  by  the 
fly-wheel  at  the  expense  of  energy  stored  in  it.  It  is  mechan- 
ically advantageous,  however,  as  furnishing  a  gradually  in- 
creasing cushion  effect  against  the  reciprocating  pdrts  to  arrest 
them,  and  to  put  them  under  the  strain  of  tension  or  com- 
pression to  which  the  next  working  stroke  is  to  subject  them. 
The  temperature-entropy  diagram  shows  the  point  at  which 
this  compression  should  begin  if  adiabatic  compression  of  the 
entrapped  steam-vapor  is  to  raise  the  pressure  to  that  corre- 
sponding to  7",.     (See  §  200.) 

236.  Calculation  of  Mean  Effective  Pressure  when 
Clearance    and  Compression    are    Considered. — The   ac- 


ti 

>j*--4— -^ 

)                   \ 

^Vy- 

\     *   ^-^ 

1 

1    _ 

X' 

.\    \   - 

..*— »— "i         B 

n 

^ ^ 

— -> 

Fig.  102. 


cepted  method  for  calculating  mean  effective  pressure  when 
the  diagram  of  the  indicator  shows  both  clearance  and  com- 


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336  HEAT  AND   HEAT-ENGINES. 

pression  is  an  extension  of  principles  already  laid  down.  If 
L  in  Fig.  102  is  the  length  of  the  stroke,  /  the  length  of  the 
admission  line,  x  the  period  of  the  exhaust-stroke  after  com- 
pression begins,  c  the  clearance  length  proportional  to  the 
clearance  volume,  while  the  capital  letters  A,  B^  C,  and  D 
represent  the  areas  on  which  they  are  placed,  and  the  pres- 
sures are  respectively/,  at  admission,  /*  during  exhaust,  and 
p^  at  the  end  of  compression,  we  shall  have  the  total  area  of 
the  enclosing  figure  from  §§  164-167: 

Area  of  ABCD  =  A(^+  ^)(i  +  hyp.  \og^^). 

But  by  similar  reasoning  the  area  of  the  parts  B^  C,  and 
D  will  be  given  by  the  equations 

B=p,{L--x); 
C=p^{i+hypAog^) 

=  A(^  +  r)(i  +  hyp.log^^); 

Hence  the  area  of  the  net-work  diagram  A  will  be 
Area  of  -^  =  ABCD  -  (B  +  C+  D) 

=  A(/+^)(H-hyp.log^^) 

-  [a(Z  -  ^)  +  pix  +  0(1  +hyp.  \o<g  ^^)  +^^^-./,(;r+r)] 

=  A(^+^)(i  +  hyp.log^") 

-  P,[{L  -  ^)  +  (;r  +  .)  hyp.  log  ^']  -  /,.. 


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THE   CYCLE   OF  THE  ACTUAL   STEAM-ENGINE.       337 

Hence,  since  the  mean  eflfective  pressure  will  be  the  result  of 
dividing  the  area  of  the  work-diagram  by  its  length,  we  have 

Mean  effective  pressure  = ■= , 


237.  Friction  in  Steam-pipes. — When  the  volume  of 
steam  required  by  the  engine  is  known  per  unit  of  time,  ex- 
perience shows  that  loss  of  pressure  and  temperature  from 
friction  or  wire-drawing  will  be  inappreciable  if  the  cross-sec- 
tion of  pipes  or  passages  is  so  made  that  the  linear  velocity  of 
the  steam  shall  not  exceed  100  feet  per  second.  Length  is 
not  without  effect,  but  for  short  distances,  and  where  engine 
and  boiler  are  close  together,  the  velocity  may  be  increased. 

238.  Loss  of  Pressure  and  Temperature  from  Cooling: 
in  Pipes. — When  steam  is  moving  in  pipes  which  are  ade- 
quately clothed  with  non-conducting  coverings  there  is  no 
doubt  a  loss  by  eddies  and  by  a  higher  velocity  at  the  begin- 
ning than  at  the  end,  due  to  the  long  travel.  Experiments, 
however,  on  any  considerable  or  adequate  scale  are  lacking 
to  enable  this  difference  to  be  more  than  guessed  at,  under 
the  wide  variation  of  condition  as  to  exposure  and  effective- 
ness of  covering.  Designers  usually  allow  for  a  loss  of  5  per 
cent  of  pressure  in  long  runs  of  over  250  feet,  and  allow  varia- 
tions from  this  allowance  by  climate  and  season  and  deterio- 
ration of  the  insulation  to  be  met  by  changing  the  pressure 
at  the  source  of  heat. 

239.  Efficiencies  Experimentally  Determined  in  Terms 
of  Thermal  Units. — The  calculation  of  §  218  showed  that 

33000  ^ 

:i|-— =  42.164 
778 

thermal  units  per  minute  per  horse-power  would  be  required 
by  an  ideal  engine. 

If  an  actual  engine  be  tested  and  found  to  consume  n 


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338  HEA  T  AND   HEA  T-ENGINES, 

pounds  of  water  per  horse-power  per  hour,  it  will  be  obvious 
that  the  thermal  units  consumed  by  that  engine  per  horse- 
power will  be  the  product  of  the  weight  n  into  the  specific 
heat  unity  into  the  range  of  temperature  used  by  the  engine. 
This  range  will  be  the  difference  between  the  total  heat  of 
the  steam  at  the  temperature  used  and  the  temperature  of 
the  feed-water  as  supplied  to  the  boiler.     Hence 

_.^  .  42.4164  X  60 

when  A.  is  the  total  heat  at  Z",,  and  /  is  the  temperature  of  the 
feed-water.  Usually  the  boiler  is  combined  with  the  engine, 
and  the  efficiency  is  thus  taken  together.  In  the  case,  how- 
ever, where  it  is  desirable  to  separate  them,  the  calorific 
power  of  the  fuel  being  known,  and  the  total  heat  above 
feed-water  temperature  being  given,  it  will  be  obvious  that 
the  product  (total  heat  —  feed-water  heat)  X  (pounds  of  water 
so  heated)  should  be  equal  in  theory  to  that  calorific  power. 
The  efficiency  of  the  boiler  should  be  the  ratio : 

„^  .  Actual  pounds  evaporated  per  pound  of  fuel 

Efficiency  =  =1 f—. -. ^    .   ^ ? — :• 

Iheoretical  evaporation  per  pound  of  that  fuel 

Then  the  efficiency  with  the  theoretical  cycle  having  been  cal- 
culated between  the  limits  7",  and  T',,  or  the  theoretical  water 
consumption,  the  actual  water  consumption  is  compared  with 
the  theoretical,  the  latter  being  taken  as  100  per  cent;  then 

^^  .  ^        .  Actual  water  per  H.  P.  per  hour 

Efficiency  of  engine  = ; 


Theoretical  water  per  H.  P.  her  hour' 


The  combined  efficiency  is  the  product  of  the  two  efficiencies 
in  percentage. 

This  method  is  fairer  than  the  comparison  with  unity  of 
perfection  in  the  Carnot  cycle.  The  difficulty  with  the  steam- 
engine  is  that  the  fuel-temperature  of  2000**  F,  in  the  furnace 


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THE   CYCLE   OF  THE  ACTUAL   STEAM-ENGINE.       339 

gives  aj  yet  only  a  400®  temperature  of  the  heat  medium  for 
physical  reasons.  While  the  limits  imposed  by  temperature 
are  such  as  yet  as  to  keep  theoretical  limits  of  efficiency  far 
beyond  our  present  practice,  and  induce  earnest  research 
either  after  media  which  shall  not  be  subject  to  these  limita- 
tions, or  to  extend  the  limits,  yet  on  the  other  hand  it  is  un- 
fortunate not  to  be  able  to  appreciate  how  excellent  our  heat- 
engines  are  when  the  perfection  realizable  within  these  limits 
is  taken  into  the  calculation. 


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CHAPTER   XVII. 
THERMAL  ANALYSIS  OF  HEAT-ENGINES. 

240.  Introductory. — It  has  been  repeatedly  emphasized 
in  previous  chapters  that  the  character  of  the  reactions  caus- 
ing loss  of  heat  and  efficiency,  and  the  action  of  the  appliances 
devised  to  mitigate  these  losses,  were  matters  demanding  ex* 
perimental  investigation  for  each  particular  engine.  Skilful 
designers  however  must  have  general  principles  to  use,  and 
their  skill  will  consist  in  the  wise  application  of  these  to  the 
problem  then  in  hand.  But  the  ultimate  criterion  even  in 
duplicate  engines  must  be  the  actual  test  and  the  analysis  of 
the  results. 

The  testing  of  engines  and  the  interpretation  of  the  data 
of  such  tests  have  long  been  matters  interesting  the  foremost 
grade  of  practitioners,  and  form  a  field  too  wide  to  be  entered 
on  here  except  in  a  summary  way.  The  use  of  the  indicator 
and  the  deductions  from  its  diagram  with  respect  to  distribu- 
tion, value  for  mean  effective  pressure,  and  horse-power  must 
be  studied  elsewhere.  This  chapter  will  discuss  only  the 
deduction  of  water  per  horse-power,  the  Him  analysis,  and  the 
temperature-entropy  diagram  as  giving  the  distribution  of  the 
heat  energy. 

241.  Pounds  of  Heat  Medium  per  Horse-power  Calcu- 
lated Theoretically  from  an  Indicator-diagjam. — The 
steam  used  in  a  steam-engine  weighs  the  same  as  the  water 
furnished  to  the  boiler  (less  wastes)  when  observed  over  a 
long  enough  interval.  The  heat  delivered  to  the  engine  will 
be  proportional  to  the  weight  of  steam  which  it  consumes. 

340 


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THERMAL  ANALYSIS  OF  HEAT-ENGINES. 


341 


Hence  the  most  satisfactory  test  is  to  weigh  the  water  used  by 
the  engine  by  catching  it  in  a  surface  condenser.  Where  this 
cannot  be  done,  and  often  also  where  it  is  possible,  it  is  desir- 
able to  determine,  from  the  indicator-card  of  data  on  the/z; 
plane,  what  weight  of  water  the  diagram  corresponds  to.  In 
Fig.  103,  let  L  be  the  length  of  the  stroke  in  feet;  A  the  area 


(« 

>(*-4— H^ 

% 

i    < 

it 

K^ 

^-L. 

-*— «•— i         B 

a- 

^- 1 -> 

Fig.  103. 


of  the  piston  in  square  inches,  so  that  —  is  the  area  in 

144 

square  feet;  iV=  number  of  strokes  per  minute;  /  the  per- 
centage of  the  stroke  completed  at  the  point  of  cut-ofT,  if  the 
water  rate  is  to  be  computed  for  that  point,  or  at  the  re- 
lease, if  the  rate  is  to  be  there  computed;  c  the  percentage 
which  clearance  volume  bears  to  piston-displacement,  and 
hence  the  same  relation  to  the  stroke  length ;  w  the  weight 
per  cubic  foot  of  steam  at  the  pressure  at  which  the  water 
rate  is  to  be  calculated,  and  w'  the  weight  belonging  to  the 
pressure  at  the  end  of  any  compression  that  there  may  be. 
Then 


Cubic  feet  per  stroke  =  Z( j 


A 
144' 


The  clearance  volume  will  be  = 


LcA 
144  X  100' 


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342  HEAT  AND   HEAT-ENGINES. 

The  weight  of  steam  in  pounds  per  stroke  will  be  the  cubic 
feet  times  Wy  or 


\  lOO  /  144 


144 

and  the  weight  in  the  clearance  volume  w^  will  be 

LAcw' 

w  = 

•       14400 ' 

The  total  weight  per  strqke  will  be  the  difference  between 
W^  and  «/„  or 

M^  _  «-.  _  r(^^'^'^^^'^\      LAcii/ 


r,  r(IAw  +  cAw\      L 

\      14400     /       i^ 


14400     /       14400 
LA 


14400 


\il-\-c)w-{cw')-\. 


This  becomes  weight  of  water  per  hour  by  multiplying  by 
60iV,  or 

W  =  ^Q^^^[(/+  c)w  -  (^zc;')]- 
14400  "-^     '     ''  V      yj 

In  this  result  all  data  are  on  the  indicator-diagram,  or  are 
from  tables  and  observations.  To  reduce  this  to  weight  of 
water  per  horse-power  per  hour,  both  members  are  to  be  di- 
vided by  the  equality 

PLAN 


H.P.  = 


33000  ' 


in  which  P  is  the  mean  effective  pressure  from  the  diagram. 
Hence 

^oLAN_ 

H.P.  ~  PLAN  P      LV'T^JW      K'^n- 

33CXX) 


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THERMAL  ANALYSIS  OF  HEAT-ENGINES.  343 

For  compound  or  multiple  engines  P  will  be  the  mean 
pressure  reduced  to  the  low-pressure  cylinder  volume,  assum- 
ing all  work  to  be  done  in  that  cylinder. 

This  equation  repeats  the  statement  of  §  236.  If  the 
pressure  in  the  clearance  is  carried  by  compressfon  so  that 
-ze/  =  z«/,  then 

W        1 37-50/ 


H.P. 


.{Iw). 


If,  however,  there  is  no  compression,  and  ze/  =  zero,  then  the 
consumption  per  horse-power  is- 

The  ditference  between  the  water  supplied  to  the  engine 
and  the  value  for  W  ixova  the  card  is  known  as  **  water  not 
accounted  for  by  the  indicator"  which  has  been  expended  in 
the  initial  condensations,  leakages,  etc.,  which  constitute  the 
losses  hitherto  discussed. 

The  above  values  for  w  refer  only  to  points  chosen  be- 
tween cut-off  and  release.  The  results  at  these  two  terminal 
points  are  likely  to  differ.  The  amount  of  their  difference  is 
a  rough  gauge  of  the  amount  of  re-evaporation  in  the  cylin- 
der. The  indicator  will  imply  the  greatest  weight  at  release 
for  this  reason. 

242.  Hirn's  Analysis. — The  thermal  analysis  most  in  use 
in  America  and  Europe  was  first  proposed  and  elaborated  by 
the  great  Alsatian  engineer  G.  A.  Hirn,  and  applied  by  his 
distinguished  pupil  and  colaborer  Octave  Hallauer.  In  the 
form  most  used  it  bears  the  impress  of  later  study  by  Prof, 
V.  Dwelshauvers-D^ry  of  Li^ge,  Belgium.  The  first  step  in 
applying  it  is  to  select  a  representative  indicator-card,  whose 
curves  on  the/z/  surface  shall  give  the  normal  performance 
of  the  engine  over  a  considerable  time,  and  representing  prac- 
tically constant  conditions.     A  weight  of  steam  Mva  pounds 


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344  I^£A  T  AND   HEA  T-ENGINES. 

is  supplied  to  the  cylinder  per  stroke  (or  per  lOO  strokes  if 
desired)  occupying  the  volume  up  to  the  point  of  average  cut- 
off by  diagram,  which  will  be  denoted  by  V^.  The  closure  of 
the  exhaust-valve  on  the  previous  stroke  has  entrapped  a  vol- 
ume F,  or  a  weight  M^  of  steam  and  water  mixture  in  the 
clearance  volume  (F.).  The  quantity  M  may  be  called  the 
cylinder-feed;  the  quantity  M^  may  be  called  cushion-steam 
and  is  found  by  selecting  on  the  average  card  the  earliest  point 
at  which  the  valve  is  known  to  be  closed  on  the  exhaust- 
stroke,  calculating  the  volume  from  this  abscissa,  and  adding 
the  clearance  volume.  The  weight  for  this  pressure  and  this 
volume  is  found  from  tables.  It  is  assumed  that  the  steam 
is.  dry  and  saturated  at  the  compression-point. 

The  weight  M  is  of  course  most  satisfactorily  found  by 
measurement  directly  from  a  surface  condenser  where  this  is 
possible;  if  not  convenient,  the  feed  to  the  boiler  should  be 
the  same  as  the  feed  to  the  cylinder  if  no  other  apparatus  is 
supplied  by  the  boiler,  such  as  pumps,  jackets,  injectors, 
leakage,  and  the  like.  To  make  the  case  general,  it  should 
be  assumed  that  the  steam  is  wet,  or  that  a  percentage  x  is 
vaporized,  while  \  —  x  remains  as  water.  Hence  the  volume 
of  one  pound  of  the  mixture,  if  u  represents  the  increase  in 
volume  of  the  water  when  it  becomes  steam  and  cr  is  the  vol* 
ume  of  the  liquid  water, 

z/  =  ;r«  +  cr, 
and  for  M  pounds  this  will  be 

Mv^  V=M{xu  +  (r). 

If,  then,  the  subscript  letters  represent  the  various  points 
at  which  volumes  are  noted  on  Fig.  104,  and  the  correspond- 
ing states  of  the  mixture,  we  have 

Fj  =  MJ^x^u^  +  d)  for  admission ; 

F.  +  F,  =  (J/+ J/.)(;r,//,  +  cT)  -  cut-ofif ; 
Fo  +  F.  =  (iir  +  M:){x,u,  +  (t)  * '  release ; 
F,  +  F,  =  MJ^x^u^  +  ^)  **    compression. 


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THERMAL  ANAL  YSIS  OF  HEA  T-ENGINES. 


345 


Assuming  evaporation  complete  at  compression  makes  this 
last  equation  present  x^  as  unity,  and  therefore 

M.  =  ^•. 

But  u^'\'  o  will  be  the  volume  of  one  pound  of  completely 
evaporated  steam  at  the  point  of  compression  F",,  and  this 
volume  will  be  the  reciprocal  of  the  weight  *u/  of  one  cubic 
foot  at  that  pressure  from  tabular  values.     Hence 

This  value  for  M^  can  be  inserted  in  the  equations  above, 
and  the  values  for  x^y  ;r„  and  x^  calculated  for  admission, 
cut-off,  and  release,  respectively. 

In  the  second  place,  the  heat  brought  into  the  cylinder  by 


1 n r 

I 1^^ . 


M  pounds  of  steam  will  be 

when  q  is  the  heat  of  the  liquid  and  r  is  the  latent  heat  of 
vaporization  for  the  percentage  x  which  has  been  vaporized. 
If  the  steam  is  superheated,  then  Q  becomes 

a  =  ^W'[\  +  .48o(/.-/)] 


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346  HEAT  AND  HEAT-ENGINES. 

if  t,  is  the  temperature  of  the  superheat  and  .480  is  the  spe- 
cific heat  of  steam  at  constant  pressure. 

But  it  is  necessary  to  separate  the  entire  heat  energy  into 
those  fractions  which  correspond  to  outer  or  external  work, 
and  those  which  represent  intrinsic  heat  energy,  which  can  be 
otherwise  disposed  of  than  in  doing  such  external  work.  If 
the  heat  equivalent  be  called  H^  then 

//p  =  MJ^q^  +  xj>^  for  admission ; 

H,  =  {M,  +  M){q,  +  ;r,/).)  '  •    cut-off ; 
.   //;  =  {M,  +  M){q^  +  xj>^  *  *   release ; 
H^  =  (J/,  +  M){q^  +  ;r,/),)  *'    compression. 

The  symbol  p  replaces  r  because  the  factor  must  contain 
only  the  heat  equivalent  for  the  internal  \\OT\a  of  vaporization 
of  one  pound,  and  not  that  corresponding  to  both  internal 
and  external  work  of  vaporization. 

In  the  third  place,  it   becomes  apparent  that   when  the 

steam  entered,  bringing  Q  units  of  heat,  it  found  already  the 

clearance  volume  filled  with  a  steam  whose  energy  was  H.. 

At  the  end  of  admission  when  cut-off  takes  place,  an  external 

work  in  foot-pounds  W  has  been  done,  whose  heat  equivalent 

W 
is  - — u,  or  A  W^-  and  there  remains  an  intrinsic  energy  H^  in 

addition  to  any  transfer  to  the  cylinder-walls  of  heat  which 
has  disappeared  in  initial  condensation  or  otherwise.     Hence 

or 

if  Qa  denote  such  lost  heat  during  admission. 

During  the  expansion  period  external  work  Wi,  is  done, 
and  at  release  an  intrinsic  energy  H^  remains.  Whether  H^ 
or  H^  will  be  numerically  the  larger  must  depend  on  whether 
the  walls  by  jacket  or  otherwise  supply  heat  to  the  working- 


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THERMAL  ANAL  YSIS  OF  HEA  T-ENGINES.  347 

cylinder-feed  steam  or  are  withdrawing  it.  In  any  case, 
calling  the  transfer  (2^  and  assuming  that  it  denotes  an  absorp- 
tion, the  intrinsic  energy  at  cut-off  must  balance  the  work, 
the  loss  from  condensation,  and  leave  the  remainder  H^  of 
energy  to  be  present  at  release.     Hence 

or 

During  the  third  period,  or  exhaust,  the  engine  is  pumping 
out  the  exhaust  steam,  or  is  doing  a  negative  work  W^ ,  and 
at  the  end  of  exhaust,  or  when  compression  begins,  there  must 
remain  an  intrinsic  energy  represented  by  //,.  If  the  heat  of 
the  liquid  water  resulting  from  the  condensation  in  a  condens- 
ing engine  be  represented  by  ^^,  which  is  the  hot-well  temper- 
ature with  a  surface  condenser,  then  a  quantity  of  heat  repre- 
sented by  Mq^  is  carried  into  the  condenser.  If  G  pounds  of 
condensing  water  are  used  to  effect  this  condensation,  and  de- 
livered at  injection  temperature  qi  are  raised  to  the  outflow 
temperature  qj, ,  then  an  amount  of  heat  disappears  in  this  pro- 
cess of  cooling  which  will  be  represented  by  ^(^^  —  y,).  If  a 
jet  condenser  is  used,  t^  of  hot-well  and  condenser  outflow  /j^ 
will  be  the  same.  The  loss  to  the  walls  being  denoted  by 
Q^y  the  heat  energy  //",  must  balance: 

H,^H,-\^Mq,+  G{qu  -  ^,)+  a  ^  AW,, 
or 

Q^^H^^H,-  Mq,  -  G{s,^q^JrAW^ 

If  the  release  leads  the  ends  of  the  stroke,  some  of  the 
expulsion  work  will  be  done  by  the  working  fluid.  If  this 
happens,  W^  will  be  the  difference  between  the  lengths  of 
these  two  parts  of  the  stroke  in  which  the  exhaust  is  done  by 
the  driving  steam  of  the  stroke,  and  the  length  of  the  expul- 
sion done  by  the  steam  of  the  following  stroke^ 


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348  HEA  T  AND   HEA  T-ENGJNES. 

During  the  fourth  or  compression  period  a  work  W^  is 
done  by  the  engine.  Any  losses  Qj^  must  leave  the  energy 
represented  by  //,  at  the  end  of  the  compression,  so  that 

or 

Finally,  there  is  whatever  expenditure  of  heat  is  repre- 
sented by  the  jackets  of  cylinders,  receivers,  and  the  like.  Let 
m  represent  the  weight  of  water  collected  per  stroke  (or  per 
lOO  strokes),  with  x'  its  percentage  of  dryness,,  r'  its  heat  of 
vaporization,  and  q'  its  heat  of  liquid,  while  <^'  is  the  heat  of 
the  liquid  withdrawn  as  water  from  the  jackets;  then  if  Q^ 
be  the  heat  so  supplied  to  the  jackets. 

It  is  obvious  on  the  other  hand  that  the  quantity  Q  supplied 
to  the  engine  must  be  great  enough  to  do  the  following: 
(rt)  do  the  external  work  W,  which  will  be 

W^  W,+  IV,"  W,"  W^, 

or  the  work  corresponding  to  the  entire  net  area  of  the  indi- 
cator-card ; 

{b)  supply  the  heat  carried  into  the  condenser  and  away 
by  the  injection 

{c)  meet  all  the  losses  by  radiation,  condensation,  or 
otherwise;  the  summation  of  all  the  losses 

a  =  a  +  a+a+G^. 


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.      THERMAL  ANALYSIS  OF  HEAT-ENGINES.  349 

To  help  out  the  quantity  (2»  the  jacket  heat  Qj  must  be 
supplied  in  addition,  and  it  may  be  treated  as  if  it  were  also 
supplied  per  stroke  as  an  addition  to  the  working  fluid.    Hence 

from  which  it  follows  that,  by  addition  of  equations, 

and  also 

=  QJ^Q.-Mq,-  G{3,-q^-AW, 

all  of  which  latter  quantities  are  capable  of  experimental  ob- 
servation in  a  properly  arranged  engine-test,  and  should  check 
with  the  summation  of  the  losses  in  each  part  of  the  cycle. 

243.  Application  of  Hirn's  Analysis. — If  a  thermal 
analysis  is  to  be  applied  to  an  engine-test,  the  foregoing 
equations  have  shown  the  quantities  which  are  to  be  observed 
and  recorded.  For  the  determination  of  (2  =  Mixr-^-  q)  the 
weight  of  cylinder-feed  per  stroke  observed  from  the  con- 
denser is  to  be  multiplied  by  the  percentage  of  dry  steam 
present  in  the  cylinder-feed,  and  this  must  be  determined  by 
a  calorimeter  so  located  as  to  give  the  indication  of  quality 
which  is  prevalent  in  the  cylinder.  This  is  not  always  easy, 
and  offers  scope  both  for  skill  and  for  care. 

The  data  concerning  the  cylinder  must  involve  not  only 
length  and  diameter,  but  also  the  points  of  cut-off,  release, 
and  compression  from  both  head  end  and  crank  end,  the  clear- 
ance volumes  at  both  ends,  and  the  piston-displacements  at 
both  ends.  These  latter  quantities  are  rarely  or  never  the 
same  for  both  ends,  because  the  connecting-rod  introduces  an 
irregularity  of  path  of  the  piston  by  its  angular  motion,  and 
the  piston-rod  fills  a  part  of  the  clearance  volume  at  one  end 
and  not  at  the  other.  It  is  usual  to  take  the  half-sum  of  the 
volumes  in  working  out  numerical  values. 


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3 so  HEAT  AND   HEAT-ENGINES. 

Then  from  the  average  diagram  the  absolute  pressures  are 
ascertained  by  measurement,  adding  to  them  the  barometer- 
reading  on  the  day  of  the  test  so  as  to  locate  the  atmospheric 
line  in  its  proper  place  above  a  true  vacuum.  These  pres- 
sures being  observed  for  cut-off,  release,  compression,  and  Cor 
the  point  on  the  compression  at  which  the  inlet-valve  opens 
for  admission  on  both  crank  end  and  head  end,  it  is  conven- 
ient to  tabulate  the  corresponding  values  for  y,  r,  p,  and  u 
derived  from  tables;  and  similarly  to  work  out  the  value  of 

W 

— ^  for  each  section  of  the  card  from  the  mean  pressure  prev- 
alent when  Wa^  W^,  W^^  and  W^  respectively  is  being  per- 
formed. The  mean  pressure  into  the  area,  both  in  square- 
inch  units,  multiplied  by  the  length  in  feet  through  which 
that  effort  is  exerted,  gives  a  value  for  W  in  foot-pounds, 
which  is  reduced  to  the  equivalent  in  heat-units  by  dividing 

by  yySy  since  A  =  y^     '^^^  volumes  in  cubic  feet  are  then 

calculated  for  Fi,  V^,  Fi,  and  V^  for  both  head  and  crank 
ends. 

The  longer  the  duration  of  the  test,  the  less  the  chances 
for  error,  and  the  more  insignificant  its  percentage.  This  is 
particularly  trufc  of  the  weight  of  steam  per  stroke: 

_         Total  weight  of  steam  used  in  the  test 

""  2  X  number  of  revolutions  during  that  period  * 

and  also  for  the  weight  of  condensing  water  per  stroke,  which 
will  be. 

__  Total  weight  of  condensing  water  during  period  of  test 
""  2  X  number  of  revolutions  during  that  period 

The  temperatures  of  the  condensed  steam  in  the  hot-well, 
and  of  the  injection  before  and  after  use  in  the  condenser, 


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THERMAL   ANALYSIS  OF  HEAT-ENGINES.  351 

have  to  be  observed  with  sufficient  frequency  to  represent 
average  conditions. 

These  data  having  been  prepared,  M  and  M^  are  calcu- 
lated ;  the  values  for  x^  H^  and  Q  with  their  several  subscript 
values  are  worked  out  from  tables. 

The  work  per  stroke  having  been  found  in  foot-pounds 
from  the  pv  indicator-card  and  reduced  to  heat-units  for 
the  foregoing  calculations  by  dividing  by  778,  the  horse- 
power will  be  found  by  multiplying  the  heat-unit  work  by  the 
factor  778  and  dividing  by  the  foot-pounds  in  one  horse- 
power for  the  same  period.  If,  as  is  usual,  the  work  in  heat- 
units  per  hour  is  the  result  of  the  calculation,  then 

TT  T>         778  X   fT  X  2Rpni  X  60 

II.Jl  .  = - 

60  X  33000 

when  W  is  the  heat-unit  work  for  one  stroke.  Then  it  is  ob- 
vious that  the  steam  per  horse-power  is  the  quotient  resulting 
from  dividing  the  total  weight  of  steam  used  by  the  number 
of  horse-power  developed  during  that  same  period. 

The  quantity  Q  is,  however,  the  principal  object  sought, 
and  when  found  for  one  revolution  can  be  expressed  per  min- 
ute or  per  hour  or  per  horse-power  as  desired. 

The  table  on  page  352  will  show  an  illustrative  analysis 
involving  the  foregoing  details. 

244.  Limitations  of  Hirn's  Analysis. — If  the  engine  is  a 
non-condensing  one,  the  quantities  depending  on  the  con- 
denser will  vanish.     But  since  it  is  true  that 

Q  =.  Q+  Q.^  Mq,-  G{Q,-  Q,)  ^  AW, 

the  equation  of  the  previous  paragraph  for  Qc  may  be  written 

by  substitution. 


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352 


HEAT  AND   HEAT-ENGINES. 


THERMAL   ANALYSIS — DATA   AND    RESULTS   PER  lOO  REVOLUTIONS. 


Quantities. 


Symbols 


Formulae. 


I.  Steam  enterinfp  workinfp  cylinder,  pounds. 
9.  Steam  at  adm'ssion,  pounds 

3.  Steam  used  by  calorimeter,  pounds 

4.  Steam,  total,  pounds 

5.  Heat  of  condensed  steam 

6.  Condensed  water,  pounds   

7.  Heat  given  to  condensing^  water 

8.  Heat  supplied  to  engi  ne. 

9.  Sensible  neat  at  admission 

10.  Internal  heat  at  admission 


M 


ioo(K<rH-^'o)H-Wo 


M<fg 


II.  Sensible  heat  at  cut-ofiF 

Z2.  Internal  heat  at  cut-off 

23.  Sensible  heat  at  release 

X4.  Internal  heat  at  release 

25.  Sensible  heat,  beginning  of  compression. 
16.  Internal  heat,   beginning  of  compression. 

27.  Cylinder  loss  during  admission 

18.  Cylinder  loss  during  expansion 

19.  Cylinder  loss  during  exhaust 

ao.  Cylinder  loss  during  compression 

ax.  Heat  discharged,  and  work 

aa.  Jacket 

33.  Jacket 


G  (9k  -  ^|) 
M  {xr-X-q) 

'°°      y^     Po 

'oo — ;; — -Pi 
(.4f-|-.Vo)^t 
,00-^;—^ 

Q  +  //„-L  ///-  H.-  //,'-  A  Wa 

//,4-  //,'-  //•-  //»'-  A  iVi, 

H^  -f  A  a'  -  ^f%-  Hi'—K-K*  -  A  IVg 

//,  -^  //,'-  //o-  //o'-  AlVi 

K+  K'-^Ah^ 

Q-B 

Qa^Qb  +  Qc  +  Qd 


24.  Quality  of  steam  entering. . 
35.  Quality  of  steam  at  cut-off. 


36.  Quality  of  steam  at  release. 


97.  Quality  of  steam  at  compression . 
aS.  Quality  of  steam  at  admission. . . . 
39.  Quality  of  steam  in  exhaust. . . .   . 

30.  Heat  lost,  admission 

31 .  Heat  restored,  expansion 

3a.  Heat  rejected,  exoaust 

33.  Heat  lost,  compression 

34.  Heat  utilized,  work 


per  calorimeter per  < 

r4  Vt 


per  calorimeter.. 


-*-r,.. 


Heat  lost,  radiation 

Ratio,  radiation  to  work 

Ratio,  cylinder  condensation  to  work.. 

Thermodynamic  efficiency 

Actual  efficiency 

Efficiency  compared  with  ideal 


E 


Sr^ 

-^H-^ 

778  ^ 

Radiation -I- ^ * 

A*  -4-  w 
a  -\-  w 

(/-/|)-i-(46o+/) per  ( 

AW-\-Q • 

E^-^E 


Special  symbols,  Vg  =  volume  clearance,  i  =s  measured  temperature.    Subscript  5  applies 


to  exhaust,  i  to  injection,  k  to  discharge,  ^  to  air-pump  discharge.    A  as 
Correct  for  steam  used  by  calorimeter,  when  necessary. 


778 


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THERMAL  ANAL  YSIS   OF  HEA  T-ENGINES.  353 

The  usual  custom  is  to  assume  that  the  steam  at  the  end 
of  compression,  or  just  when  the  inlet  opens,  is  quite  dry  and 
saturated,  or  that  x^  is  unity.  It  has  been  already  said  that 
the  condition  of  the  steam  corresponding  to  jr,  at  the  begin- 
ning of  compression  or  the  end  of  exhaust  was  considered  to 
be  that  of  dry  steam ;  hence  while  the  presence  of  any  con- 
siderable quantity  of  water  in  the  clearance  volume  is  un- 
likely, it  is  not  entirely  justifiable  to  assume  that  the  steam 
is  dry.  The  difficulty  of  ascertaining  the  truth  of  this  funda- 
mental assumption  has  made  many  feel  a  dissatisfaction  with 
the  calculated  results,  and  furthermore  it  vrill  be  apparent  that 
the  errors  of  observation  and  computation  in  the  successive 
equations  for  Q  are  cumulative  in  their  effect  upon  the  final 
value  for  C«»  and  may  make  a  large  percentage  of  its  value. 

245.  Thermal  Analysis  by  Temperature-entropy  Dia- 
gram — The  methods  given  for  a  transfer  from  the /z;  dia- 
gram to  a  T.E.  diagram  in  §  205  require  to  be  extended  when 
clearance  and  compression  volumes  are  to  be  considered. 
But  the  inspection  of  the  T.E.  diagram  resulting  from  such 
a  transfer  will  give  the  thermal  analysis  more  clearly  thari  the 
analytic  method  by  Him  and  Dwelshauvers,  although  of 
course  when  correctly  done  the  results  in  both  should  agree. 

The  method  followed  here  was  first  advanced  by  Boulvin, 
and  has  been  further  elaborated  by  Prof.  Reeve. 

The  steps  for  the  transfer  will  involve  much  of  the  same 
procedure  as  above: 

(i)  The  drawing  or  selection  of  an  average  and  represent- 
tive  indicator-card  on  the  pv  plane. 

(2)  The  indicated  horse-power  is  to  be  worked  out,  and 
the  total  feed-water  supplied  to  the  cylinder  during  the  test. 
From  this  is  derived — 

(3)  The  water  rate  per  horse-power  per  hour.  The  rate  per 
stroke  fed  to  the  cylinder  will  be  the  total  water  consump- 
tion divided  by  twice  the  number  of  revolutions  per  hour. 

(4)  What  is  needed,  however,  is  the  reciprocal  of  (3J  or 


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354 


HE  A  T  AND   HEA  T-ENGINES. 


the  number  of  strokes  needed  to  make  up  a  pound  of  the  cyl- 
inder feed.  In  large  engines  this  may  be  a  fraction  less  than 
unity;  in  small  engines  it  will  be  a  whole  number,  and  per- 
haps a  large  one. 

(5)  Find  the  weight  of  cushion-steam  as  in  Hirn's  analy- 
sis. Find  first  the  clearance  volume,  add  the  volume  given 
by  the  indicator-card  when  the  exhaust-valves  close,  and  mul- 
tiply this  by  the  volume  resulting  from  the  calculation  in  (4). 
This  volume  at  the  compression  pressure  can  be  reduced  to 
weight  from  steam-tables.  With  multiple-cylinder  engines 
this  should  be  done  separately  for  each  cylinder. 

Checking  these  with  the  methods  followed  in  §  243,  it  will 
appear  that  (3)  corresponds  to  J/ and  that  (5)  corresponds  to- 
M^,  The  next  steps  will  be  the  proper  graphical  plotting  of 
the  pv  card,  that  the  proper  entropy  values  may  be  meas- 
ured from  it.  The  object  sought  is  to  pass  from  the  piston- 
displacements  given  by  the  indicator  to  the  volumes  of  heat 
medium  supplied  to  the  cylinder,  the  temperature  of  such 
volume  being  that  in  each  case  which  belongs  to  that  pres- 
sure. 

(6)  Construct  a  diagram  (Fig.  105)  which  shall  represent 
by  the   curve  MN  the   saturation    curve  for  one  pound  of 


p 

A 

C              M 

/        1 
/       / 

// 

/D         0 

FiG.105. 


steam  measured   for  complete  vaporization  from  a  zero  line 
OPy  and  having  the  height  of  the  point  M  above  the  line  ON 


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THERMAL  ANALYSIS   OF  HEAT-ENGINES,  355 

correspond  to  the  absolute  pressure  in  the  boiler  above  the 
line  of  perfect  vacuum  on  the  same  scale  as  the  indicator-card 
or  proportional  to  it,  so  that  iV  would  correspond  to  complete 
expansion,  or  to  the  pressure  corresponding  to  the  limit  value 
of  7",  as  may  be  preferred.  The  vertical  OP  would  be  the 
point  to  measure  the  cylinder-feed  volumes  if  there  were  no 
clearance  and  no  cushion-steam  in  such  volume  or  in  the  re- 
ceivers undergoing  expansion  and  compression  at  each  stroke, 
and  therefore  affecting  the  actual  volume  of  cylinder-feed. 
Since  this  cushioning  weight  is  varying  in  volume  as  the  pres- 
sure varies  in  the  cylinder,  the  line  to  be  drawn  to  the  left  of 
OP  to  represent  this  increase  in  actual  volume  due  to  clear- 
ance will  not  be  a  straight  line,  but  will  be  an  adiabatic  for 
the  clearance  volume  V^  between  the  limits  of  the  back  pres- 
sure and  the  admission  pressure.  The  methods  for  drawing 
adiabatic  curves  have  been  given  elsewhere  (§§  123  and  125). 
A  curve  AB  results  in  Fig,  105  which  is  as  far  to  the  left  of 
the  axis  OP  zs  the  varying  volume  of  the  expanding  cushion- 
steam  adds  to  the  volume  of  the  cylinder-feed  at  any  pres- 
sure. The  horizontal  lengths  between  the  curves  AB  and  MN 
at  any  pressure  give  the  total  volume  of  steam  in  the  cylin- 
der at  that  pressure,  «vhich  will  be  the  sum  of  the  volumes 
of  cushion-steam  and  cylinder-feed  steam,  assuming  vaporiza- 
tion complete.  Hence  if  the  cushion-steam  does  not  show 
the  volume  to  be  expected,  this  will  mean  that  some  of  it 
has  been  condensed  to  meet  demands  for  heat  from  the 
working  volume,  for  which  heat  something  should  give 
account. 

(7)  If,  then,  horizontal  lines  intercepted  between  the 
curves  AB  and  MN  measure  the  sum  of  the  cushion-steam  in 
clearances  and  the  cylinder-feed,  a  curve  must  be  capable  of 
being  drawn  between  AB  and  MN  which  shall  intercept  the 
volume  of  the  cushion-steam  from  the  curve  AB  at  each 
pressure,  and  which  shall  establish  the  zero  line  of  piston- 
displacements,  which  are  the  units  of  the  indicator-diagram. 


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356 


HEAT  AND   HEAT-ENGINES, 


This  is  done  by  measuring  from  AB  to  the  right  at  a  suffi- 
cient number  of  horizontal  distances  a  length  which  shall  be 
the  product  of  Ihe  clearance  volume  into  the  number  of 
strokes  per  pound  of  cylinder- feed  (4).  The  dotted  curve 
CD  results  in  Fig.  105,  and  would  appear  to  be  the  axis  curve 
from  which  horizontal  lines  of  the  indicator-diagram  were  to 
be  measured  for  each  pressure,  if  the  indicator-card  had  given 
pressures  corresponding  to  volumes  of  cylinder-feed  steam 
instead  of  volumes  of  piston-displacement  only. 

(8)  Hence  if  from  CD  as  an  axis  of  volumes  the  indicator- 
card  from  the  actual  engine  be  laid  down,  taking  vertical  dis- 
tances as  measured  from  the  line  of  perfect  vacuum,  and  lay- 
ing off  the  horizontal  distances  from  the  curve  CD  at  the  same 
height,  a  diagram  of  cylinder-feed  volumes  indeca  results  (Fig. 
106).     It  will  usually  be  within  the  saturation  curve  MN^  be- 


Pia.XOe. 
cause  the  volumes  are  made  less  than  the  theoretical  by  the 
condensations  which  measure  the  heat  losses.     The  only  case 
where  the   actual  could   pass  beyond  the   saturation    curve 
would  be  where  superheating  was  practised. 

(9)  The  diagram  of  volumes  for  the  cylinder-feed  or  M 
can  now  be  transferred  to  the  theoretical  temperature-entropy 
diagram  by  the  principle  laid  down  in  §  205,  that  horizontal 
lines  on  the  pv  theoretical  diagram  and  the  T.E.  theoret- 
ical diagram  are  divided  proportionally  by  the  points  of  the 


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THERAfAL  ANAL  YSIS   OF  HEA  T-ENGINES. 


357 


actual  diagram.  The  height  of  the  line  AB  above  the  hori- 
zontal axis  of  entropy  measures  the  temperature  correspond- 
ing to  the  boiler-pressure ;  the  point  C  is  distant  from  the 
temperature  axis  a  distance  which  is  the  entropy  counted 
from  an  assumed  zero,  and  the  line  CD  is  the  increase  in  the 
entropy  during  complete  vaporization  at  the  temperature  7",. 
The  line  FG  belongs  to  7",,  and  its  length  is  the  measure  of 
the  decrease  in  entropy  belonging  to  the  feed-water  temper- 
ature. The  line  OC  is  the  logarithmic  curve  representing  the 
gradually  heating  cylinder- feed,  with  temperature  and  entropy 
increasing  together.  The  plotting  of  the  diagram  from  Fig. 
io6  may  cause  it  to  appear  on  the  T.E.  diagram  somewhat 
like  Fig.  107. 


Fro.  107. 
246.  Losses    Revealed    by  the    Temperature-entropy 
Diagram — (i)  The  line  in,  representing  the  period  of  admis- 
sion in  the  actual  engine,  will  not  be  as  long  as  CD  if  the 

CH 
steam  carries  any  moisture.     The  relation  -^-  is  that  given 

by  the  calorimeter,  and    is   the   proportion   of  dryness   at 
admission. 

(2)  The  drop  from  C  to  n  indicates  a  fall  of  temperature. 
This  is  the  result  of  friction  and  loss  of  pressure  through  too 
small  ports  or  throttling  passages. 

.  {^  If  it  were  the  case  that  there  were  no  wire-drawing 
nor  any  initial  condensation  before  cut-off,  the  entropy  line 


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358  HEAT  AND   HEAT-ENGINES 

should  move  to  /?,  and  the  heat-unit  supply  should  have  been 
greater  than  it  is  by  the  sum  of  the  areas  nicH  -{-  HDKLn. 
If  niCHh^  charged  to  wire-drawing,  the  rest  is  the  result  of 
the  condensation  before  cut-oflf,  or  initial  condensation.  The 
determination  of  the  point  H  or  n  hy  calorimeter  is  to  this 
extent  unreliable  and  unsatisfactory,  since  the  initial  conden- 
sation will  mask  the  other  condensation,  because  greater  in 
amount, 

(4)  The  expansion  curve  between  H  and  L  on  the  pv 
diagram  becomes  the  curve  nud  on  the  T.  E.  diagram.  If  the 
expansion  were  truly  adiabatic  from  cut-off,  it  would  descend 
on  the  line  ;/A,  which  is  the  isentropic  line;  but  since  condcn 
sation  usually  continues  after  cut-off,  the  curve  falls  behind 
the  line  «Z,  until  abstraction  of  heat  ceases.  This  occurs 
where  the  line  nL  crosses  the  expansion  line. 

(5)  Re-evaporation  sets  in,  and  a  gain  in  entropy  follows 
from  the  heating  action  of  the  walls.  It  is  here  that  any 
action  caused  by  the  jackets  would  also  appear. 

(6)  At  d  the  exhaust  opens.  If  expansion  had  been  com- 
plete within  the  cylinder,  d  should  have  been  on  the  temper- 
ature level  given  by  the  line  FG.  The  expansion  at  exhaust 
is  into  the  exhaust-pipe,  instead  of  against  the  external  resist- 
ance. The  curve  of  constant  volume  dc  (§§  201,  202)  is 
drawn,  with  the  attendant  loss  of  area  below  it. 

(7)  At  c  the  back-pressure  line  begins.  If  c  is  not  on  the 
line  FG,  it  indicates  that  either  the  vacuum  is  not  as  good  as 
it  might  be  in  the  condenser,  or  that  the  back-pressure  in  non- 
condensing  engines  is  unduly  high. 

(8)  At  a  the  exhaust  closes,  and  an  area  ast  of  work  is 
done  on  the  cylinder-feed  which  is  a  loss. 

(9)  When  the  point  t  is  passed,  the  gain  in  heat  is  the  re- 
sult of  a  warming  by  the  cylinder-walls.  The  two  together 
may  balance  each  other,  although  usually  the  sum  is  a  loss. 
If  the  compression  of  the  cushion-steam  were  just  so  adjusted 
that  it  would  fill  the  clearance  volume  with  cushion-steam  at 


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THERMAL  ANALYSIS  OF  HEAT  ENGINES,  359 

boiler  pressure,  and  if  the  compression  were  truly  adiabatic, 
the  curve  atri  would  be  the  logarithmic  curve  OC^  If  the 
compression  is  insufficient,  making  ast  greater  than  tri^  the 
difference  measures  the  net  loss. 

Hence  it  will  appear  that  the  differences  between  the  area 
of  the  actual  and  the  theoretical  heat-diagram  measure  the 
losses  for  the  whole  cycle,  and  the  lost  areas  under  each  phase 
measure  the  values  corresponding  to  Qay  Qb,  Go  and  Q^  in 
the  preceding  analvtical  method. 

When  the  engine  is  steam -jacketed  and  an  allowance  is  to 
be  made  for  the  consumption  of  steam  in  the  jackets,  so  that 
their  net  effect  may  be  observed,  the  usual  plan  is  to  con- 
struct a  diagram  to  the  right  of  the  0,  ordinate,  having  the 
same  7]  value  as  the  working  steam  from  the  boiler,  but  hav- 
ing a  horizontal  or  entropy  length  as  much  less  than  that  of 
the  working  steam  as  the  weight  of  steam  per  stroke  in  the 
jackets  is  less  than  the  working-steam  weight  per  stroke. 
This  enables  the  heat-unit  area  to  be  compared  directly. 
The  jacket-steam  parts  with  its  heat  energy  by  contact  with 
the  cooler  metallic  surfaces,  as  the  working  steam  parts  with 
its  heat  in  non-expansive  working  when  it  flows  out  to  the 
condenser.  The  lower  temperature  limit  is  that  of  the  water 
condensed  in  the  jacket  and  removed  by  traps. 

247.  Reeves'  Entropy-temperature  Diagram  Chart 
— Prof.  Reeves  arranged  in  1897  a  most  convenient  chart  for 
the  application  of  the  foregoing  principles.  Following  Boulvin, 
he  divides  a  large  sheet  into  four  quadrants,  allotting  the 
lower  ordinates  below  the  central  horizontal  line  to  pressures,* 
and  the  ordinates  above  the  central  horizontal  to  entropy. 
From  the  central  intersection  of  the  horizontal  and  vertical 
axes,  abscissae  to  the  right  are  volumes,  and  to  the  left  are 
temperatures.  This  divides  the  chart  so  that,  as  appears  in 
the  diagram  (Fig.  108),  the  four  angles  give  each  a  diagram 
in  terms  of  the  double  unit.  In  the  pressure-temperature 
segment  are  drawn  a  number  of  different  adiabatics  for  differ- 


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360  HEAT  AND   HEAT-ENGINES. 

ent  weights  of  cushion-steam,  and  in  the  temperature-entropy 
segment  are  the  curves  of  entropy  for  water  and  for  steam 
similar  to  Fig.  106.  If  then  the  metamorphosed  indicator- 
diagram  be  drawn  on  the/.i;.  segment  with  the  line  ABot  Fig. 
106  inserted  in  its  proper  location,  it  will  be  apparent  that 
simple  projection  of  points  first  upon  the  proper  line  in  the 
volume-temperature  segment  and  thence  into  the  T.E.  seg- 
ment will  locate  the  points  of  the  desired  experimental  T.E. 


ENTROPY 
TEMPERATURE 


PRESSURE 
TEMPERATURE 


ENTROPY'^ 
VOLUME 


PELESSURE 
VOLUAIB 


Pig.  108, 

diagram.     The  diagram  also  presents  other  data  which  are 
intended  to  make  its  application  more  easy. 

248.  Conclusion. — It  is  to  be  emphasized  anew  that  these 
thermal  analyses  are  based  on  the  knowledge  as  to  the  quality 
of  the  steam  v/ith  respect  to  dryness  within  the  cylinder  at 
portions  of  the  stroke,  and  can  be  no  more  accurate  than  the 
observations  or  the  assumptions  concerning  this  quality.  It 
is  furthermore  not  always  easy  to  determine  with  exactness 
the  point  of  cut-off  with  single-valve  engines,  and  hence  to  fix 
the  volume  F,  -f-  F,  for  the  computations.  Hence  the  con- 
servative attitude  towards  them  is  that  all  tests  and  experi  • 
ments  should  be  so  directed  as  to  be  made  available  when  these 
disputable  facts  shall  have  been  settled  by  an  accumulation  of 
knowledge  concerning  them,  rather  than  that  dogmatic  asser- 
tions can  be  now  made  concerning  the  results  of  such  analysis. 
These  results  may  be  called  suggestive  rather  than  conclusive. 


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CHAPTER    XVIII. 
COMPRESSED-AIR  ENGINES. 

250.  Introductory. — The  foregoing  chapters  have  been 
mainly  concerned  with  the  use  of  steam  as  a  heat  medium, 
because  it  is  in  the  first  place  the  most  used  of  all  such 
media,  and  is  the  most  accessible  of  the  vapor  class.  Next 
to  steam  as  a  heat  medium,  the  accessibility  and  harmlessness 
of  air  puts  it  as  the  most  to  be  preferred  of  media  of  the  per- 
manent-gas class,  treating  it  as  a  permanent  medium  at  the 
usual  range  of  temperatures  and  pressures. 

Before  passing  to  the  study  of  air  as  a  medium  to  which 
energy  is  imparted  by  the  action  of  heat  from  combustion,  as 
in  the  caloric  or  hot-air  engine  and  in  the  gas-engine,  it  will 
be  convenient  to  refer  to  a  class  of  air-engines,  using  air  as  a 
motor  fluid  to  which  a  degree  of  energy  has  been  imparted 
by  mechanical  means  so  as  to  raise  its  capacity  for  doing  work 
to  a  level  higher  than  that  exhibited  by  the  ordinary  atmos- 
phere. The  air-compressor  (Chapter  XIII)  is  constructed  to 
raise  the  entropy  of  air  above  its  atmospheric  condition,  in 
isothermal  aspiration,  and  to  raise  its  temperature  by  adiabatic 
compression.  In  so  doing  a  quantity  of  energy  is  stored  in 
each  pound  of  air  so  compressed  which  is  available  for  work 
in  a  piston-motor  similar  to  the  steam-engine.  The  com- 
pressed-air engine  receives  from  the  reservoir  a  charge  of  avail- 
able energy  just  as  the  steam-engine  receives  its  charge  from 
the  boiler.  A  mechanical  pressure  is  exerted  against  the  pis- 
ton at  constant  pressure  isothermally  up  to  cut-off,  with  a 
drop  in  entropy  till  cut-off  is  reached,  after  which  adiabatic 

361 


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362  HEAT  AND   HEAT-ENGINES. 

expansion  should  drop  the  temperature  in  a  complete  expan- 
sion back  to  where  the  cycle  began.  It  will  be  obvious, 
therefore,  that  if  both  compressor  and  air-motor  were  perfect 
and  frictionless,  the  latter  could  drive  the  former  and  together 
they  would  make  the  reversible  combination  conceived  by 
Carnot.  In  practice,  however,  the  air-machine  is  to  do  some 
outside  work  at  a  point  more  or  less  remote  from  the 
compressor.  The  latter  has  therefore  to  receive  a  heat  or 
other  energy  from  some  source,  transform  that  energy  to  the 
form  in  which  it  exists  in  the  compressed  air,  and  permit  that 
stored  energy  to  be  transmitted  to  the  remote  point,  there  to 
be  released.  It  is  the  convenience  and  safety  of  the  trans- 
mission and  storage  of  energy  by  compressed  air  that  has 
made  it  so  important  and  widespread  a  feature  of  modern  en- 
gineering. Storage  of  great  energy  in  small  bulk  and  with 
little  weight  in  strong  tanks  is  the  element  of  strength  for 
compressed  air  for  street-car  service  or  where  the  motor  can- 
not be  conveniently  continuously  connected  to  the  delivery  of 
the  compressor.  The  convenient  return  of  the  exhaust  to 
the  atmosphere  is  in  many  places  an  advantage,  as  under- 
ground or  in  submarine  work;  and  the  harmlessness  of  the 
air  in  case  of  accident,  breakage,  leakage^  and  the  like,  are 
often  valid  claims  for  the  use  of  such  air-engines. 

Compressed  air  may  be  used  in  air-engines,  receiving  it 
from  receivers  or  direct  from  the  compressing  cylinders,  in 
three  general  ways.  There  can  be  no  condensation  with  air, 
so  that  the  lowest  pressure  level  to  which  it  can  fall  is  that  of 
the  atmosphere.  When  it  does  so,  all  the  mechanical  energy 
is  withdrawn  from  it,  and  the  engine  is  said  to  work  with 
complete  expansion.  The  objection  to  complete  expansion 
is  the  low  terminal  effort  towards  the  end  of  the  stroke,  which 
may  not  be  enough  to  overcome  the  friction  of  the  motor 
itself.  Hence  the  second  method  is  that  of  partial  or  incom- 
plete expansion  where  there  is  a  pressure  acting  at  the  mo- 
ment when  the  exhaust  opens.     The  energy  resident  in  the 


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COMPRESSED  AIR  ENGINES,  36;> 

air  which  exhausts  is  thus  lost,  but  a  smaller  cylinder  will 
serve  to  give  a  given  horse-power,  because  the  mean  forward 
pressure  is  greater,  and  a  lighter  fly-wheel  will  secure  a  given 
degree  of  regularity  in_speed. 

The  third  method  is  to  deliver  air  to  the  cylinder  at  full 
pressure,  to  work  without  reduction  of  pressure,  and  to  ex- 
haust a  cylinder  full  of  air  at  the  receiver  pressure  at  each 
stroke.  Here  the  air  works  without  expansion.  These  three 
types  will  be  discussed,  and  the  losses  in  transmitting  energy 
to  a  distance. 

251.  Loss  of  Energy  in  Transmitting  Air  through 
Pipes. — The  most  considerable  loss  in  well-planned  systems 
will  be  the  loss  down  the  temperature  scale  by  radiation  and 
conduction  in  the  long  pipe-line.  It  does  not  pay,  as  a  rule, 
to  protect  the  pipes  to  mitigate  this  loss,  and  furthermore  the 
cooling  processes  at  the  compressor  are  planned  to  carry  away 
excess  of  temperature  for  the  sake  of  lessening  the  com- 
pressor work.  As  the  air  cools,  however,  its  volume  lessens, 
or  its  pressure,  or  both  together,  so  that  the  velocity  of  flow 
through  the  long  pipe  should  in  theory  be  increasing  slightly 
from  the  beginning  to  the  end.  Furthermore,  to  cause  a 
flow  of  the  compressed  air  in  the  pipe  from  the  compressor 
end  toward  the  motor  there  will  require  to  be  a  difference  in 
pressure.  This  may  be  called  (/,  —A)  ^'^^  ^s  a  quantity  to 
be  assumed  by  the  designer  of  the  pipe  transmission.  To  al- 
low it  to  be  ID  pounds  difference  is  a  large  value,  and  would 
only  be  justified  where  the  temporary  character  and  small  im- 
portance of  the  work  made  economy  of  plant-cost  of  more 
importance  than  running  or  working  economy.  From  3  to  5 
pounds  loss  in  transmissions  up  to  10,000  feet  would  not  be 
considered  bad  practice.  It  will  be  apparent,  therefore,  that 
length  and  diameter  of  pipe  will  enter  the  formula,  and  the 
density  or  degree  of  compression  to  which  the  air  is  brought 
at  the  upper  or  compression  end;  there  must  be  also  an  ex- 
perimental coefficient  to  embody  the  actually  observed  effect 


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364  HEAT  AND   HEAT-ENGINES. 

of  the  condition  of  the  pipe,  inside,  upon  the  air  flowing 
through  it.  The  slower  the  linear  flow  per  unit  of  time  the 
less  effect  will  the  pipe  have  upon  the  difTerences  of  pressure. 
Hence  it  appears  that  all  the  factors  entering  into  any  formula 
are  likely  to  be  varied  by  the  influence  of  the  others  which 
enter  it,  making  any  but  an  empirical  formula  a  somewhat 
uncertain  dependence. 

252.  The  D'Arcy  Formula  for  Compressed  Air. — The 
original  formula  of  D'Arcy  for  flow  of  water  in  hydraulic  dis- 
tributions has  been  modified  to  apply  to  an  elastic  medium 
like  air,  and  in  its  most  accepted  form  appears: 


In  this  D  is  the  cubic  feet  of  air  in  cubic  feet  per  minute  dis- 
charged at  the  pressure  /,  at  the  end  of  the  pipe-line  when 
the  latter  has  a  length  in  feet  denoted  by  /  and  a  diameter  in 
inches  denoted  by  d.  Therefore  the  factor  /,  — /,  will  be 
the  permitted  drop  in  pressure  from  the  compressor  pressure 
/,  to  secure  the  demanded  final  pressure/,  at  the  air-engine. 
The  factor  w^  will  be  the  weight  in  pounds  per  cubic  foot  of 
this  compressed  air  entering  the  pipe  at  the  compressor  or  the 
reciprocal  of  the  volume  occupied  by  one  pound  at  the  pres- 
sure/j.  Since  the  weight  of  a  cubic  foot  of  air  at  62®  F.  and 
atmospheric  pressure  is  .0761  pounds,  the  weight  at  any 
other  pressure  /,  will  be 


fT.  =  .0761(1+^). 


in  which  /,  is  in  gauge  pressure  in  pounds  per  square  inch. 
This  appears  more  conveniently 

W^  =  .0761(1  +  o.o68/j). 

Values  for  the  factor  c  i^d^  have  been  worked  out  as  fol- 
lows: 


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COMPRESSED-AIR  ENGINES. 


365 


Diameter  of 
Pipe. 

1  inch.  .  .  . 

2  "    

3  "    ...• 

4  "    .... 

5  "   .... 

6  "   .... 

7  "   .... 
S  '     


c^/d?' 

Jjia 

45.3 

9 

297.0 

10 

876.0 

II 

1856.0 

12 

3298.0 

13 

5273.0 

14 

7817.0 

15 

10988.0 

16 

CJ^d^ 


Diameter  of 
Pipe. 

9  inches 14872 

*   19480 

*   24800 

*   30926 

'    37898 

*    45690 

*  54462 

*   64102 


The  values  for  the  expression  c  Vd^  in  the  above  table 
will  require  to  be  increased  if  any  unusual  conditions  as  to 
multiplicity  of  bends  are  to  be  met  or  the  constrictions 
caused  by  valves  with  complicated  passages.  One  bend  at 
right  angles  has  been  considered  to  offer  the  resistance  of 
one  length  of  pipe  of  the  same  calibre.  It  is  here  that  the 
judgment  of  the  engineer  must  come  in  until  exhaustive 
experiment  shall  have  given  reliable  figures. 

Another  experimental  formula  of  considerable  acceptance 
is  the  result  of  the  practice  at  the  Mont  Cenis  tunnel  excava- 
tions. If  n  denote  the  velocity  in  feet  per  second,  d  the 
diameter  of  the  pipe  in  inches,  and  /  the  length  in  feet, 

«*/ 
A-A  =  0.00936-j, 

when  /,  and  /,  are  the  pressures  in  pounds  per  square  inch 
at  the  beginning  and  end  of  the  pipe. 

253.  Compressed  Air-engine  with  Complete  Expan- 
sion.— This  is  the  preferred  plan,  because  the  air  in  expand- 
ing from  the  pressure  /,  at  which  it  enters  the  air-cylinder  to 
the  pressure  of  the  atmosphere  p^  at  which  it  goes  out,  leaves 
the  cylinder  without  carrying  with  it  any  available  pressure 
energy.  As  in  the  case  of  the  compressor,  the  work  of  the 
engine  will  be  made  up  of 


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366  HEAT  AND   HEAT-ENGINES. 

'  p^v^ admission  work 

ff^j  =  -j  -j-   /     pdv,  .  .  .expansion  work 


^  p^v^ back-pressure  work. 


or 


W. 


in  terms  of  the  initial  volumes  and  pressures  for  one  pound 
of  air  received,  or  if  the  terminal  pressures  and  volumes  be 
preferred, 


^■- ^'^-i^kiy  -  \ 


from  which  the  mean  effective  is  derived  by  dividing  through 
by  the  final  volume  v^y  giving 


M. 


Ih  this  n  is  the  ratio  1.41  between  the  specific  heats,  since 
Cp  =  1.41C,.  The  work  for  M  pounds  of  air  would  be  M 
times  greater.  The  expansion  is  considered  to  be  adiabatic, 
as  was  the  compression. 

254.  Compressed  Air-engine  at  Full  Pressure  without 
Cut-oflf. — This  is  a  very  usual  case  where  the  conditions  must 
not  permit  of  the  down-drop  of  temperature  in  the  adiabatic 
expansion.  The  air  enters  full  stroke  at  /,  and  fills  a  volume 
F,  the  latter  representing  M  times  the  volume  of  one  pound 
at  the  pressure  /„  when  M  pounds  are  expended  per  unit  of 
time.      There  is  therefore  no  internal  temperature  change. 


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COMPRESSED-AIR  ENGINES,  367 

but  an  isothermal  entropy  increase  during  the  stroke,  and  at 
exhaust  the  pressure  drops  to  p^  and  the  temperature  from  T^ 
to  T^  at  the  free  expansion  into  the  open  air,  with  the  loso 
represented  by  the  product  778(71,  —  7"^.  In  other  words, 
the  air  is  used  as  an  inelastic  fluid  like  water  to  displace  the 
working  piston,  and  no  increase  in  intrinsic  energy  resulting 
from  the  compression  is  withdrawn  from  it  in  the  air-engine. 
It  leaves  the  latter  with  just  as  much  as  it  had  when  it  en- 
tered it. 

The  work  of  such  an  air-engine  will  be  the  difference  be- 
tween the  initial  and  final  pressures  into  the  volume  V^  occu- 
pied by  the  M  pounds  of  air;  or 


w.^vip^-p:^. 

but 

p,v,  =  MRT,; 

hence 

]V,  =  MRT,[i-t) 


=  77SM(C,-C;)T,{i-^y 


since  by  definition  C^^  C^=z  —^  (§§  116  and  183). 

To  compare  this  with  the  work  of  complete  expansion,  the 
expression  for  the  work  of  one  pound  is  transformed  by  the 
relations 


Hence,  since ^,F,  =  RT^,  and 


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368  HEAT  AND   HEAT-ENGINES. 

the  expression 

«'.=A^.J^[--(|)T 
can  be  written 

for  one  pound  of  air;  or  for  M  pounds 

This  expression  also  gives  the  temperature  range  for  any 
assigned  work  given  in  pressure  relations,  with  complete  ex- 
pansion. The  work  at  full  pressure  may  therefore  be  con- 
veniently equated  to  an  expression  of  the  abovie  form  in 
which  an  unknown  temperature  T^  shall  replace  the  final  tem  • 
perature  T^  in  this  last  equation.     That  is, 

w,  =  77iMic, .  Q(r.  -  r,)  =  ntMCiT,  -  r,), 

which  will  express  that  final  temperature  giving  the  same 
work  in  a  complete  expansion  as  was  given  by  the  full-pres- 
sure condition.     Solving  for  T^  it  becomes 


^.=L-+"-^-^:]^- 


whence  the  ratio  between  7",  and  T^  becomes  when  the  numer- 
ical value  for  n  is  inserted: 

T  A  ' 

^  =  0.71  +0.29-. 

T^  is  a  temperature  having  no  experimental  or  actual  value; 
but  from  it  the  relations  of  the  work  done  by  complete  expan- 
sion and  full  pressure  for  any  values  of  the  ratio  ~  can  be 
worked  out. 


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COMPRESSED'AIK  ENGINES,  369 

255.  Compressed-air  Engine  with  Incomplete  Expan- 
sion.— The  third  case  is  perhaps  the  most  usual,  where  air  is 
received  at  a  pressure  /, ,  volume  F, ,  and  temperature  T^  up 
to  cut-off;  is  expanded  adiabatically  down  to  conditions  /^, 
F/,  and  T^  above  the  exhaust  conditions  represented  by/^, 
V^ ,  and  T^.  The  air  expands  freely  from  //  down  to  p^ , 
doing  no  external  work,  but  there  has  been  some  lowering 
of  the  initial  pressure  in  doing  work  during  the  partial 
expansion.     As  before, 

r  /,  F, admission  work 

fF,  =  J  -f-  77^MCJ,T,  —  T/) expansion  work 

(  —  A  ^/ back-pressure  resistance. 

Following  the  same  plan  as  in  the  preceding  case,  and  substi- 
tuting an  ideal  temperature  T^  in  an  equation  of  the  form 
given  with  complete  expansion  which  shall  give  the  same 
work  at  full  expansion  as  is  given  jn  the  actual  case  of 
incomplete  expansion,  the  above  expression  for  W^  will  be 
placed  equal  to  the  ideal  expression,  and  solved  for  T^,. 
That  is, 

^K=AK  +  77SMCXT,  -  r/)  -p,v:  =  779,MC{T,  -  T,). 

But  since 

and 

this  becomes  when  divided  through  by  JjiM 
(C,-C;)T,-\-CXT,-T:)-{C,-QT:p,=  C/^T,-r;). 


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370  HEAT  AND    HEAT-ENGINES. 

whence  by  performing  operations, 

which  gives 

T^       Cv   .    Cp  —  Cvp^        I     ,    «  —  I A  .  A 

which  is  the  same  ratio  as  found  for  the  non-expansive  work- 
ing.    Hence  for  both  cases 


and 


W,  =  77^MC,{T,  -  r,)  =  77iMCpT{i  -  ^\ 


The  values  of  T^  can  be  found  for  any  relation  of  A  and  p/ 
from  the  foregoing  identical  formulae. 

256.  Compressed-air  Engine  with  Isothermal  Expan- 
sion.— This  is  a  very  unusual  case,  because  it  means  heating 
the  working  air  so  as  to  have  the  same  terminal  temperature 
as  at  the  entry,  by  some  hot  jacket  or  similar  device.  It  is 
conceivable,  however,  if  the  high  temperature  of  exhaust 
were  to  be  thought  desirable. 

The  work  per  stroke  will  be : 

A^i admission  work, 

I     pdv,  .  .  .expansion  work, 

— A^'4' back-pressure  work, 

when  expansion  is  incomplete,  and 

A^« admission  work, 

I     pdv.  .  .  .expansion  work, 

*/  t'4 

—  A^/ back-pressure  work> 


»;  = 


w.= 


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COMPRESSED-AIR  ENGINES.  37^ 

when  expansion  is  complete.     Hence 

^, = A^.  [i  +  hyp-  log  I7 -^]. 


and 


W^  =/.t/.  hyp.  log^  =A^.hyP-  log  r, 


when  r  is  the  ratio  of  expansion,  or  the  ratio  between  the 
volumes  at  cut-off  and  at  release.  With  complete  expansion 
the  terminal  pressure  p^  at  end  of  expansion  equals  the  back- 

pressure/^,  or  -— S  =  i. 

257.  Volume  of  the  Cylinder  of  a  Compressed  Air- 
engine. — The  design  of  an  air-engine  cylinder  usually  presents 
itself  with  the  air-pressures  given,  the  ratio  of  pressures  at 
beginning  and  end,  and  the  foot-pounds  or  horse-power  of 
work  to  be  done.  Hence  the  formula  of  §§  168  and  181  is 
directly  available.  If  the  known  horse-power  reduced  to  foot- 
pounds is  divided  by  2«,  when  n  is  the  number  of  revolu- 
tions per  minute,  the  quotient  will  be  the  work  to  be  done 
in  one  stroke.  Substituting  this  for  W^  and  solving  for  v^,  the 
necessary  final  volume  of  cj^linder  is  found,  neglecting  clear- 
ance loss.  The  final  volume  will  be  the  product  of  the  two 
factors  area  X  stroke,  which  must  be  proportioned  to  each 
other  according  to  any  determining  conditions  as  to  either. 

Or,  the  mean  pressure  value  (§§  184,  253)  can  be  substi- 
tuted in  the  equation 

H.P.  =  ^^-^ 

for  the  factor  P,  and  the  equation  solved  for  LA.  Clearance 
will  increase  the  cylinder  volume  according  to  the  data  of  §§ 
233-236. 

258.  Compound  Compressed-air  Eng^ine. — The  use  of  a 
non-condensing  type  of  engine  is  forced  upon  the  designer  of 


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372  HEAT  AND   HEAT-ENGINES. 

an  air-engine.  Hence  when  large  powers  are  to  be  stored  in 
small  bulk  the  use  of  high  pressures  is  made  necessary,  and, 

with  a  fixed  lower  pressure  limit,  a  large  ratio  between   ~. 

To  secure  this  high  degree  of  expansion  or  early  cut-off  in  a 
single  cylinder  forces  the  use  of  disadvantageous  crank-angles 
for  the  admission  pressures,  making,  therefore,  unsatisfactory 
working  of  the  engine  from  the  great  range  of  pressures  over 
the  area  of  the  piston.  This  evil  is  much  mitigated  by  the 
use  of  the  multiple-expansion  system,  using  cylinders  of  pro- 
gressive areas  or  volumes  as  the  pressures  fall  during  expan- 
sion, and  enabling  each  cylinder  to  have  a  longer  and  more 
advantageous  admission  (§§  172-174).  The  difficulties  from 
cylinder  condensation,  which  are  of  such  moment  in  the 
steam-engine,  are  of  less  moment  in  the  air-engine  and  may 
be  disregarded,  although  there  is  an  interchange  of  heat  with 
the  metal  walls  and  the  working  fluid.  Hence  the  work  of 
the  entire  expansion  from  /,  to  p^  is  divided  equally  between 
the  two,  three,  or  four  cylinders  of  the  series  by  laying  down 
a  diagram  having  an  area  equal  to  the  whole  work  under  the 
assumed  degree  of  expansion  supposed  to  take  place  in  one 
cylinder,  and  then  dividing  this  area  of  work  into  halves, 
thirds,  or  quarters,  and  giving  to  each  cylinder  in  the  series 
a  volume  proportioned  to  the  pressures  within  which  it 
works. 

The  compound  or  multiple  system  permits  a  reheating 
between  the  cylinders  if  desired,  whereby  unpleasantly  low 
terminal  temperatures  may  be  mitigated  and  the  expansion 
be  brought  nearer  to  the  greater  work  of  the  isothermal  curve 
of  pressures  and  volumes.  That  is,  if  there  be  two  cylinders,, 
and  the  terminal  pressure  and  temperature  in  the  first  cylin- 
der be//  and  7"/.     Hence 

W,  =  77&C/>{T,  -  T:)  =  77^CpT,  [i  -  [yf^'\. 


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COMPRESSED-AIR  BNGINPS. 


373 


If  in  an  intermediate  receiver,  by  any  source  of  heat,  the 
expanded  air  is  raised  again  to  Z",,  the  terminal  temperature 
will  become   7"/'  and  the  work  in  the  second  cylinder  will  be 


W^„  =  mCp(^T,  -  T:)  =  778C/r.[i  -  (^)  "  ]. 
so  that  the  sum  of  the  two  effects  will  be 


W,  +  ^..  =  77iCpT[2  -[f)"  -  [^)  '  ]. 

The  work  will  be  a  maximum  when  the  last  two  terms 
are  a  minimum.     This  occurs  when 

p:  =  ^pJo 

as  was  the  case  with  the  compound  compressor  (§  189).  The 
question,  however,  is  not  yet  answered  by  experiment, 
whether  the  loss  in  clearances  and  free  expansion  drop  be- 


a h". 


Fig.  109. 


tween  the  cylinders,  when  added  to  the  interest  cost  of  the 
smaller  cylinders,  offsets  the  mechanical  gain  from  the  use  of 
the  additional  cylinders.  In  street-car  motors,  where  two 
cylinders  are  wanted  in   any  event    to  prevent    stalling  on 


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374  HEAT  AND   HEAT-ENGINES. 

centres,  the  compound  method  offers  great  advantages.  It 
will  be  interesting  to  compare  the  diagram  of  the  advantage 
from  intercooling  in  compression  of  air  (Fig.  109)  with  the 
increase  of  volume  resulting  from  interheating  between  cylin- 
ders which  causes  an  adiabatic  expansion  in  the  air-engine 
to  approximate  more  closely  to  the  isothermal  condition. 

259.  Combined  Efficiency  of  Compressor  and  Air- 
engine. — Since  the  compressed-air  engine  can  only  be  oper- 
ated in  connection  with  a  compressor  which  has  antecedently 
raised  the  pressure  and  temperature  level  of  the  air,  it  ber 
comes  of  moment  to  compare  the  work  of  the  two  machines 
in  the  light  of  the  foregoing  discussion,  so  as  to  reveal  the 
directions  for  effort  to  make  the  air-engine  return  in  mechan- 
ical energy  all  the  energy  put  into  the  compressor  by  the 
prime  source  of  power.  Since  the  temperatures  are  the  sig- 
nificant factors,  the  work  of  the  compressor  will  be  trans- 
formed from  the  expression  in  §  169  by  the  method  followed 
iA  §  254,  whence 

W,  =  778C,{T,  -  T, 

The  work  of  the  air-engine  will  be 

IV,  =  77^C,{T,^  7;). 

The  efficiency,  being  the  quotient  of  the  delivered  work 
by  the  applied  work,  becomes 


W,_77SC,iT,-  T,) 


E=-^A  = 


<'  -  ?•) 


W.      778C,(7-,-r.)-^,,__7;^' 
which  can  be  transformed  into  pressure  relations  by  writing 


£  = 


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COMPRESSED-AIR  ENGINES.  375 

If  the  compressor  and  air-engine  operate  v/ith  about  the 
same  ratio  or  range  of  pressures,  the  ratio  of  the  bracketed 
factors  is  not  far  from  unity.  This  makes  it  appear  chat  the 
nearer  the  temperature  of  inlet  into  the  air-engine  approaches 
the  temperature  of  the  delivery  from  the  compressor,  the 
nearer  will  the  efficiency  become  unity.  Hence  the  wisdom 
of  preheating  the  air  for  the  air-engine,  if  the  latter  is  at  any 
distance  from  the  motor  so  as  to  have  lost  any  of  its  higher 
temperature  T',. 

It  must  not  be  forgotten,  however,  that  it  is  not  mechan- 
ically possible  to  reach  an  efficiency  of  unity,  even  with  pre- 
heating at  the  air-engine,  if  the  work  of  the  engine  part  of  the 
compressing  plant  be  taken  as  the  starting-point.  If  the  com- 
pressor return  to  the  air  80  per  cent  of  the  work  put  into  the 
compressor,  and  the  air-engine  deliver  80  per  cent  of  the 
work  which  it  received,  the  double  transmission  and  trans- 
formation returns  at  the  air-engine  as  its  net  work  only  80  per 
cent  of  80  per  cent  of  the  steam-cylinder  work,  or  only  64  per 
cent,  even  with  complete  expansion,  unless  the  efficiency  of 
the  air-engine  can  be  made  greater  than  unity  by  adding 
extra  heat  energy  at  the  point  where  the  engine  works. 

If  7",  is  the  temperature  of  the  atmosphere  at  the  air- 
engine,  it  would  be  an  advantage  to  lower  T^  by  cooling  or 
otherwise.  This  confirms  the  advantage  from  isothermal 
compression  or  two-stage  compression  when  the  loss  of  energy 
in  the  cooling  water  is  of  less  moment  than  the  other  compen- 
sating gains. 

260.  Heat  Range  in  the  Air-engine  Cylinder. — The  ex- 
pression for  the  work  of  the  air-engine,    » 

leads  at  once  to  the  conclusion  that  if  the  air  enter  the  air- 
engine  at  atmospheric  temperatures — between  60®  and  68°  F. 


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37'5 


HEAT  AND   HEAT-ENGINES. 


— it  will  leave  it  at  very  low  temperatures  if  there  is  any  con- 
siderable range  of  pressures.  The  following  table  gives  values 
for  7*4  absolute  and  Fahrenheit  calculated  from  the  relation 


assuming 


7;  =  459-4  +  68°. 


A. 

Final  Absolute 

Final 

A. 

Final  Absolute 

Final 

Temperature 

Fahrenheit 

Temperature 

Fahrenheit 

/4 

'4. 

U- 

/* 

'4. 

^. 

2 

431.4 

-    28 

9 

278.9 

—  180.5 

3 

383-5 

-    75.9 

10 

270.5 

—  188.9 

4 

352.8 

-106.6 

II 

263.1 

-196.3 

5 

330.7 

—  128.7 

12 

256.6 

—  202.9 

6 

313-7 

-145.7 

13 

250.7 

—  208 . 7 

7 

299.98 

-  159.4 

14 

245.3 

—  214.1 

8 

288.5 

-  170.9 

15 

240.5 

—  218.9 

These  values  for  the  temperature  of  the  exhausted  air  lead 
to  the  consideration  and  feasibility  of  mechanical  refrigeration, 
which  will  be  considered  in  a  subsequent  chapter,  and  also  to 
the  signal  advantage  of  preheating  the  air  before  it  enters  the 
air-engine.  It  further  makes  clear  the  objection  to  the  pres- 
ence of  moisture  in  the  air  used,  because  such  moisture  be- 
comes snow  or  ice  in  the  exhaust-passages  and  clogs  them. 

261.  Preheating  the  Air  for  the  Air-engine. — Large-scale 
experiments  with  compressed-air  plants  without  preheating  of 
the  air  at  the  motor  show  an  efficiency  ranging  from  less  than 
30  per  cent  up  to  about  40  per  cent.  Preheating  may  reduce 
the  losses  to  something  over  20  per  cent  only,  realizing  an 
efficiency  between  70  and  80  per  cent.  That  is,  to  heat  the 
air  to  a  temperature  of  480®  F.  at  the  motor  will  result  in  an 
increase  of  efficiency  of  30  per  cent. 

Methods  of  heating  the  air  involve  either  some  form  of 
stove,  or  the   use  of  hot  water   under  pressure.     The  stove 


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COMPRESSED'AJR  ENGINES.  377 

plan  in  its  simplest  form  is  to  force  the  compressed  air  through 
an  air-tight  vessel  in  which  anthracite  coal  or  charcoal  is  kept 
incandescent  by  the  union  of  the  carbon  and  the  oxygen  of  the 
compressed  air.  The  trouble  with  this  arises  from  the  ash  and 
dust  of  the  fuel  going  forward  through  the  engine.  For  the 
small  compressed-air  motors  of  Paris,  a  stove  of  cast  iron  lined 
with  fire-clay  is  heated  by  a  gas-jet  or  a  small  coke  fire.  A 
coil  of  pipes  in  a  fire  forms  another  type.  The  fuel  consump- 
tion is  so  small  as  to  be  scarcely  noticeable,  or  about  0.2  of  a 
pound  of  fuel  per  horse-power  per  hour.  Seventy  per  cent  of 
the  available  heat  in  the  fuel  went  into  the  air,  raising  its 
temperature  from  170®  to  3CX)°  F.  above  the  temperature  in 
the  conducting  pipe. 

A  form  of  preheater  which  has  been  used  for  street-car 
service  causes  the  compressed  air  to  pass  through  a  pressure- 
tank  filled  with  superheated  water  at  330°  F.  This  avoids 
carrying  live  fire  on  the  car.  The 
water  carries  more  heat  per  unit  of 
weight  than  any  other  body,  and  the  air, 
taking  up  some  water  mechanically, 
causes  it  to  become  vapor  in  the  cylin- 
der, adding  to  the  propelling  effect.  This 
is  the  feature  of  the  Mekarsky  system. 
Other  plans  inject  hot  water  in  jets  into  ^^®'  ^^^• 

the  air  storage  reservoir.  It  will  be  apparent  that  preheating 
raises  the  value  of  7",  to  that  of  T^  in  the  formula  of  §  259  and 
tends  towards  an  efficiency  of  unity.  Fig.  1 10  shows  a  cut  of 
such  preheater  using  oil. 

262.  Temperature-entropy  Diagram  for  Compressed- 
air  Engine. — While  the  air-engine  acts  like  the  non-condens- 
ing steam-engine  in  one  sense,  yet  it  is  only  possible  to  treat 
it  satisfactorily  in  connection  with  the  compressor,  of  which 
it  is  the  complement  (§§  263  and  264),  since  the  cycle  is  not 
closed  otherwise.     If,  for  example,  the  perfect-expansion /«/ 


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378 


HEAT  AND   HEAT-ENGINES. 


diagram  be  chosen  (Fig.  115),  the  admission  of  air  at  constant 
pressure  from  the  receiver  ab  is  not  an  isothermal  at  the 
temperature  7",  because  the  pressure  is  not  maintained  by 
adding  heat  to  the  reservoir;  but  if  the  latter  is  of  finite 
volume,  the  pressure  is  maintained  by  the  inlet-supply  from 
the  compressor.  Hence  the  line  on  the  temperature-entropy 
diagram  (Fig.  116)  will  be  a  line  of  constant  pressure 
descending  by  a  logarithmic  curve  from  the  point  b  \.o  a  for 


c'* 


PlG.115. 


Pig.  116 


which  the  upper  limit  (7i  or  T^  is  the  temperature  of  the  air 
leaving  the  compressor,  and  the  lower  limit  is  the  tempera- 
ture (Ta  or  T^  at  which  after  cooling  by  radiation  the  air 
enters  into  the  cylinder  of  the  air-engine.  Hence  the  rela- 
tion of  the  co-ordinates  will  be 

T 
^^  Cp  hyp.  log  y. 

At  the  point  a  the.  air  begins  to  expand  in  the  air-engine 
proper  (it  will  be  observed  that  the  line  ab  really  belongs  in 
the  compressor  process),  and  by  hypothesis  such  expansion 


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COMPRESSED-AIR  ENGINES. 


379 


is  adiabatic,  and  is  accompanied  by  a  drop  in  temperature 
without  entropy  change,  giving  the  h'ne  ad^  corresponding  to 
the  expansion-line  be  on  the  pv  diagram.  In  the  absence  of 
preheating  (§  261)  7"^  is  much  lower  than  the  atmospheric 
temperature  with  usual  points  of  cut-off  in  the  air-engine,  so 
that  7"^  gives  a  point  d  (§  260)  lower  than  the  air  into  which 
the  exhaust  escapes.  Hence  a  constant  pressure-curve  dc  is 
required  to  return  the  exhausted  cold  air  to  the  normal 
atmospheric  condition,  and  its  equation  will  be 


7; 


<t>=Cp  hyp.  log -^r. 


It  will  be  apparent  that  the  adiabatic  compression  of  the  air- 
compressor  will  be  required  to  close  such  a  diagram  by  a 
compression  from  T^  up  to  7^  from  which  the  process  began. 
If,  however,  the  process  be  an  incomplete  expansion,  as  in 
the  dotted  pv  diagram  of  Fig.  2,  or  without  any  expansion 
whatever,  as  in  Fig.  i,  the  temperature-entropy  diagram  will 
appear  like  the  left-hand  part  of  Fig.  117  for  the  first  case, 
and  the  right-hand  part  for  the  second. 


R       Tj      E 


Fig.  117 


The    greater  relative   area  of  rejection  of  heat  in  these 
latter  cases   is  the  measure  of  their  less  economy  as  com- 


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380  HEA  T  AND   HEA  T-ENGINES. 

pared  with  the  full-expansion  class,  provided  that  the  greater 
capacity  of  the  working  cylinder  for  a  given  power  by  reason 
of  the  lower  mean  pressure  is  not  an  offset  in  part  to  the 
greater  heat-rejection  per  stroke. 

263.  Temperature-entropy  Diagram  for  the  Air-com- 
pressor.— The  compressing  cylinder  cd  being  full  of  air  at 
atmospheric  pressure  T^  (^'ig.  118),  the  return  of  the  piston 


^ — ^^ 


FiG.iia 

compresses  air  adiabatically  up  temperature  along  the  vertical 
ordinate  cb  (Fig.  116),  without  change  of  entropy  to  the 
pressure  and  temperature  belonging  to  T^,  Then  the  valves 
of  the  receiver  open  in  the  actual  case  and  the  air  passes  at 
constant  pressure  by  slow  discharge  of  its  heat  energy  down 
the  curve  of  constant  pressure  to  the  condition  as  to  tem- 
perature which  belongs  to  surrounding  objects.  This  is  the 
line  ba  of  Fig.  118,  and  may  logically  attach  itself  to  either 
the  compressor  or  the  air-engine.  Strictly,  of  course,  it  must 
be  supposed  to  occur  in  the  compressor-cylinder,  after  the 
adiabatic  compression  is  complete  to  the  pressure/,.  Then, 
in  the  absence  of  any  adiabatic  expansion  and  drop  down 
temperature,  the  diagram  should  close  by  an  entropy  change 
at  constant  temperature  T^  =  T^  so  as  to  be  capable  of  com- 
pression again  to  the  point  b. 

If  the  cooling  is  not  permitted  at  the  constant  pressure /, 
of  the  receiver,  then  the  increase  of  entropy  value  does  not 
occur,  and  the  diagram  becomes  the  straight  isometric  cb, 
first  up,  and  then  down.     This  represents  a    cycle  of  pure 


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COMPRESSED-AIR  ENGINES.  38 1 

adiabatic  type,  with  full  storage  and  restoration  of  the  heat 
energy  of  the  compression,  so  that  the  air  finishes  with  the 
same  energy  that  it  began  with,  and  acts  like  a  spring.  No 
effective  outside  work  has  been  done,  however,  because  no 
energy  has  been  expended.      7V0  has  a  zero  value. 

If,  on  the  other  hand,  the  air  reached  the  air-engine  at 
Ti,  by  an  isothermal  heating  process,  the  point  a  would  lie  on 
a  horizontal  through  ^,  and  the  adiabatic  expansion  through 
the  temperature-range  represented  by  ad  =  cb  would  bring 
the  final  temperature  to  that  of  the  intaken  air,  and  the 
exhaust  in  escaping  would  retain  sufficient  energy  to  return 
by  a  constant  pressure-curve  up  again  to  ^,  if  it  were  not 
cooled  by  outside  means.  In  practice,  of  course,  the  ex- 
hausting air  is  cooled  by  contact  with  the  atmospheric  air, 
and  this  potential  energy  is  lost. 

264.  Temperature-entropy  Diagram  for  the  Combined 
Air-compressor  and  Air-engine. — A  much  more  valuable 
conception  and  application  of  the  heat  diagram  results,  there- 
fore, from  the  consideration  that  the  compressor  and  the 
engine  which  it  drives  are  one  apparatus,  the  exhaust  from 
the  air-engine  forming  the  aspiration  volume  of  the  com- 
pressor, and  the  discharge  from  the  latter  forming  the 
admission  volume  for  the  stroke  of  the  air-engine.  The 
compressor  always  works  with  complete  expansion;  the  air- 
engine  must  be  of  the  same  capacity  and  work  with  complete 
expansion  down  to  the  intake-pressure.  The  object  is  to 
have  no  loss  in  transmission,  and  the  external  work  done  by 
the  air-engine  should  be  the  same  as  that  done  by  the  steam- 
engine  cylinder  of  the  compressor.  Then  the  constant 
pressure-line  and  the  adiabatic  at  the  higher  entropy  belong 
to  the  air-engine,  and  the  lower  constant  pressure-line  and 
the  adiabatic  at  the  lower  entropy  are  the  complementary 
parts  of  the  compressor  cycle.  The  atmospheric  ocean  is  the 
receiver  for  the  air  exhausted  from  the  air-engine,  and 
delivers  it  without  change  of  state  to  the  compressor-inlet. 


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382 


HEAT  AND   HEAT-ENGINES. 


The  extent  to  which  the  actual  combination  departs  from  this 
ideal  complete  cycle  made  up  of  their  partial  diagrams 
measures  the  heat  losses  of  efficiency,  by  reason  of  the  failure 
of  the  entropies  to  equalize,  or  because  a  temperature  loss  or 


PlG.119., 


piG.l^Q, 


a  pressure  loss  by  cooling  and  radiation  has  compelled  an 
expenditure  of  energy  at  the  compressor  greater  than  that 
exhibited  by  the  air-engine. 

h 

r 


Fio.  121. 


Fig. 122 


Let  it  be    supposed,   for  example,  that  the  pv  diagram 
(Fig.  119)  is  the  card  from  the  compressor,  and  Fig.  120  is 


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COMPKESSED'AIR  ENGINES.  383 

the  adiabatic  card  from  the  complementary  air-engine.  The 
compression  of  the  air  is  adiabatic,  and  after  passing  through 
pipes  and  storage  its  volume  at  the  air-engine  is  reduced,  as 
is  made  clear  by  the  superposition  of  the  two  cards  (Fig. 
121).  The  shaded  area  lying  between  the  two  adiabatics  is 
the  loss  of  work  as  revealed  by  the  pv  representation  of  it. 
The  temperature-entropy  diagram  in  Fig.  122  deduced  from 
the  two  foregoing  paragraphs  and  resulting  from  their  super- 
position shows  that  the  heat  energy  furnished  by  the 
compressor  is  the  area  baNR,  and  the  energy  rejected  by  the 
air-engine  is  represented  by  the  unshaded  area  cdNR.  Hence 
the  available  or  utilizable  energy  should  be  their  difference, 
or  the  shaded  area  bade. 

The  effect  of  preheating  if  carried  so  far  as  to  raise  the 
point  a  to  the  same  temperature-level  as  b  is  made  evident 
by  an  increase  in  the  area  denoting  energy  supplied,  enabling 
a  greater  degree  of  adiabatic  expansion  if  the  same  tempera- 
ture-level d  is  fixed,  or  a  higher  value  for  d  can  be  permitted, 
provided  the  designer  is  willing  to  increase  the  area  of  rejected 
energy  for  the  same  work  in  the  air-engine  cylinder.  If 
now,  on  the  other  hand,  the  compression  were  isothermal, 
and  the  air  by  the  abundant  use  of  cooling  water  were  not 
allowed  to  rise  in  temperature,  the  temperature  ^  entropy 
diagram  will  be  a  line  through  c  parallel  to  the  entropy 
axis,  since  7*,  =  7",,  and  the  receiver  is  supposed  to  be 
large  enough  not  to  have  its  temperature  raised  by  the 
displacement  of  the  compressed  air  into  it.  This  means, 
then,  that  the  cooling  water  has  carried  away  with  it  (per- 
haps to  waste)  a  quantity  of  heat  energy  equal  to  the  work 
of  the  compression,  and  the  compressed-air  receiver  has  taken 
up  the  work  of  displacement  by  molecular  movement  and 
eddies  in  the  air  itself.  When,  then,  the  air-engine  receives  its 
air  at  atmospheric  temperature  from  such  an  isothermal  com- 
pression, and  uses  it  in  complete  adiabatic  expansion,  the  air 


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384  HEAT  AND   HEAT-ENGINES. 

must  drop  down  temperature  on  expansion  by  an  amount 
which  would  cool  that  weight  of  cooling  water  back  to  its 
original  temperature  if  it  could  be  kept  for  this  purpose.  If 
the  water  has  been  wasted,  then  the  universe  at  large  has  re- 
ceived the  heat  from  the  cooling  water,  and  has  to  supply  that 
which  warms  the  exhaust-air  up  to  Z",  again.  The  heat  of  the 
fuel  burned  to  compress  the  air  in  the  first  place  is  wastefully 
used  in  this  process,  when  referred  to  the  power  developed  at 
the  air-engine. 

Or,  again,  if  the  expansion  at  the  air-engine  were  made 
isothermal  by  heating  the  air  as  it  was  working  as  well  as  before 
admission,  making  7",  =.  T^,  the  temperature-entropy  diagram 
becomes  a  line  also,  and  the  heat  to  be  supplied  will  be  that 
which  will  be  the  area  of  the  finite  diagram  which  would  have 
been  generated  with  true  adiabatic  expansion. 

These  observations  lead  to  the  generalization  which  might 
have  been  foreseen  in  advance,  that  compressed  air  or  other 
elastic  media  are  only  effective  storage  media  for  mechanical 
energy,  and  act  like  a  spring,  provided  that  means  are  taken  on 
the  expansion  to  replace  the  heat  conditions  in  inverse  order 
which  attended  the  compression.  Or  in  other  words,  air  acts 
as  water  or  other  incompressible  fluid  transmission  would  to 
transmit  the  energy  of  the  steam  or  other  motor,  if  pains  are 
taken  to  prevent  either  uncompensated  rise  or  fall  of  tempera- 
ture while  in  use  as  a  medium  ;  and  in  this  case  friction  in 
pipes,  valves,  and  bends  would  be  the  only  source  of  loss. 

Finally,  if  heat  is  supplied  to  the  air-engine  by  preheaters, 
such  heat,  adding  to  that  received  from  the  compressor,  adds 
an  area  to  the  temperature-entropy  diagram  which  helps  to 
compensate  for  the  losses  of  energy  which  will  appear  in 
actual  conditions. 

265.  Concluding  Summary. — It  must  not  be  overlooked 
that  the  air-engine  and  the  air-compressor  are  not  heat-engines 
in  the  sense  in  which  this  treatise  uses  this  term.     They  do 


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COMPRESSED-AIR  ENGINES.  385 

not  create  a  mechanical  energy  or  liberate  it  from  a  reservoir 
of  stored  heat  energy.  The  mechanical  energy  being  created 
or  liberated  so  as  to  be  available,  these  appliances  store  and 
restore  that  mechanical  energy.  Their  claim  for  consideration 
IS  based  upon  the  fact  that  the  relations  of  pressure  volume 
and  temperature  are  so  interrelated  by  natural  laws  that  the 
principles  underlying  the  compressor  and  compressed-air  engine 
must  conform  to  those  broader  and  more  fundamental  ones 
which  the  science  of  thermodynamics  must  consider  as  its  own. 
The  special  field  of  compressed-air  engineering  bears,  however, 
to  the  general  subject  of  motive-power  engineering  the  same 
relation  which  is  borne  by  the  electric  dynamo  and  motor  in 
Its  parallel  department :  the  energy  having  been  liberated  or 
made  available,  each  is  a  convenient  and  satisfactory  method 
of  transmitting  that  energy  to  desired  points  and  utilizing  it 
there.  The  economic  advantages  of  large-scale  installations  for 
the  generation  of  mechanical  energy  are  reaped  by  either 
system,  and  the  choice  of  that  which  is  to  be  preferred  must 
often  be  guided  by  considerations  outside  of  the  purview  of 
pure  theory. 


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CHAPTER   XIX. 
HOT-AIR    ENGINES. 

266.  Introductory. — In  the  preceding  chapter  a  class  of 
engines  using  cool  or  cold  air  has  been  discussed,  in  which  the 
propelling  energy  to  drive  the  piston  was  given  by  raising  the 
pressure  of  air  as  a  medium  by  means  of  mechanical  energy 
previously  available.  This  chapter  is  to  discuss  air-engines  in 
which  the  pressrure  to  drive  the  piston  is  given  to  the  air  as  a 
heat  medium,  by  increasing  its  temperature  and  entropy 
directly  by  the  application  of  heat  to  it.  They  may  or  may  * 
not  include  also  the  conception  of  a  compression  of  that  air, 
but  the  rise  of  its  temperature  is  the  primary  feature. 

The  relatively  low  specific  heat  of  air : 

at  constant  volume 0.16847,         (C,) 

and  at  constant  pressure 0.23751,         (C^) 

together  with  the  reluctance  with  which  heat  is  transferred  to 
it,  except  by  contact  in  thin  films  or  small  subdivided  masses, 
not  only  limit  the  size  and  weight  of  these  engines  to  relatively 
low  powers,  but,  by  making  the  storage  process  inconvenient 
between  the  source  of  heat  and  the  engine,  the  boiler  and  its 
appendages,  have  been  thrown  out  which  form  so  considerable  a 
feature  of  the  steam-engine  and  constitute  one  of  its  dangers. 
The  usual  underlying  principle  is  the  heating  and  cooling  of 

386 


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HOT' AIR  ENGINES.  387 

the  air  for  each  stroke  between  the  limits  of  /,  and  /,  in 
the  cylinder  itself,  or  in  small  chambers  without  it,  or  both. 
Carnot's  principle  applies  most  closely  to  such  engines,  because 
the  same  weight  of  air  is  often  used  over  and  over  again  in  a 
strictly  closed  cycle.  The  term  **  caloric  "  engine  is  a  sort  of 
trade  name  applied  by  John  Ericsson  in  1833  to  his  engines  of 
this  sort,  and  is  properly  going  out  of  use. 

267.  Types  of  Hot-Air  Engine. — The  fact  that  air  as  a 
heat  medium  is  also  a  supporter  of  combustion,  and  the  high 
temperature  directly  realizable  from  such  combustion,  has  at- 
tracted  designers  to  the  use  of  engines  in  which  the  heat 
energy  should  be  directly  liberated  in  the  working  cylinder. 
Such  engines  will  be  called  internal-conibustion  engines,  the 
furnace  being  practically  within  the  cylinder  or  in  communica- 
tion with  it.  The  engine  works  rather  with  the  products  of 
combustion  than  with  air  as  a  medium,  and  for  this  reason 
such  engines  are  sometimes  called  "  products  of  combustion  ** 
engines.  The  fuel  may  be  solid,  liquid,  or  gaseous  (Chapter  V). 
The  importance  of  the  gas-engine  will  command  a  subsequent 
chapter  for  itself ;  the  oil-engine  makes  the  fuel  gaseous  before 
it  is  consumed,  and  is  in  the  gas-engine  class. 

The  alternate  plan  is  to  have  the  furnace  exterior  to  the 
working  cylinder,  heating  the  working  medium  by  transfer 
through  a  metal  wall.  This  is  the  more  usual  type  where  the 
fuel  is  solid,  and  these  form  the  hot-air  engine  properly  so 
called. 

A  second  classification  of  type  must  be  made  which  shall 
include  in  one  class  those  engines  which  operate  their  cycle 
upon  the  same  mass  or  weight  of  air  continuously,  only  taking  in 
a  fresh  charge  to  replace  leakage  losses  or  to  increase  the  mass 
in  use.  This  type  might  be  called  the  closed-cycle  type.  The 
other  class  in  this  division  would  be  the  open-cycle  type,  where 
at  each  stroke  a  new  charge  is  drawn  in  from  the  atmosphere 


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388  HEAT  AND  HEAT-ENGINES^ 

and,  after  being  heated  and  expanded,  is  exhausted  again  into 
the  atmosphere,  as  occurs  in  the  non-condensing  steam-engine. 
The  first  class  can  evidently  be  operated  independent  of  atmos- 
pheric pressure,  or  with  an  initial  tension  selected  at  pleasure. 

Air-engines  will  again  differ  according  as  they  use  or  do 
not  use  the  principle  of  the  **  regenerator  "  to  absorb  heat  on 
the  outflow  of  the  air,  and  to  restore  such  entrapped  heat  to 
the  incoming  cooler  air. 

Finally,  engines  of  the  closed-cycle  type  may  differ  by  hav- 
ing the  temperature  change  in  the  air  take  place  at  constant 
pressure  or  at  constant  volume.  Each  type  is  identified  with 
the  name  of  some  designer  or  engineer.  It  will  be  apparent 
that  the  closed-cycle  hot-air  engines  operate  on  the  lines  of  the 
Carnot  cycle,  as  the  steam-engine  can  only  be  made  to  do  by 
making  the  feed-pump  or  air-pump  an  integral  part  of  the 
series  of  organs. 

268.  Regenerator  for  Hot-air  Engine.— The  desirability 
of  an  appliance  within  a  heat-engine  itself  which  could  absorb 
heat  on  its  way  to  rejection  at  2",  and  give  it  up  to  the  air  on 
its  way  to  become  heated  up  to  7",  was  early  realized  by  stu- 
dents of  the  Carnot  theorem.  If  it  could  be  made  to  work, 
such  an  appliance  could  replace  some  of  the  necessity  for 
adiabatic  expansion  and  compression  (particularly  the  unde- 
sirable latter).  The  first  to  apply  the  idea  was  Robert 
Stirling  (1816  and  1827),  and  Ericsson  used  it  in  1833  and 
thereafter.  The  ideal  plan  would  be  to  have  a  chamber  of 
such  thermal  capacity,  and  such  absence  of  self-conductivity, 
that  the  air  entering  it  at  7",  at  its  cool  end  should  be  heated 
to  7\  by  the  time  it  had  reached  the  other  or  hot  end ;  and 
such  heat  as  was  thus  absorbed  should  have  been  imparted  to 
the  chamber  by  the  flow  of  the  hot  air  entering  in  the  reverse 
direction  at  a  temperature  T^  so  as  to  leave  the  chamber  at  the 
cooler  end  at  7",,     This  hypothesis  is  of  a  distinctly  reversible 


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HOT-AIR  ENGINES.  3^9 

process,  but  fails  of  course  from  the  actual  conduction  and 
radiation,  and  from  the  necessarily  limited  capacity  for  heat  of 
a  regenerator  of  practicable  size  and  weight. 

These  regenerators  as  applied  to  hot-air  engines  are  either 
wire-gauze  nettings  or  thin  brass  plates  on  edge  for  small 
engines,  or  are  coils  or  grids  of  copper  wire  for  larger  ones. 
The  Ericsson  hot-air  ship  of  1853  had  a  wire  regenerator 
whose  aggregate  length  of  wire  exceeded  fifty  miles.  The 
weight  of  material  used  in  the  regenerator  in  British  practice 
seems  to  have  been  about  forty  times  the  weight  of  air  used 
per  stroke.  The  waste  from  practical  causes  seems  to  have 
ranged  from  one  tenth  to  one  twentieth  of  the  heat  alternately 
withdrawn  and  restored  per  stroke.  The  closed-coil  feed- 
water  heater  using  exhaust-steam  embodies  this  regenerator 
idea.  •  ' 

It  must  not  be  overlooked  that  the  action  of  the  ideal 
regenerator  has  nothing  to  do  with  the  taking  in  and  rejection 
of  heat  by  the  engine  for  the  purpose  of  doing  work  with  that 
heat.  The  regenerator  becomes  thus  an  integral  part  of  the 
engine,  and  is  to  be  so  considered. 

269.  Hot-air  Engine  with  Temperature  Changes  at 
Constant  Volume.  Stirling's  Engine.— The  engine  designed 
by  Robert  Stirling  (1816)  and  improved  by  James  Stirling 
(1827)  is  one  of  the  simplest  of  the  closed-cycle  external-fur- 
nace type,  and  embodies  regenerator  and  Carnot  cycle.  It  is 
shown  in  ideal  section  in  Fig.  125. 

The  working  cylinder  is  By  with  its  piston  connected  to  a 
beam  and  so  to  the  rotative  mechanism.  A  passage  or  pipe 
connects  the  working  cylinder  with  the  larger  chamber  in 
which  the  heat  changes  occur.  /?  is  a  displacing  piston  or 
plunger  made  of  a  sheet-metal  casing  filled  with  a  non-con- 
ducting  material  like  plaster  or  brick-dust.  The  furnace-fire 
surrounds  the  hemispherical  cast-iron  vessel  at  the  bottom, 


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390 


HEA  T  AND   HEA  T-ENGINES. 


but  IS  prevented  from  reaching  above  the  diameter.  In  the 
upper  part  at  C  are  coils  of  small  copper  pipe  in  which  circu- 
lates  cooling  water  forming  the   refrigerator.     Between  the 


*^^^it^~^^A^ii^ 


Fig.  125. 

points  A  and  C  is  the  regenerator  E  of  thin  plates.  The 
displacing  plunger  D  does  not  fit  the  casing,  but  an  inner 
lining  of  it,  which  lining  is  perforated  at  the  bottom.  The 
working  air  is  thus  forced  to  pass  through  the  regenerator  on 
its  way  to  and  from  the  working  cylinder.  The  displacing 
plunger  D  is  so  adjusted  as  to  its  phase  of  movement  that  the 
up-stroke  shall  occur  when  the  working  piston  in  B  is  down 
or  nearly  so,  and  the  descent  of  D  shall  take  place  when  B  is 


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HOT-AIR  ENGINES, 


391 


near  the  beginning  of  its  idle  or  descending  stroke.     The 
engine    is   single-acting   unless  made 
with    double    cylinders.      The    cycle 
presented  on  the/z;  diagram  is  there- 
fore shown  by  Fig.  126. 

(i)  The  air  at  7",  from  the  action 
of  the  regenerator  receives  heat  at 
that  temperature  from  the  furnace.  It 
expands  isothermally  along  ab^  doing 
work  through  the  piston  B,  The 
heat  taken  in  per  pound  of  air  will  be 
CjT^  hyp.  log  r,   in  which   r  is  the  FiG.12a. 

ratio  between  the  initial  and  final  volumes  of  the  air.     The 
increase  in  entrop;^  during  that  isothermal  expansion  will  be 

0,  —  0,  =  -^  hyp.  log  r. 

(2)  The  air  returns  without  change  of  its  volume  through 
the  refrigerator  from  the  T^  end  to  the  7",  end.  The  pressure 
falls  along  be  proportionally  to  the  fall  in  temperature.  The 
heat  stored  in  the  regenerator  plates  is  C^  {T^—T^. 

(3)  The  ascent  of  the  displacing  plunger  compresses  the 
air  along  cd^  reducing  its  volume,  but  withdrawing  any  heat 
by  the  passage  over  the  coils  of  the  refrigerating  surface  in 
DC.  Heat  is  rejected  to  the  cooling  water  to  the  amount  of 
CpT^  hyp.  log  r.  The  entropy  change  should  be  the  same  as 
in  the  expansion,  t^ut  in  reverse  direction. 

(4)  ThQ  air,  passing  again  through  the  regenerator  from  the 
T^  end  to  the  hot  end,  is  heated  to  T^  isothermally  at  constant 
volume  along  da^  and  the  heat  taken  up  by  the  air  should  be 
that  furnished  to  the  regenerator  on  the  other  transit  of  the 
air,  or  C,  (T",— 7",). 

270.  Temperature  -  entropy  Diagram  for  a  Stirling 
Hot-air  Engine. — If  the  regenerator  were  ideally  perfect, 
and  replaced  the  adiabatic  expansions  and  compressions  per- 


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392 


HEAT  AND   HEAT-ENGINES. 


fectly,  the  temperature-entropy  diagram  would  be  the  rectangle 
whose  width  was  (Fig.  127) 

0>— 01  =  R  hyp.  log  r 

and  whose  length  was 

T  —  T 
and  whose  area 

(0.-0.)  (7-- 7;) 
would  give  the  mechanical  energy  per  pound  of  air  per  stroke. 
The  relation  of  this  quantity  to  the  applied  heat, 

(0-0.)7'., 
would  be  the  efficiency.     The  rejected  heat  would  be 

(0,-0,)7'.- 

But  while  the  regenerator  gives  when  perfect  in  action  a  tem« 
perature-entropy  area  equal  to  that  of  the  Carnot  cycle  since, 

CTy^  hyp,  log  r  -—  CT^  hyp,  log  r  _  T^—T^ 
CT,  hyp.  log  r  ""      T^"' 

the  diagram  is  not  of  precisely  the  same  form,  because  there 
will  be  a  gradual  decrease  in  entropy  during  the  cooling,  and  a 


a  h 


T 


d 


/Mr,r' 


-f-t- 


!  !    tt 
I  I    I 

I 


i'ii 


P    e 


FiG.137.  Fio.128. 

gradual  increase  during  the  heating  process.     Hence  the  dia- 
gram will  take  the  form  of  Fig.  128.     The  curve  dc  replace:. 


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HOT' AIR  ENGINES,  393 

the  isentropic  drop  in  temperature,  and  the  curve  da  repre- 
sents the  corresponding  rise.  If  the  regenerator  is  perfect, 
these  two  curves  will  be  similar,  because  each  transfer  in  one 
direction  is  the  same  as  the  transfer  between  the  same  tem- 
perature limits  in  the  other.  The  value  for  the  abscissa  at 
any  temperature  T  will  be 

0  =  C;  hyp.  log  T 

when  the  transfer  is  at  constant  volume,  as  in  the  case  under 
consideration.  For  the  other  class  the  specific  heat  will  be 
that  at  constant  pressure. 

The  area  pbcq  shows  the  heat  taken  in  by  the  regenerator, 
and  the  area  madn  shows  the  heat  given  out  to  the  air. 

Taking  the  actual  experimental  data  for  a  Stirling  air- 
engine  used  many  years  ago  in  a  foundry  at  Dundee,  and 
quoted  from  the  Institute  of  Civil  Engineers  of  Great  Britain, 
some  interesting  conclusions  may  be  drawn.  The  observed 
quantities  were 

7",  =  1 1 1 1  /i  =  240  rf  =  16  inches 

7;  =  61 1  r  =  1.25  /  =  4  feet 

Rpm  =  zS 

Volume  of  cylinder 

at  admission  and  end  of  exhaust  =  1.709 

at  end  of  expansion  and  beginning  of  exhaust  =  2. 119 

Expenditure  of  heat  in  heating  the  air,  or  latent  heat  of 
expansion, 

ff^  =  P^(f>  =  R  hyp.  log  rXPx^  11.647  X  mi  =  12942 

Waste  heat  in  regenerator, 

mK,{T,  -  7;)  =  13  X  500  =    6500 
{m  is  called  from  -^  to  ■^) 


Total  heat  expended  per  pound  per  stroke  19442 


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394  HEAT  AND   HEAT-ENGINES. 

Rejected  heat,  //,  =  T^(f)  =  1 1.647  X  61 1  =    71 19 

Mechanical  energy  per  stroke  per  pound, 

<f>{T,  -  r,)  =  11.647  X  SOO  =    5823 
Efficiency  of  fluid, 

Mechanical  energy        5823 

Heat  applied       ~"  19443  ""    *^ 

Volume  of  piston  displacement  per  stroke, 

=  1.06  cubic  feet. 

2 

Mean  effective  pressure, 

Mechanical  energy  5823 

Volume  of  displacement  =  T.^  =  ^437  lbs.  per  square  foot ; 

=  35.7s  "      «         "      inch. 
The  horse-power, 

37.75  X  200  X  4  X  28  X  2  _ 

33000  ";  5^"^' 

The  relatively  small  capacity  for  its  volume  of  cyHnder 
and  the  relatively  low  mean  pressure  for  the  high  initial  are 
features  to  be  observed.  The  engine  referred  to  has  long 
been  regarded  as  a  classic,  but  it  was  abandoned  from  the  dif- 
ficulty of  maintaining  the  heating-chamber.  Usually  it  was 
run  at  a  lower  temperature  and  pressure,  and  developed  an 
average  of  20  H.P. 

Laubereau's  engine  is  a  more  modern  form  of  the  Stirling. 

271.  Hot-air  Engine  with  Temperature  Changes  at  Con- 
stant Pressure.  Ericsson's  Engine. — The  hot-air  engine  of 
1852-3  designed  for  a  2200-ton  sea-going  vessel  by  John 
Ericsson  has  much  the  same  classic  and  historic  interest  as 
the  Stirling  engine.  The  engine  was  calculated  to  be  of  600 
H.P.,  but  actually  ran  at  about  300.  There  were  four  cylin- 
ders, each  14  feet  in  diameter  and  having  6  feet  stroke,  causing 


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HOT-AIR  ENGINES. 


395 


nine  revolutions  per  minute.  The  air  entered  at  about  380®  F. 
It  burned  8  tons  of  coal  per  twenty-four  hours,  which  is  i.i 
pounds  per  H.P.  per  hour  if  the  larger  figure  is  taken,  and  2.2 
pounds  if  the  smaller  figure  is  correct.  Its  bulk  and  weight 
were  its  defects.  In  1854  it  was  replaced  by  a  steam-engine. 
In  i860  Ericsson  brought  out  his  early  design  of  horizontal 
small  motor,  and  later  (1880)  the  latest  form  adapted  for 
house-pumping  was  produced.      Fig.   129  shows  the  Ericsson 


Fio.  129 


Fig.  130. 


pumper  in  perspective,  and  Fig.  130  in  section.  The  fire  of 
coal  or  gas  is  below  the  longer  cylinder  d^  which  again  is  water- 
jacketed  at  the  upper  end,  xx.  In  tank-pumping  engines  the 
pumped  water  circulates  through  the  jacket.  A  is  the  hollow 
displacing  piston,  and  B  is  the  working  piston  proper.  The 
displacer  is  coupled  to  the  *bell-crank  beam  K^  and  so  to  the 
crank,  while  the  beam  proper  is  linked  directly  to  the  crank. 


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396 


HEAT  AND   HEAT-ENGINES, 


Hence  the  two  pistons  are  practically  quartering.  Fig.  131 
shows  a  reproduction  of  an  actual /z/ diagram,  and  Fig.  132 
the  theoretical  curves.     The   straightness  of  the  isothermal 


Fig.  181. 


F 

• 

'*—^--<^ 

^ 

1 

\ 

^. 

\ 
\ 

K 

::^, 

t 

i  \ 

r 

1 

i 
t 
Y 

1 
1 
1 

^0 

i   !     i. 

1 

!<> 

r|        t 

0 

V- 

— J 

Fig.  183. 

lines  shows  the  variation  of  pressure  to  be  slight  compared 
with  the  change  of  volume. 

The  temperature-entropy  curve  diagram  for  the  Ericsson 
engine  will  be  the  same  as  for  the  Stirling  (Fig.  128,  §  270), 
except  that  the  coefficient  will  be  Cp  for  the  logarithmic 
curves,  instead  of  C,. 

The  Rider  hot-air  pumping-engine  separates  the  hot  and 
cold  cylinders,  and  places  a  regenerator  H  between.  The 
Ericsson  pumper  does  not  use  a  regenerator  (Fig.  133). 

272.  Other  Forms  of  Hot- Air  Engine.  —  The  engineers 
and  designers  of  the  continent  of  Europe  have  made  more  trials 


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HOT-AIR  ENGINES. 


397 


with  hot-air  engines  than  have  been  made  in  America,  but  the 
limited  extent  to  which  even  successful  forms  have  been  intro- 
duced have  made  "their  engines  but  little  more  than  names. 
Richard  Unger  combined  a  separate  compressing  cylinder  for 


Fio.  188. 

raising  initial  tension,  with  the  plan  of  lowering  the  initial  vol- 
ume of  such  air  by  injecting  cool  water  into  it.  Some  of  this 
water  heated  by  the  compression  becomes  steam.  The  hot 
products  of  combustion  from  the  furnace  mix  with  part  of  the 
cooled  compressed  air,  and  thence  go  to  the  valve-chest  of  the 
engine. 

The  Stirling-Laubereau  engine  had  the  working  piston  acted 
on  at  high  heats  by  the  air  used,  and  a  certain  volume  of  air 
fills  clearance  volumes  which  underwent  heat  changes  without 
doing  work  by  its  expansion.  Lehmann's  hot-air  engine 
combined  the  low  piston  temperature  secured  by  Ericsson,  and 


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398  HEAT  AND  HEAT-ENGINES. 

avoids  unnecessary  heating  and  cooling  of  a  part  of  the  air  at 
each  revolution, 

The  plan  of  separate  compression  and  the  use  of  high- 
tension  air  in  a  closed  cycle  are  features  of  the  Woodbury^ 
Merrill  engine  of  American  origin.  Other  American  designers 
have  been  Shaw,  Roper,  Wilcox.  Other  foreign  types  are 
represented  by  Franchot,  Siemens,  Robinson,  Bailey. 

Special  interest,  however,  attaches  to  a  principle  put  forth 
as  early  as  1851  by  Dr.  Joule,  which  leads  to  the  operation  of 
internal-combustion   engines,  to  be  later  discussed. 

273.  Hot-air  Engines  with  Separate  Compressing^ 
Cylinder. — It  is  necessary  to  add  to  the  organs  of  a  hot-air 
cycle-engine  a  pump  which  shall  draw  in  air  from  the  atmos- 
pheric supply  without,  and  deliver  it  to  the  working  cylinder 
if  the  cycle  is  to  be  an  open  one.  This  aspirating  pump  is 
usually  also  a  compressing  pump,  driven  from  the  working 
shaft,  and  hence  absorbing  a  certain  amount  of  the  energy 
developed  by  the  heating  of  the  air.  The  energy  required  for 
compression  is  usually  restored  completely  by  the  increased 
energy  of  the  working  stroke,  but  of  course  extra  weight  is 
needed  in  the  fly-wheel  to  redistribute  this  restored  energy. 

This  separate  pump  is  a  prime  requisite  of  products  of 
combustion  engines,  and  is  present  also  in  others. 

The  ideal  indicator-diagram  of  such  an  engine  on  the  pv 
plane  will  have  a  form  such  as  Fig.  134. 

The  pump-piston  starting  at  the  point  represented  by  d 
above  the  vacuum  line  a  distance  corresponding  to  atmospheric 
pressure  draws  in  a  volume  F,  =  Hd,  representing  that  of  one 
pound.  By  the  return  or  compressing  stroke  of  the  pump  the 
air  is  first  compressed  adiabatically  along  da^  and  when  the 
pressure  of  the  receiving  chamber  (the  furnace  of  a  products-of- 
combustion  engine)  is  reached,  the  valves  to  it  open  and  the 
compressed  charge  enters.  The  pressure  is  practically  constant 
because   the  working  cylinder  is  withdrawing  air  during  this 


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HOT' AIR  ENGINES. 


399 


displacement  process,  provided  the  heating  chamber  is  of  suf- 
ficient volume,  but  the  heat  is  not  supplied  isothermally  as  in 
previous  cases. 

The  working  cylinder  draws  hot  air  at  constant  pressure 
from    the   receiver  or  furnace  to   an  extent   represented    by 


the  line  ATif,  when  cut-ofif  occurs  and  adiabatic  expansion  down 
the  line  be,  until  atmospheric  pressure  is  reached  if  the  expan- 
sion is  complete,  when  the  exhaust  opens  to  the  atmosphere 
and  the  line  cd  is  the  return  stroke.  Such  an  engine  is  like 
the  combination  of  air-compressor  and  air-engine,  or  steam- 
engine  without  condensation,  whose  diagram  is  closed  by  the 
compression  of  the  boiler-feed  pump.  The  net  work  is  the 
shaded  area,  the  white  or  plain  part  being  the  work  of  the  com- 
pressing pump.  Using  as  subscripts  the  notation  of  Fig  134, 
the  area  of  the  feed-pump  work  diagram  will  be  KadH^  which 
will  be  the  sum  of 

NdaM  +  KaMO  -  HdNO. 

=  c^{T^  -  Tj  +  {C,  -  Q(r,  -  7;) 


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40O  HEAT  AND  HEAT-ENGINES. 

The  area  far  the  working-cylinder/z^  diagram  will  be  simi- 
larly found  to  be  KbcH,  if  the  same  scale  of  volumes  be  used 
as  for  the  pump,  which  will  become 

The  difference,  or  net  work,  will  be 

^-fl=<:,(r.-r,-7;  +  7;). 

The  heat  expended  in  the  receiver  is  expended  in  raising 
the  temperature  of  the  air  from  that  caused  by  the  adiabatic 
compression  7\  to  the  temperature  Z.  Calling  it  Qy  as  the 
pressure  is  constant, 

Q=C,{T,-T,). 

T^  is  known  as  the  receiver  temperature,  and  T^^can  be  calcu- 
lated when  r,  is  atmospheric  temperature  by  the  adiabatic 
formulae  (§  154). 

The  heat  rejected  is  given  out  to  the  atmosphere  during 
any  cooling  from  7,  (at  which  the  air  exhausts)  down  to  T^,  the 
atmospheric  temperature.  T^  is  similarly  found  from  the  T^ 
value  by  the  adiabatic  formula  (§  154).    Hence  the  efficiency  is 

Q     -  T-T,  -'     T.-T: 

Since  the  volume  of  the  feed-pump  should  be  to  the  volume 
of  the  working  cylinder  in  the  relation  of  the  temperatures  at 
the  points  a  and  b,  the  pressures  being  constant,  and  these 
volumes  should  bear  also  the  same  relation  at  d  and  at  ^,  the 
equality  can  be  written 

V  T,_T, 

by  which  relations  the  equation  of  efficiency  transforms  into 

T,-T~    r,    ~    r. 


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HOT' AIR  ENGWES. 


401 


when  working  with  complete  expansion.  The  latter  expression 
shows  the  value  of  increased  compression  by  the  feed-pump, 
and  of  high  pressure  in  the  receiver  to  which  the  T^  cor- 
responds. The  first  expression  shows  the  value  of  having  the 
expansion  go  down  to  the  temperature  T^  if  possible,  when  the 
efficiency  would  become  unity,  as  would  be  expected.  This 
means,  however,  that  the  compressing  pump  must  be  more 
nearly  equal  to  the  working-cylinder  volume  than  is  convenient 
or  practicable. 

274.  Temperature  -  entropy  Diagram  of  a  Hot-air 
Engine  Changing  Temperatures  Non-isothermally. — The 
Stirling  and  Ericsson  engines  changed  temperatures  at  constant 
temperatures:  the  foregoing  type  changes  temperatures  at 
constant  pressure,  but  the  temperature  is  changing  during  the 
heating  process.  If,  therefore,  the  pv  diagram  be  as  shown  in 
Fig.  132  or  134,  the  te  diagram  will  appear  as  in  Fig.  135,     The 


adiabatic  change  from  ^  to  ^i  from  the  compression  of  the  feed- 
pump is  followed  by  the  logarithmic  change  of  entropy  caused 


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402  HEAT  AND  HEAT-ENGINES. 

by  the  heating  process;  such  change,  being  at  constant  pressure, 
will  produce  a  curve  whose  abscissa  at  any  point  will  be 

0  =  C;  (hyp.  log  r-hyp.  log  T^ 

when  the  temperature  T  is  given.  Then  from  ^  to  ^r  will  be 
the  adiabatic  expansion  in  the  working  cylinder,  and  cXo  d  the 
cooling  under  constant  volume  during  the  exhaust  process 
back  to  the  point  in  the  temperature  range  where  compression 

begins  by  the  pump.     The  ratio  -=7,  which  is  -=t,  should  be 

lb  Kb 

Ka 
the  same  as  the  ratio  -t^t  on  the  pv  diagram,  and  is  the  ratio 
Kb 

m  between  the  pump  and  working  cylinder  which  it  supplies 

The  efficiency  will  be 

area  abed  _  ^7],  —  T^  _  <f>(Ti  —  7*^) 
area  abRN "         <t>T^         "~     "    7; 

which  is  less  than  the  perfect  engine  would  offer  which  took 
in  and  rejected  all  the  heat  at  the  same  extreme  limits  of  tem- 
perature. In  proportion  as  the  curves  ah  and  cd  approach 
straight  lines,  by  as  much  does  the  area  of  the  mechanically 
utilized  work  approach  the  area  of  the  perfect  engine  diagram. 
275.  Joule's  Equivalent  Hot-air  Engine  with  Closed 
Cycle. — While  the  foregoing  designs  are  of  present  practical 
interest,  it  may  be  desirable  to  say  that  Dr.  Joule  proposed  a 
closed-cycle  engine,  involving  the  same  transformations  in  185 1. 
While  the  engine  was  never  built,  yet  its  reverse  lies  at  the 
basis  of  certain  types  of  refrigerating  machine,  and  its  cycle 
would  be  the  equivalent  closed  cycle  to  that  of  an  actual  prod- 
ucts-of-combustion  engine.  Fig.  136  shows  a  diagrammatic 
scheme  of  such  a  closed-cycle  engine.  C  is  the  piston  of  the 
compressing-pump,  on  the  same  rod  with  M^  the  piston  in  the 
working  cylinder.  H  is  the  furnace-chamber  at  T^,  and  C  is 
the  receiver  with  cooling  water  circulating  in  its  tubes  to  main- 
tain it  at  7,.     If  these  were  large  enough,  the  pressures  in 


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HOT' AIR  ENGINES. 


403 


them  would  not  vary.  The  air  compressed  by  C  to  T^  passes 
through  the  valve  v  and  is  further  heated  to  7",,  and  expands 
through  u  to  drive  M.  On  expanding  into  the  cool-chamber 
C  the  temperature  drops  to  7^  by  adiabatic  expansion,  and 
from  Tg  to  T^  by  logarithmic  cooling,  as  above  explained. 
The  only  changes  necessary  to  transform  Joule's  engine  into 


r 


,  MOTOR 


::c^OLER  Tj 


f 
i/ 


T 


HEATER  \ 


f 


COMPRESSOR 


H 

PiQ.136. 

an  internal-combustion  engine  in  principle  are  those  involved 
in  making  the  chamber //  the  furnace-chamber.  with  provisions 
for  introducing  the  fuel  into  it  as  required.  The  chamber  C 
can  also  be  the  outside  air  into  which  the  working  cylinder 
exhausts  and  from  which  C  shall  take  in  its  supply  at  T^  at 
each  stroke. 

276.  Internal  Combustion  Hot-air  Engine  Using  Solid 
Fuel.— The  introduction  of  the  gas-engine  and  the  oil-engine, 
and  the  perfecting  of  the  processes  for  gasifying  fuel  in  pro- 
ducers  (Chapter  V),  have  resulted  in  giving  to  the  engines  of 
the  earlier  inventors  an  interest  which  is  merely  historic,  in 
their  attempts  to  heat  the  working  air  by  passing  it  through  fire 
of  solid  fuel  (Fig.  137).  The  furnace  was  placed  in  a  chamber 
strong  enough  to  withstand  the  pressure  /,.  The  compressing- 
pump  B  forced  air  below  the  ash-pit  up  through  the  fire,  where 


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404 


BEAT  AND  HEAT-ENGINES. 


it  was  expanded  by  heat  and  by  combination  with  carbon. 
Being  admitted  to  the  working  cylinder,  against  the  piston  A, 
it  was  exhausted  into  the  chimney-stack.  The  furnace  had  to 
be  charged  with  fresh  fuel  through  a  combination  of  double- 


FiG.  187. 


doors  on  the  air-lock  principle,  D.  The  foreign  names  identified 
with  this  type  of  engine  are  those  of  Sir  George  Cayley  and  of 
Wenham  (1873)  and  Duckett  in  England,  and  Dr.  Avenier  de 
la  Gree  in  France.  The  American  engines  have  been  those  of 
Shaw,  Roper,  and  Wilcox.  The  difficulties  have  been  those 
caused  by  flue-dust  and  grit  in  the  cylinders;  the  rapid  de- 
struction of  working  surfaces  and  valves  by  the  intense  heat, 
and  the  difficulties  of  lubrication.     They  were  also  more  bulky 


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HOT-AIR  ENGINES.  405 

than  the  closed-cycle  engine  in  proportion  to  the  power 
developed.  If  it  were  desirable  to  follow  their  working,  the 
foregoing  principles  can  be  applied,  using  for  initial  volume 
not  that  of  one  pound  of  air,  but  the  volume  produced  by  sup- 
plying one  pound  of  air  to  the  furnace,  as  given  by  the  data  of 
Chapter  IV. 

277.  Concluding  Summary. — The  hot-air  engine  in  small 
sizes  is  more  economical  than  the  steam-engine  of  the  same 
capacity.  In  larger  sizes  it  has  about  the  same  economy  as 
the  less  economical  steam-engine,  measured  in  coal  consumed 
per  horse-power.  It  has  the  advantage  of  avoiding  the  steam- 
boiler  as  a  magazine  or  reservoir  of  energy  which  may  be  lib- 
erated by  accident  so  suddenly  as  to  be  explosive.  It  can  be 
run  by  less  skilled  and  expensive  labor  and  no  steam-runner's 
license  is  demanded.     It  is  safe  and  odorless. 

The  objections  to  the  hot-air  engine  are  the  greater  bulk 
and  greater  weight  for  the  same  power  than  is  required  with 
the  steam-engine ;  the  low  mean  pressure  with  high  initial  pres- 
sure, which  latter  compels  great  strength  of  structure ;  the  de- 
terioration of  heating-surfaces  exposed  to  high  heats  and  con- 
sequent oxidation ;  the  difficulties  of-  packing  and  lubricating 
at  high  temperatures;  the  difficulty  of  regulation  closely  to 
varying  resistance. 

If  there  is  any  danger  to  the  present  supremacy  of  the 
steam-engine,  it  will  be  in  relatively  small  plants  that  a  hot- 
air  engine  can  be  a  substitute ;  the  gas  or  internal-combustion 
engine  is  more  to  be  feared  than  the  hot-air  engine  proper. 


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CHAPTER   XX. 

INTERNAL-COMBUSTION   ENGINES. 
THE  GAS   AND   THE   OIL  ENGINE. 

280.  Introductory — Historical. — The  first  suggestion  of 
an  engine  exploding  a  nnixture  of  gas  and  air  behind  a  piston 
belongs  to  a  considerable  antiquity,  when  gunpowder  was  also 
similarly  considered  by  Huyghens  as  early  as  1680.  The  first 
English  patent  dates  back  to  1794  (Robert  Street).  The 
Lenoir  engine  of  Paris  in  i860;  the  Hugon  engine  of  1865, 
with  water  injection;  the  Otto  and  Langen  (Cologne,  1867), 
while  great  advances  upon  the  early  types  are  only  of  historic 
interest  since  the  introduction  in  1876  of  the  "  Otto  Silent " 
gas-engine  and  the  cycle  represented  by  this  class.  The  idea 
of  compressing  the  gas-charge  before  explosion  was  brought 
forward  as  early  as  1801  ;  early  names  in  English  practice  are 
those  of  Barnett  (1838)  and  Sir  C.  W.  Siemens  (1862).  French 
engineers  have  been  Million  (i86i)and  Beau  de  Rochas(i862), 
who  proposed  the  four-stroke  cycle,  now  known  by  Dr.  Otto's 
name.  The  Dugald  Clerk  engine  (1880)  and  the  Atkinson 
(1885)  are  types  involving  features  not  common  to  all  which 
have  been  recently  brought  forward  under  a  great  variety  of 
trade  or  proprietary  names. 

It  will  be  seen  that  the  introduction  of  a  combustible  gas 
into  a  mass  of  air  required  to  burn  it,  and  the  ignition  of  the 
gas  in  the  air  within  a  confined  volume,  results  in  an  expansion 
of  that  air  which  will  exert  a  pv  pressure,  which  can  be  made 
to  do  work  by  means  of  piston  and  engine  mechanism.     The 

406 


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INTERNAL-COMBUSTION  ENGINES. 


407 


gas  engine  is  therefore  a  hot-air  engine  of  the  internal-furnace 
class  and  works  upon  an  open  cycle,  since  it  draws  in  a  fresh 
charge  of  gas-fuel  and  air  at  each  working  stroke,  and  rejects 
the  products  of  the  combustion  with  the  exhaust.  It  is  also  a 
"  products  of  combustion  **  engine,  but  using  a  fuel  without 
grit  or  ash.  Oil-engines,  gasefying  the  oil  and  mixing  it  with 
air,  belong  to  this  same  class,  requiring  only  proper  provisions 
for  pumping  and  vaporizing  the  oil-fueL 

The  fuel-engine  cycle  (§§  273-75)  's  the  usual  and  typical 


OJU  Km  Alfl  VAtV* 


hot-air  gas-engine  cycle.  Chemical  considerations  must  be 
borne  in  mind  for  their  effect  in  modifying  both  the  theory 
and  action  of  the  gas-engine. 

281.  Lenoir  Gas-engine  of  i860.— The  cylinder  of  this 
early  engine  was  a  water-jacketed  steam-engine  cylinder  (Fig. 
140).      During  the  first  part  of  the  outgoing  stroke  air  and  gas 


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408 


HEAT  AND   HEAT-ENGINES. 


in  proper  proportions  of  i  of  gas  to  about  12  or  14  of  air 
air  were  drawn  into  the  cylinder  by  aspiration.  The  inlets 
being    closed,   the    mixture   was    fired    by  a    spark   from    a 


Fig.  1406. 

Ruhmkorflf  induction-coil.  The  increase  of  volume  following 
the  explosive  ignition  increased  the  pressure  at  about  half 
stroke,  which  fell  till  the  end  was  reached,  when  the  expulsion 
of  the  products  of  combustion  took  place  on  the  return  of  the 
piston.     Fig.  141    shows  a  ^typical  pv  diagram.     It  took  95. 


Fig.  141. 


cubic  feet  of  gas  per  horse-power  per  hour  (which  is  more  than 
four  times  the  present  requirement),  and  the  high  temperature 
and  the  noise  were  objectionable.     The  platinum  points  of  the 


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INTERNAL-COMBUSTION  ENGINES.  409 

sparking  electrodes  were  also  liable  to  become  clogged  with 
lampblack  or  soot  deposit  A  large  amount  of  the  available 
power  was  lost  in  the  impact  effect,  whose  heat  was  absorbed 
and  wasted  by  the  jacket, 

282.  Hugon's  Gas-engine  of  1865.  —  Hugon's  improve- 
ment on  the  Lenoir  type  followed  from  the  injection  of  water 
with  the  gas  and  air  mixture.  The  vaporization  of  this  injec- 
tion absorbed  some  heat  and  gave  it  out  in  the  work  of  ex- 
panding, although  the  expansive  force  was  diminished.  The 
distribution  of  the  effort  made  the  moving  parts  suffer  less  and 
diminished  repair  expenses,  and  made  the  engine  more  durable, 
especially  at  packed  surfaces,  such  as  piston  surfaces,  stuffing- 
boxes,  etc.     Gas-jets  were  used  to  fire  the  charge. 

A  form  of  engine  known  as  Bischoff's  is  the  only  survivor 
of  the  purely  explosive  non-compression  type,  and  burns  120 
cubic  feet  of  gas  per  H.P.  per  hour. 

283.  Otto  and  Langen  Atmospheric  or  Free -piston 
Gas-engine  of  1867. — To  avoid  the  loss  from  impact  effect,* 
when  positive  connection  to  the  crank-shaft  forced  the  piston 
to  yield  but  gradually  to  the  sudden  increase  of  volume  of  the 
charge.  Otto  and  Langen,  in  Germany,  and  Barsanti  and 
Matteucci,  in  Italy,  proposed  to  have  the  vertical  cylinder  of 
some  height,  and  the  piston-rod  to  rise  without  effect  on  the 
crank-shaft  during  the  stroke  caused  by  the  gas  ignition.  The 
piston  yielded  like  a  projectile  and  rose  to  the  top  of  its 
traverse.  The  sudden  expansion  of  the  gas-mixture  cools  it 
also  suddenly,  and  as  its  tension  falls  below  the  atmospheric 
tension,  the  pressure  of  the  atmosphere  acts  to  force  the  piston 
back  downward.  The  piston-rod  is  connected  to  the  shaft  by 
a  rack  and  pinion-gear,  operated  by  a  pawl  and  ratchet-wheel, 
so  that  the  pawl  clicks  idly  on  the  up-stroke,  but  the  rack  and 
pinion  transmit  the  atmospheric  effect  on  the  down-stroke 
(Fig.  142).  This  engine  was  obviously  noisy  and  irregular.  It 
consumed,  however,  about  30  to  40  cubic  feet  of  gas  per  H.P, 


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410 


HEA  T  AND  HE  A  T-ENGINES. 


"Fig.   142. 


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INTERNAL  COMBUSTION  ENGINES.  4^ 

hour,  and  was  manifestly  a  distinct  gain  on  its  predecessors. 
Ignition  was  effected  by  an  outside  gas-flame. 

284.  Brayton  Gas-engine  or  Ready  Motor  of  1873. — ^A 

gas-engine  forming  a  type  by  itself  was  brought  out  and  intro- 
duced to  a  limited  extent  in  eastern  America  in  which  a  mix- 
ture of  gas  and  air  drawn  into  a  pump-cylinder  on  its  aspirating 
stroke  was  compressed  by  the  return  stroke  into  a  reservoir 
under  a  pressure  of  about  70  pounds  per  square  inch.  From  this 
reservoir  it  was  allowed  to  fiow  to  the  working  cylinder  during 
.perhaps  one-half  of  the  outgoing  stroke  of  the  piston.  The 
mixture  was  ignited  in  the  working  cylinder  by  a  flame,  the 
back-flow  of  flame  to  the  reservoir  being  prevented  by  wire- 
gauze  at  the  inlet.  The  mixture  thus  simply  increased  in  vol- 
ume but  without  rise  in  pressure,  since  the  connection  with  the 
reservoir  was  still  open,  and  followed  the  piston  up  to  cut-off 
at  half  stroke.  The  rest  of  the  stroke  was  operated  by  the 
expansive  energy  of  the  gas-mixture,  and  on  the  return  stroke 
the  contents  of  the  cylinder  were  exhausted.  Such  an  engine 
had  no  explosive  ignition,  but  the  slow  inflammation  took  place 
as  fast  as  the  mixture  was  admitted  and  was  continuous  during 
such  admission.  The  pump-piston  had  the  same  cross-section 
as  the  working  cylinder  in  the  beam  form  of  engine,  but  one- 
half  the  stroke.  In  steeple-engines  the  two  pistons  had  the  same 
stroke,  but  half  the  area  was  given  to  the  compressing  piston. 

The  principle  of  slow  inflammation  is  wasteful  with  a 
water-jacketed  cylinder,  since  a  loss  of  energy  or  increased  gas- 
consumption  results  from  the  necessity  of  sustaining  pressure 
and  temperature.  The  terminal  or  exhaust  temperature  of  the 
gases  was  high  from  this  cause,  as  well  as  the  mean  tempera- 
ture. The  efficiency  as  measured  by  the  work  done  by  I 
cubic  foot  of  air  with  the  Brayton  engine  was,  however,  0.36,  as 
compared  with  0.21  given  by  the  previous  types,  having  no 
compression  and  working  by  explosion.  It  was  displaced,  how- 
ever, by  the  superior  economy  of  the  Beau  de  Rochas  or  Otto 


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412  HEAT  AND   HEAT-ENGINES. 

four-phase  cycle,  whose  efficiency  was  measured  by  0.45  for  a 
cubic  foot  of  air  used  under  the  same  assumed  conditions. 

285.  Four-phase  Cycle  of  Beau  de  Rochas. — What  is 
generally  called  the  Otto  cycle  was  first  suggested  in  a  French 
patent  of  1862  by  Alphonse  Beau  de  Rochas,  who  also  advo- 
cated the  advantages  of  previous  compression  of  the  combus- 
tible mixture,  and  proposed  to  do  away  with  the  separate 
compressing  pump  by  making  only  one  stroke  in  four  to  be 
the  working  stroke  in  a  single-acting  engine.  The  Beau  de 
Rochas  or  Otto  cycle  involves : 

1.  Aspiration  of  the  mixture  of  gas  and  air  in  proper  pro- 
portions during  an  out-going  stroke  of  the  piston  (1-2  in  Fig. 

143). 

2.  Compression  of  the  mixture  by  the  return  of  the  piston 
(2-3-4).  This  compression  fills  a  comparatively  large  clear- 
ance volume  behind  the  piston,  which  must  be  so  adjusted  to 
the  displacement  by  the  piston  that  there  shall  be  no  danger 
of  such  elevation  of  temperature  from  the  compression  as  to 
ignite  the  mixture  as  the  result  of  compression  alone. 

3.  The  piston  being  at  or  near  its  inner  dead  point  (4),  the 
compressed  mixture  is  ignited  by  some  acceptable  and  reliable 
device,  at  which  the  pressure  rises  at  once  (4-5)  and  exerts  its 
outward  effort  to  drive  the  piston  forward.  Expansion  is  fol- 
lowed by  gradual  lowering  of  pressure  during  this  working 
stroke  (5-6-7). 

4.  The  products  of  combustion  are  discharged  into  the  open 
air  through  the  exhaust-valve  by  the  return  of  the  piston  to  its 
inner  dead  centre  (8-1).     The  cycle  then  repeats  itself. 

It  is  apparent  that  a  heavy  fly-wheel  must  be  used  to 
equalize  the  motion  of  the  crank-shaft,  having  energy  enough 
stored  in  it  by  the  working  stroke  to  overcome  the  resistance 
during  the  ^ime  of  the  other  three  strokes,  and  cause  also  the 
piston  to  perform  the  acts  of  the  cycle  in  the  cylinder.  High 
rotative   speed    is   therefore   an  advantage.     Furthermore,   a 


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INTERNAL-COMB USTJOJ^  ENGINES. 


413 


high  initial  pressure  and  temperature  are  desired,  with  a  low 
terminal  value  for  both,  so  as  to  secure  a  high  mean  value. 
Rapid  inflammation  is  therefore  desired,  and  the  methods  of 
ignition  become  important. 


Max.  i.  IVU^Q, 


FiG.143. 


Fig.  143. 

286.  Otto  Silent  Gas-engine  of  1876. — The  propositions 
of  the  French  patent  were  not  embodied  in  industrial  form 
until  Dr.  Otto  reinvented  the  cycle  and,  as  the  result  of  much 
experimental  study,  brought   out  the  prototype  of  all  the 


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414 


HE  A  T  AND   HEA  T-ENGINES. 


modern   gas-engines,    to   which   he   gave   the   trade-name    of 
"  Silent,"  to  distinguish  it  from  his  earlier  noisy  type. 

The  engine  was  single-acting,  of  trunk  design  to  secure 
compactness.  The  cylinder  and  valve-casing  were  water-jack- 
eted. The  valve-gear  was  operated  by  a  shaft  driven  from 
the  main-engine  shaft  at  half  its  rate.  Cams  opened  the 
valves  at  proper  intervals.  Regulation  of  effort  was  caused 
by  making  the  inlet-cam  miss  its  stroke  when  a  centrifugal 
governor  driven  from  the  main  shaft  was  turning  too  fast. 
Hence  this  type  of  engine  has  become  known  popularly  as  the 
"  hit-or-miss '*  gas-engine.  The  mixture  was  ignited  in  early 
forms  by  a  flame.  The  clearance  volume  was  about  one 
half  the  cylinder  volume.     (Fig.  144.) 


Fig.  144. 
Under  the  Otto  patents  many  modifications  were  intro- 
duced, such  as  to  use  two  cylinders  driving  the  same  crank- 
shaft, one  of  which  should  be  two  phases  ahead  of  the  other^ 
and  thus  diminish  the  interval  between  working  strokes.  The 
cylinders  have  been  placed  vertically  instead  of  horizontally ; 
different  igniting  devices  have  been  used  ;  the  front  or  idle 
side  of  the  piston  has  been  used  as  the  aspirating  and  com- 
pressing side;  double-acting  types  have  been  used  with 
ignitions   on    both   sides,    occurring   alternately.      Since    the 


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INTERNAL-COMBUSTION  ENGINES. 


415 


expiration  of  the  Otto  basal  patents,  many  new  forms  and 
names  have  come  forward,  both  in  England  and  America. 

287.  Dugald  Clerk  Gas-engine  of  1880. — The  twinning  of 
the  cylinders  to  secure  an  impulse  every  revolution  makes  a 
costly  engine  by  reason  of  the  expense  of  the  two  mechanisms. 
The  most  satisfactory  plan  is  to  separate  the  aspirating  and 


Pig.  145. 


compressing  operations  from  the  other  two  doing  the  former 
work  in  the  separate  pump-cylinder.  In  the  Clerk  engine  this 
arrangement  is  secured.  At  the  back  end  of  the  working 
cylinder  is  placed  the  clearance  volume,  which  is  a  conical  or 
trumpet-shaped  space,  communicating  through  a  lift-valve  with 
the  compressing  cylinder.  The  pump  or  displacer  crank  leads 
the  working  crank  by  90°.  The  exhaust-ports  from  the  work- 
ing cylinder  are  at  the  front  or  outer  end  of  the  bore,  and  are 


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4l6  HEAT  AND   HEAT-ENGINES. 

uncovered  by  the  working  piston  as  it  nears  the  outer  end  of 
its  traverse.  The  displacing  piston  is  then  returning,  com- 
pressing the  charge  aspirated  on  its  outer  stroke,  and  the, flow 
of  fresh  mixture  into  the  clearance  drives  the  expanded  prod- 
ucts of  combustion  in  front  of  it,  expelling  the  previous  charge 
through  the  exhaust-ports.  The  expanding  trumpet-shape  by 
lowering  the  velocity  of  the  new  charge  lessens  the  likelihood 
of  wasteful  mixture  of  the  new  and  old  mixtures.  Any  union 
which  does  take  place  is  a  gain  from  preheating  the  new 
charge,  and  thereby  cooling  the  old.  The  return  of  the  motor- 
piston  compresses  the  new  mixture,  which  is  ignited  by  a  flame 
as  the  crank  passes  its  dead-centre  at  each  revolution.  Fig.  145 
shows  the  Clerk  engine  in  section,  A  being  the  working  cylin- 
der, C  its  piston,  G  the  conical  clearance  volume,  and  E  the 
exhaust-ports. 

288.  Atkinson  Differential  or  Cycle  Engine  of  1885. — 
The  peculiar  features  of  this  engine  are  the  unusual  linkage 
between  the  pistons  and  the  crank-shaft,  whereby  the  pistons 
can  be  made  to  act  as  their  own  valves,  and  whereby  a  greater 
expansion  is  attainable  than  with  fixed  clearance  volumes  to 
be  filled  with  gas-mixture.  The  engine  has  appeared  in  two 
forms.  In  that  selected  in  Figs.  146  and  147  there  are  two 
trunk-pistons,  linked  to  the  crank-pin  by  the  two  curved  beams 
The  latter  are  borne  on  the  two  massive  beam-centres,  whose 
location  to  each  other  is  so  chosen  as  to  force  the  pistons  out 
of  symmetry  or  phase  as  the  crank  passes  the  four  cardinal 
points  as  indicated  in  Fig.  147.  In  the  first  position,  with  the 
crank  at  the  extreme  left,  the  pistons  are  close  together.  An 
automatic  lift-valve  admits  a  charge  of  gas  and  air  between 
them  as  they  separate  by  the  quarter  revolution  of  the  crank 
to  the  position  2.  This  movement,  and  the  further  movement 
toward  position  3,  closes  the  admission-  and  the  exhaust-port, 
and  as  the  pistons  move  toward  each  other,  compression  of  the 
charge   takes   place.     The   compression   being  completed   in 


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INTERNAL'COMBUSTION  ENGINES. 


417 


position  3,  the  charge  is  fired  and  the  pistons  separate,  per- 
forming the  working  stroke,  expanding  the  mixture  by  the 
increase  of  volume.  The  exhaust-port  is  uncovered  and 
discharge  begins  when  the  pistons  reach  position  4,  at  which 
time  the  left-hand  piston  is  moving  rapidly  to  the  right,  while 
the  left  one  is  nearly  stationary.     The  four  usual  operations  of 


Fig.  146a. 
the  cycle  are  provided  for  in  the  single  cylinder,  and  an  impulse 
occurs  under  full  load  at  ev^ry  revolution.  The  unusual  char- 
acter of  the  Atkinson  linkage  limited  it  to  experimental  sizes 
and  low  speeds  and  powers,  and  the  design  modified  from  it 
never  attained  any  commercial  importance  for  business  reasons. 


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4i8 


HEAT  AND   HEAT-ENGINES. 


Pig.  14«6. 


Fig.  147. 


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INTERNAL-COMBUSTION  ENGINES. 


419 


Fig'   148  shows  the  cycle  or  single-piston  engine  of  Atkinson. 
The  connecting-rod  does   not   drive   the   crank  directly,  but 


B.C .SUCTION  BTROKE 
C.W.COMPftESSJON  " 
WX.WORKINO  STROKE 
5*EXHAuaT  STROKE 


FlQ.    148. 

a  toggle-lever,  pivoted  at  the  centre  as  appears  in  Fig.  149.    The 
connecting  rod  to  the  crank  is  T  shaped,  bearing  at  its  lower 


Fig.  149. 
end  the  short  transverse  portion  which  forms  the  arms  of  the 
T.     The  piston-rod  couples  to  the  further  end  of  this  trans- 


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420  HEAT  AND   HEAT-ENGINES. 

verse  member,  and  the  toggle-lever  is  jointed  to  it  at  the 
end.  It  will  appear  from  this  ingenious  arrangement  that  the 
piston  will  make  two  strokes  in  each  direction  for  one  revo- 
lution of  the  crank,  and  that  these  will  not  be  of  the  same 
length.  The  first  outstroke  or  intake  stroke  will  be  longer  than 
the  return  or  compressing  stroke,  so  that  a  compression  volume 
is  left.  The  explosion  then  occurs  followed  by  the  longest 
outstroke,  giving  the  greatest  expansion  volume.  Then  the 
longest  stroke  of  all  takes  place,  from  furthest  out  to  furthest 
in,  sweeping  out  all  products  of  combustion.  The  toggle-lever 
causes  the  doubling  of  the  strokes,  since  it  swings  through 
an  arc  only,  and  must  do  this  twice  in  one  revolution.  The 
position  of  the  cross-arm  of  the  T  as  the  toggle-lever  swings 
is  what  gives  varying  length  to  the  piston  traverse. 

289.  Classification  of  Gas-engines. — The  foregoing 
paragraphs  have  made  it  apparent,  therefore,  that  there  are 
two  general  classes  of  gas-engine. 

Class  I.  Those  making  no  useof  compression; 

Class  II.  Those  employing  compression. 

The  first  class  contains  the  purely  explosive  types  and 
presents  the  two  sub-classes  : 

{a)  Explosion  drives  the  power  stroke ; 

{U)  Explosion  lifts  the  piston  freely,  and  the  return  is  the 
working  stroke. 

Class  II  contains  the  modern  efficient  engines  and  may  be 
divided  into  : 

{a)  Compression  effected  in  working  cylinder; 

(V)  Compression  effected  in  a  separate  or  pump-cylinder. 

They  may  again  be  grouped  into  two  sections  according  to 
the  working  of  the  expanding  heat  medium  : 

[c)  Ignition  occurs  at  constant  volume,  followed  by  a 
sudden  rise  of  pressure; 

(d)  Ignition  occurs  at  constant  pressure  from  a  reservoir; 
the  gas  mixture  burns  slowly  as  volume  increases. 


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JNTERNAL'COMBUSTION  ENGINES.  421 

The  Otto  engine  belongs  in  groups  {a)  and  (r),  the  Clerk 
engine  in  groups  {b)  and  {c\  The  Brayton  engine  is  the  only 
example  of  group  (^/)  and  it  is  also  in  group  (3). 

290.  Methods  of  Igniting  the  Gas-charge.  —  Gas- 
engines  may  again  be  grouped  into  four  classes  upon  their 
mechanical  side  according  as  they  vary  in  the  method  used  to 
set  fire  to  the  mixture  of  gas  and  air  which  has  been  drawn  into 
the  cylinder  by  the  aspirating  stroke.  The  methods  practised 
by  different  designers  for  this  purpose  may  be  grouped  as 
follows  : 

(i)  Electrical  methods ; 

(2)  Flame  methods ; 

(3)  Incandescence  methods ; 

(4)  Compression  of  the  charge. 

The  first  plan  is  an  early  one.  A  pair  of  naked  electrodes 
allow  a  spark  or  an  arc  to  pass  between  them  at  the  time 
when  they  are  exposed  to  the  gaseous  mixture  by  the  with- 
drawal of  a  slide,  or  the  spark  passes  as  a  contact  is  broken 
between  two  poles  exposed  in  the  clearance.  The  breakage  of 
continuity  is  timed  by  the  motion  of  the  valve-gear. 

This  plan  avoids  the  inconvenience  of  opening  the  cylinder 
cavity  by  valve-movement  when  that  cavity  is  under  greater 
pressure  than  prevails  without  it,  and  a  consequent  tendency  to 
leakage  and  unpleasant  odor.  The  difficulties  are  those  belong- 
ing to  electric  methods  in  unaccustomed  hands,  the  clogging 
of  the  electrodes  by  lamp-black  deposit,  and  the  annoyance  in 
finding  the  cause  when  ignition  fails.  The  best  electric  igniters 
have  the  contacts  wipe  over  each  other  so  as  to  be  kept 
cleansed  by  the  scraping  action. 

The  second  plan  is  also  an  old  one.  It  was  used  in  the 
Barnett  engine  (1838)  in  a  typical  form  (Fig.  155),  depending 
on  what  may  be  called  the  air-lock  principle.  An  external 
flame  A  set  fire  to  a  stream  of  gas  entering  the  hollow  cock 
chamber  from  below  when  the  opening  i  was  turned  toward 


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422 


HEA  T  AND   HEA  T-ENCINES. 


such  outer  flame.    The  rotation  of  the  cock  through  90®  clock- 
wise  in  the  plan  brings  the  flame  in  contact  with  the  explosion 


Fig.  155. 

port  2  and  fires  the  charge,  blowing  out  the  enclosed  flame,  of 
course,  in  the  process.  It  is  relighted  by  the  reverse  motion 
of  the  cock.     The   intermittent  contact  of  the  flame  and  the 


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INTERNAL-COMBUSTION  ENGINES.  423 

explosion  port  can  be  secured  by  a  sliding  valve,  which  carries 
the  igniting  flame  first  to  the  exterior  flame  and  then  draws  it 
back  into  line  with  the  port.  This  plan  requires  the  presence 
of  sufficient  air  to  ignite  the  gas-flame  in  tKe  valve-chamber, 
A  plan  introduced  by  Clerk  of  using  the  normal  mixture  of 
gas  and  air  for  the  igniting  flame  has  much  increased  the 
rapidity  at  which  ignitions  can  occur.  In  the  Brayton  engine 
the  flame  was  continuous  on  the  upper  or  inner  side  of  the 
gauze  through  which  the  mixture  streamed. 

The  third  class  of  igniters  uses  either  a  short  coil  of  in- 
candescent wire  kept  hot  by  a  current  of  electricity  of  sufficient 
potential  running  through  it,  whose  incandescence  can  serve  to 
ignite  the  mixture  when  a  slide  is  withdrawn  from  in  front  of 
the  coil  or  the  latter  is  moved  into  line  with  the  explosion 
port ;  or  else  the  mixture  is  fired  by  passing  part  of  it  through 
a  tube  or  grating,  which  is  heated  to  incandescence  by  a  sep- 
arate flame  or  by  the  heat  of  the  explosion  of  the  previous 
strokes.  The  tube  may  be  of  wrought  iron  or  of  some  ceramic 
material,  or  (as  in  Clerk's  plan)  a  measured  stream  of  gas  at 
each  stroke  can  be  admitted  to  heat  a  cage  of  platinum  plates, 
which  cage,  being  borne  by  a  slide,  is  presented  white  hot 
opposite  the  ignition  port  at  the  proper  time  by  the  motion 
of  the  slide. 

The  fourth  plan  is  one  particularly  applicable  to  oil-vapor 
engines,  but  capable  also  of  igniting  with  a  gas-mixture.  It 
depends  on  raising  the  temperature  of  the  gas-mixture  by 
compression  in  a  non-conducting  clearance-volume  to  such  a 
temperature  that  chemical  combination  is  possible  at  that  pres- 
sure  and  temperature,  and  occurs  without  external  igniting 
appliances.  This  is  of  course  in  the  incandescence  class,  only 
the  temperature  of  the  clearance-volume  does  not  have  to  be 
so  high  by  reason  of  the  heat  in  the  mixture  due  to  the  com- 
pression. This  principle  is  used  in  the  Hornsby-Akroyd  and 
the  Diesel  engine. 


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424  HEAT  AND  HEAT-ENGINES. 

A  class  of  Igniting  methods  might  be  made  of  certain  sug- 
gestions proposing  the  use  of  spongy  platinum,  or  the  use  of 
spontaneously  igniting  compounds  such  as  phosphoretted  hy- 
drogen. They  have  not  been  reduced  to  successful  practice, 
however. 

The  objections  to  the  flame  methods  are  the  danger  from 
extinction  of  an  exterior  flame  by  draught  or  otherwise,  and 
the  odor  and  leakage  which  seem  inseparable  from  it.  The  elec- 
trical methods  are  uncertain  and  troublesome. 

291.  Indicator  Diagrams  from  the  Gas-engine. — ^The 
foregoing  types  will  give  each  his  peculiar  indicator  diagram 
of  effort  on  the  pv  plane.  Figs.  156  and  157  show  the  non- 
compressive  type  of  engine,  the  former  a  Lenoir  and  the 
latter  an  Otto  and  Langen. 

Figs.  158  and  159  show  the  motor  cylinder  and  compress- 
ing pump  of  the  Brayton  engine. 

Figs.  160  and  161  show  typical  diagrams  from  Otto  and 
Clerk  engines. 

The  lower  lines  in  Fig*  160  show  the  aspirating  and  exhaust 
lines  of  the  first  and  fourth  parts  of  the  cycle.  For  a  Clerk 
engine,  with  separate  displacing  cylinder,  a  diagram  such  as 
Fig.  162  will  be  taken  from  that  separate  cylinder. 

The  interest  attaching  to  the  first  four  is  at  present  only 
historic.  With  respect  to  the  latter  or  Otto  cycle  diagrams  it 
is  to  be  noticed  that  the  pressure  does  not  rise  to  its  maximum 
instantly,  or  while  the  engine  is  at  its  dead-centre,  nor  is  it 
dangerously  great  in  amount.  The  strain  on  the  engine 
mechanism  is  no  more  exacting  than  that  which  comes  upon 
an  engine  using  steam  of  high  pressure.  It  must  be  observed, 
however,  that  there  is  no  considerable  duration  of  that  maxi- 
mum pressure,  but  the  drop  due  to  expansion  sets  in  at  once. 
In  other  words,  there  is  no  way  of  increasing  the  power  of  a 
gas-engine  by  any  process  analogous  to  following  the  piston 
during  a  considerable  part  of  the  stroke  with  full  boiler  pres- 


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INTERNAL-COMBUSTION  ENGINES. 


425 


Fig.  15«. 


1    --TO 


90     40     60     60     70 
PERCENTAGE  OF  STROKE 


M       m 


Fig.  157. 


Pig.  158. 


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4^6 


HEA  T  AND  HE  A  T-ENGINES. 


i/V\lA\ 


Fio.  159. 


f 

1 

y 

7 

\^\ 

N 

■v 

K 
^ 

r-l 

§ 

So 

;s 

s 

9 

9 

SI 

^ 

Fig.  160. 


Fig,  161. 


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INTERNAL-COMBUSTION  ENGINES. 


427 


sure,  which  is  possible  with  the  steam-engine,  if  the  valve* 
gear  is  constructed  so  as  to  allow  it.  It  appears,  further,  that 
the  quicker  the  complete  inflammation  of  the 
mixture,  or  the  less  the  increase  of  volume  during 
ignition,  the  higher  the  initial  pressure,  and  the 
greater  the  mean  forward  effort.  It  will  be 
noted,  furthermore,  that  it  will  be  but  rarely 
that  expansion  can  be  carried  down  to  atmos- 
pheric pressure.  It  will  usually  be  incomplete, 
entailing  loss  of  available  energy  (§§  201  and 
255).  The  mean  pressure  must  be  such  in  the 
single-cylinder  Otto  engine  as  shall  be  proper  for 
over  four  times  the  average  horse-power,  since 
the  working  stroke  must  not  only  do  the  external 
work  of  that  stroke,  but  must  also  st'ore  in  the 
fly-wheel  an  amount  of  energy  for  the  external 
work  of  the  next  suceeding  three  traverses  of  the 
piston,  and  overcome  the  resistances  in  the  engine 
itself  in  the  compressing  stroke. 

Since  the  maximum  pressures  are  caused  by 
the  flaming  of  the  gas  in  the  air,  it  becomes  of 
interest  to  study  the  temperatures  to  be  expected. 

The  questions,  then,  on  which  experimental 
knowledge  must  be  sought  will  be  the  rapidity  t^ 
of  flame  propagation  and  the  relation  of  pressures 
to  actual  temperatures. 

292.  Some  Phenomena  of  Ignition  in  the  Gas-engine.— 
The  volume  of  air  required  for  the  combustion  of  a  gas  of  given 
composition  has  already  been  calculated  (§§  24-27),  as  well  as 
the  theoretical  temperature  of  a  flaming  substance  when  its 
calorific  power  is  known,  the  weight  or  volume  and  specific  heat 
of  the  products  of  combustion  being  known  or  assumed  (§§  28, 
61,  and  68).  In  a  gas  ignition  the  weight  of  combustible  per 
cubic  foot  is  not  large,  but  the  time  taken  for  its  combustion 


/ 

/ 

4 

5 

5 

5 

0 

1 

1.5 

Fia.  163. 


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428 


HEAT  AND   HEAT-ENGINES. 


is  very  short.  Hence  the  reasoning  of  §  6i  should  be  appli- 
cable, and  a  high  temperature  should  be  secured. 

The  pressure  behind  the  piston  having  been  observed  by 
the  indicator,  the  temperature  corresponding  can  be  calculated 
from  the  Gay-Lussac  law,  as  the  volume  is  constant  (§  112),, 
The  calculation  need  only  be  checked  by  the  fact  that  there  is 
a  slight  contraction  of  volume  resulting  from  the  combination 
of  the  combustible  gas  and  air  as  two  bodies  into  one  chemical 
mixture.  With  ordinary  street  gas,  and  the  minimum  dilution 
with  air,  this  contraction  will  be  less  than  four  per  cent,  and 
diminishes  with  the  dilution.  Hence  it  is  usually  safe  enough 
to  calculate  temperatures  without  allowance  for  this  contrac- 
tion. 

But  complete  combination  does  not  occur  at  once,  nor  are 
theoretical  pressures  and  temperatures  attained.  Physicists 
appear  to  agree  that  nearly  one  half  of  the  heat  present  in  the 
mixture  of  inflammable  gas  is  kept  back,  and  is  prevented  from 
causing  the  increase  in  pressure  to  be  expected  from  it.  Stan- 
dard experiments  made  by  Dugald  Clerk  have  given  the  fol- 
lowing results  with  English  illuminating-gas  (Oldham) : 


Vol.  Gas, 

Vol.  Air. 

Pounds  per  sq.  in.  Gaii|r«  Pressure. 

No. 

Observed 
Pressure. 

Calculated 
Pressure. 

I 
2 

3 

4 

14 
13 
12 
II 

40.0 

51.5 
60.0 
61.0 

89.5 

96.0 

103.0 

112. 0 

5 
6 

9 
7 

78.0 
87.0 

134.0 
168.0 

7 

6 

90.0 

192.0 

The  theories  which  have  been  advanced  to  explain  this 
suppression  of  heat  are  at  least  three.  Hirn*s  explanation  was 
that  at  these  high  temperatures  the  cylinder  walls  and  water- 
jacket  absorbed  heat  so  rapidly  that  at  a  certain  point  the 
abstraction  of  heat  was  faster  than  its  liberation  by  the  burning 


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INTERNAL-COMBUSTION  ENGINES.  4^9 

of  the  gas.  The  objection  to  this  theory  is  that  the  suppres- 
sion of  heat  does  not  seem  to  depend  on  the  cylinder  surface 
nor  on  the  efficiency  of  the  jacket.  Bunsen's  theory  is  that  at 
high  temperatures  the  phenomenon  of  chemical  combination  can- 
not occur  readily,  and  that  a  high  enough  temperature  may  be 
reached  to  dissociate  or  break  up  combinations  already  made 
or  making.  Hence,  if  the  combination  cannot  exist  at  any 
high  temperature,  the  mixture  will  remain  made  up  of  the  free 
constituents,  which  will  come  together  only  as  the  temperature 
falls.  The  fact  of  dissociation  has  been  proved  by  physicists ; 
its  applicability  to  the  gas-engine  is  still  partly  in  question  by 
reason  of  the  fact  that  suppression  of  heat  does  not  seem  to 
increase  in  proportion  as  the  temperature  increases. 

The  third  and  most  interesting  theory  is  that  advanced  by 
Mallard  and  Le  Chatellier,  that  at  the  higher  temperatures 
the  specific  heats  of  the  constituents  and  of  the  products  of 
combustion  increase.  That  is,  if,  as  seems  to  be  the  case,  the 
specific  heats  of  oxygen  and  nitrogen  double  at  or  near 
3600**  F.,  the  heat  is  completely  evolved  in  the  flame  combus- 
tion, but  twice  as  much  heat  is  taken  care  of  in  heating  these 
absorptive  gases.  This  has  the  same  difficulty  as  the  dissocia- 
tion theory ;  a  greater  proportion  of  heat  should  be  evolved  at 
the  lower  temperatures,  which  is  not  always  the  fact. 

The  soundness  of  the  dissociation  theory  seems  to  be  sug- 
gested by  what  is  known  as  the  "after-burning."  The  expan- 
sion should  fall  below  the  adiabatic  line  with  a  good  water- 
jacket,  since  heat  should  be  withdrawn  and  the  pressure 
thereby  lowered.  The  actual  curve  is  nearly  adiabatic  or  above 
it,  suggesting  an  addition  of  heat  during  expansion,  which  of 
course  must  come  from  the  combustion  of  gas  in  the  charge 
which  was  not  ignited  at  the  beginning  of  the  stroke.  Such 
gas  is  not  burned  with  the  same  economy  as  the  explosion  pro- 
portion, and  liberates  less  heat  per  unit  of  weight.  It  fattens 
the  indicator-card,  however. 


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430 


HEAT  AND   HEAT-ENGINES. 


Dr.  Otto's  claim  and  theory  for  his  silent  engine  was  that 
the  dilution  of  the  fresh  charge  with  the  products  of  combus- 
tion of  the  previous  one,  and  their  arrangement  in  a  species  of 
stratification,  caused  a  slower  propagation  of  the  flame,  and 
moreover  caused  a  cushioned  eflfort  of  the  expanded  charge 
against  the  piston.  Later  experiments  have  thrown  consider- 
able doubt  over  the  validity  of  these  contentions. 

293.  Usual  Mixtures  of  Gas  and  Air.—  The  gas  being 
the  expensive  element  in  the  mixture  of  gas  and  air  drawn  into 
the  cylinder,  it  would  appear  that  to  increase  the  proportion  of 
air  in  a  given  cylinder  volume  was  to  increase  the  economy. 
This  is  only  true,  however,  when  the  power  of  the  cylinder  is 
the  fixed  element,  provided  the  diluted  mixture  does  not  lose 
pressure  per  square  inch  in  a  more  rapid  proportion.  That  is^ 
it  may  be  necessary  to  increase  the  cylinder  volume  more 
rapidly  to  secure  a  given  power,  and  so  draw  in  more  gas  than 
if  the  proportion  of  gas  were  increased  in  a  cylinder  of  given 
volume.  It  is  desirable,  furthermore,  that  in  a  cooled  cylinder 
the  water  in  the  jacket  shall  not  lower  the  average  tempera- 
ture and  pressure  too  rapidly.  Hence  the  most  efficient  mix- 
ture  becomes  a  matter  for  experimental  determination.  The 
mixture  must  further  be  one  in  which  the  flame  propagation  or 
the  time  of  ignition  of  the  mixture  shall  bear  the  desired  rela« 
tion  to  the  speed  of  the  engine,  or  the  period  of  the  single 
working  stroke  of  the  four-phase  cycle.  The  accepted  data  are 
again  those  of  Mr.  Dugald  Clerk,  from  experiment,  as  follows: 


Maximum 

Time  of 
Explosion, 
Seconds. 

Absolute  Fahr. 

No. 

Volume  Gas. 

Volumes  Air. 

GauRC 
Pressure, 

Temperature  of 
Explosion  from 

lbs.  per  sq.  in. 

Observed  Pressure. 

2 

13 

52 

0.28 

1934* 

4 

IX 

63 

0.18 

2309 

5 

^ 

9 

69 

0.13 

•       2525 

6 

7 

89 

0.07 

3236 

7 

5 

96 

0.05 

3484 

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INTERNAL'COMBUSTION'  ENGINES.  43  f 

Mixtures  more  dilute  than  14  or  15  of  air  to  one  of  gas 
fail  to  ignite.  Six  volumes  of  air  furnish  just  about  the 
required  oxygen  for  complete  combustion.  The  time  of 
explosion  can  be  shortened  by  adapting  the  shape  of  the  ves- 
sel to  more  rapid  propagation  of  the  flame,  or  by  igniting  by 
the  injection  of  a  flame  into  the  combustible  mixture. 

When  the  capacity  of  the  mixture  for  resisting  the  cooling 
effect  of  the  walls  is  considered,  or  its  ability  to  keep  up  its 
pressure  until  a  part  of  the  stroke  is  completed,  the  best  mix- 
ture is  found  between  ^  or  -^^  or  about  one  of  gas  to  thirteen 
of  air. 

294.  Thermodynamic  Efficiency  of  the  Otto  Engine  con- 
sidered as  a  Carnot  Engine. — If  it  be  assumed  that  the 
heat  caused  by  the  explosive  ignition  of  the  gas  in  air  is  all 
imparted  to  the  air  at  that  temperature  of  explosion  {T),  and 
that  by  the  compression  either  in  pump  or  cylinder  the  tem- 
perature has  been  brought  up  to  (7).),  the  heat  supplied  to 
the  cycle  will  be  supplied  at  the  constant  volume  Vg  prevail- 
ing at  the  end  of  such  compression,  and  will  be 

H,=  CIT-  7;). 

If  the  condition  be  assumed  which  is  the  most  usual,  that 
the  fmal  volume  after  expansion  is  the  same  as  that  at  atmos- 
pheric pressure  before  compression  was  begun,  then  the  heat 
necessary  to  bring  the  mixture  back  to  its  original  state  may 
be  abstracted  also  at  constant  volume;  hence  if  7",  be  the 
final  temperature  at  exhaust,  and  T^  the  atmospheric  tem- 
perature before  compression,  the  heat  discharged  will  be 

H,  =  CIT,^  7;). 

Hence  the  Carnot  efficiency  will  be 

H,  c^r-  7;) 


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432 


ffEAT  AND  HEAT-BNGWES. 


The  two  curves  of  temperature  range  being  adiabaiic,  and 
the  volume  range  being  the  same, 


Hence 


T       T,' 


E=^-^^^-L. 


T, 


=  -r' 


when  v^  is  the  final  volume  at  the  end  of  the  stroke.  This 
says,  in  other  words,  that  the  efficiency  is  greater  as  the  ratio 
between   the   initial  and  final  volumes  of  the  compressing 


Volumes. 
PiQ.  168. 


stroke  grows  less,  or  the  greater  the  compression.  The 
exponent  n  is  the  ratio  between  specific  heats  of  air.  Fig. 
163  shows  the  perfect  diagram  corresponding  to  this  design. 


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INTERNAL-COMBUSTION  ENGINES, 


433 


The  fact  that  the  theoretical  efficiency  can  be  increased  by 
increasing  the  degree  of  compression,  which  would  not  be 
true  in  practice  to  the  same  degree,  shows  the  danger  of 
applying  Camot's  reasoning  to  cases  to  which  it  is  not 
properly  applicable. 

295.  Temperature-entropy  Diagram  for  the  Gas-engine 
— The  discussion  of  Joule's  air-engine  in  §  274,  where  the 
heat  medium  receives  its  heat  and  increase  of  entropy  at  an 
increasing  temperature,  has  opened  the  way  to  the  discussion 


n 


C"- 


"  I 


I  I 


y^ 


7 


^T 


T, 


^-<Pr-i 


iR 


— 9i -1 

Fig.  164. 


of  the  temperature-entropy  diagram  for  the  gas-engine.  In 
its  theoretical  form,  when  operated  with  compression  either 
in  a  separate  cylinder  or  in  the  working  cylinder,  the  adia- 
batic  compression  of  the  charge  raises  the  temperature  from 
^  to  ^  without  increase  of  entropy.  The  ignition  of  the 
combustible  gas  at  increasing  temperature  causes  the  entropy 
to  rise  according  to  the  law 

T 
0=  Chyp.  log-^r. 


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434  ^EA  T  AND   HEA  T-ENGINES. 

The  expansion  during  the  working  stroke  supposed  to  be 
adiabatic  would  drop  the  temperature  down  to  that  repre- 
sented by  the  point  c  on  the  temperature-ordinate,  at  which 
the  exhaust  may  be  conceived  to  open.  Then  the  curve  cd 
is  a  drop  in  entropy  and  temperature  at  the  constant  pressure 
of  the  exhausting  products  of  combustion,  to  close  the  cycle 
and  bring  back  the  condition  of  temperature  and  entropy 
belonging  to  the  mixture  as  drawn  into  the  compressing 
cylinder. 

The  difference  between  the  gas-engine  cycle  and  the 
theoretical  Carnot  cycle  is  made  clear  by  observing  that  for 
the  ideal  Carnot  cycle  the  line  ad  should  have  been  carried 
up  to  meet  a  horizontal  line  through  b  which  represents  the 
maximum  temperature  attained;  the  entropy  should  increase 
at  constant  temperature.  Secondly,  the  adiabatic  expansion 
should  lower  the  temperature  till  it  descends  along  be  to  meet 
a  horizontal  through  the  point  d\  the  rejection  must  take 
place  at  the  constant  lower  temperature.  The  relation  of 
the  shaded  area  to  the  total  T<t>  area  might  thus  be  called 
the /^55/^/^  efficiency,  while  the  ratio  between  the  rectangle 
given  by  the  lines  through  b  and  d  as  compared  with  the 
total  area  whose  base  is  NR  and  whose  height  is  bR  might  be 
called  the  ideal  efficiency. 

In  drawing  a  temperature-entropy  diagram  for  an  actual 
engine  from  its  indicator-diagram  on  the  pv  ordinates,  the 
relation  is  used  (§  124)  that  the  work  done  with  isothermal 
expansion  in  foot-pounds  should  be  equal  to  778  times  the 
heat-units  supplied.  With  permanent  gases  this  work  will  be 
expressed  by 

RT  hyp.  log  r  =  RT  hyp.  log  — , 

when  the  778  is  divided  out  to  reduce  it  to  heat-units.  But 
the  work  will  also  be 

7X0,-0.), 


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INTEPNAL-COMBUSTION  ENGINES, 


435 


whence  the  entropy  change  equivalent  to  the  actual  change 
will  become 


(p  =z  R  hyp.  log  — 


by  dividing  both  members  by  71 
This  can  be  written 

0  =  (C,  -  C.)  hyp.  log  p. 


=  Cp  hyp.  log  y-  —  C;  hyp.  log  — \ 


It  follows,  therefore,  that  points  on  the  indicator-diagram 
may  be  transferred  to  the  temperature-entropy  diagram  by 
the  graphical  expedient  of  drawing  a  line  of  constant  pressure 
through  one  point  of  a  pv  curve,  and  a  line  of  constant 
volume  through  another  (Fig.  165).     These  two  construction 


«> 


Fig.  165. 


lines  will  intersect  at  a  pv  point  which  will  have  a  corre- 
sponding temperature  7,  established  by  the  constant  relation 
PV=RT.  Then  if  in  the  left-hand  part  of  Fig.  165  the 
points  I,  2,  and  3  be  the  selected  and  resulting  points,  the 
lines  7i,  7,,  and  T^  will  indicate  the  corresponding  isothermal 


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43^  HEAT  AND   HEAT-ENGINES, 

lines.  Then  the  constant  pressure  curve  1^3  will  have  a  re- 
lation between  co-ordinates 

T  V 

Cp  hyp.  log  -^  -Cp  hyp.  log  -i, 

since,  the  pressure  being  constant,  the  temperature  will  vary 
as  the  volume.  The  constant  volume  curve  3-2  will  have  a 
relation  between  co-ordinates  given  by  the  expression 

T 
—  C,  hyp.  log  y\ 

By  the  expedient  of  multiplying  both  terms  of  the  fraction 
by  —  -yT,,  this  becomes 

+  C  hyp.  log  ^', 

which  (because  the  volume  is  constant,  which  again  makes 
the  pressure  proportionate  to  the  temperature)  may  be  written 

Cv  hyp.  log  ^^ 

since  the  line  through  the  point  i  is  a  constant  pressure  line 
and  hence/,  =/,.  Hence  the  equation  for  the  entropy 
becomes  transformed  from 

T  T 

4>^  Cp.  hyp,  log  -^  -  Cv  hyp.  log  y 

into  the  expression 

<f>=Cp  hyp.  log  J  +  C;  hyp.  log  4', 

which  can  be  used  to  transfer  points  on  one  diagram  to  the 
other,  provided  proper  values  are  found  for  the  quantities 
Cp  and  Cj,  for  the  mixture  of  air  and  gas  during  compression, 


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INTERNAL-COMBUSTION  ENGINES. 


437 


and  for  the  products  of  combustion  after  ignition  and  during 
expansion.  Mr.  Geo.  Richmond  by  a  process  of  approxima- 
tion has  proposed  values  as  follows: 


Cp 


H: 


246  on  the  compression  curve 


26 


^.=i:r 


89 


expansion 

compression 

expansion 


Following  this  method,  the  pv  diagram  at  the  left  of 
Fig.  166  gives  the  straight  line  1-5  on  the  T.E.  curve  to 
correspond  to  the  practically  adiabatic  compression  line   1-5 


P              6 

1 

r 

1 1 1 Lly 

FiQ.  166. 

on  the  pv  diagram.  From  5  to  ^  is  the  increase  of  tem- 
perature and  entropy  at  constant  volume,  corresponding  to 
the  ignition  rise  in  pressure  from  5  to  ^  on  the  indicator- 
diagram  resulting  from  the  ignition.  Points  6,  7,  8,  9,  and 
10  on  the  indicator-diagram  are  found  by  the  equation  above; 
and  from  10  back  to  i,  to  close  the  diagram,  a  constant 
pressure  curve  corresponds  to  the  drop  in  entropy  and  tem- 
perature incident  to  the  exhaust,  to  reach  the  condition  when 
compression  is  to  begin  anew.  The  calculation  made  by 
Mr.  Richmond  is  given  in  the  table  on  page  438.* 

♦  School  of  Mines  Quarterly,  Columbia  University,  vol.  xviii.  Jan.  1897, 
p.  146. 


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438 


HEAT  AND   HEAT-ENGINES. 


Point. 

PV 

7» 

.176  log /»4- .946  log  K 

♦, -♦. 

X 

475 
545 
6oo 
66i 
706 

I.OOO 

1. 147 

1.263 

I -391 
1.486 

6094 
6149 
6159 
6154 
6095 

2 

3 
4 
5 

55 
10 

-    5 
-59 

.i89log/>+.a6olog:r 

b 
6 

7 

8 

9 

lO 

1391 
1404 
1438 
1460 
1428 
1300 

2.928 
2.957 
3.027 
3.073 
3.006 
2.800 

6943 
7045 
7183 
7268 

7313 
7308 

854 

102 

138 

85 

45 

5 

The  table  makes  it  appear  that  the  changes  in  entropy 
from  I  to  5  or  during  the  compression  are  so  small  that  the 
curve  is  practically  isentropic  (§  124)  or  adiabatic,  for  the 
scale  used  at  any  rate.  This  is  doubtless  to  be  explained  by 
the  compensatory  action  of  cylinder-walls  which  are  warmer 
than  the  mixture  at  the  beginning  of  the  stroke  and  cooler 
at  the  end.  On  the  expansion  curve,  while  the  great  rise  in 
entropy  corresponds  to  the  ignition  stage  at  b^  yet  the  positive 
value  (while  a  diminishing  one)  for  the  succeeding  points 
means  doubtless  that  the  gas  continues  to  burn  with  a 
delayed  combustion  till  near  the  end  of  the  stroke.  The 
action  of  the  cooling  water-jacket  no  doubt  masks  also  to 
some  extent  the  real  value  of  the  heat  added  by  this  ''after- 
burning "  process. 

The  temperature-entropy  diagram  can  also  be  made  to 
show  the  gain  in  thermal  efficiency  resulting  from  the  exten- 
sion of  the  expansion  down  to  atmospheric  pressure.  If  the 
supposed  theoretical  diagram  be  again  referred  to,  and  the  ex- 
pansion be  carried  down  to  the  lower  temperature  5  (Fig.  167), 
instead  of  having  the  exhaust  open  at  3  before  the  pressure 
falls  to  atmosphere,  then  the  point    5  is  to  be  joined  to  4 


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INTERNAL-COMBUSTION  ENGINES, 


439 


by  a  curve  of  equal  pressure.  This  will  be  a  lower  or  more 
gently  sloping  line  than  the  curve  4-3,  and  the  triangular 
area  5-4-3  will  represent  the  thermal  gain  over  the  condition 
of  incomplete  expansion.  It  must  not  be  overlooked,  how- 
ever, here  as  elsewhere,  that  this  attempt  to  secure  complete 
expansion  is  followed  by  wide  variations  in  the  propelling 
energy  on  the  piston,  and  the  bad  effect  of  the  irregularity 


^PiG.167. 

of  motion  may  be  of  greater  consequence  than  the  thermal 
gain. 

Furthermore,  the  temperature-entropy  diagram  may  be 
used  to  make  clear  the  effect  of  the  water-jacket  in  the  gas- 
engine.  If  the  action  of  the  water-jacket  removes  both  tem- 
perature and  entropy  during  the  expansion,  so  that  when  the 
exhaust  opens  the  state  of  the  mixture  is  represented  by  a 
point  located  at  6  instead  of  at  3,  then  the  triangle  2-3-6  (Fig. 
168)  shows  the  quantity  of  heat  so  disposed  of.  The  effect 
of  the  jacket  thus  appears  to  be  to  diminish  the  heat  swept 
away  by  the  exhaust  by  the  quantity  represented  by  the  area 
under  the  line  3-6,  which  would  be  exhausted  with  the 
products  of  combustion  if  there  were  no  jacket.     The  sup- 


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440 


HEAT  AND   HEAT-ENGINES. 


pression  of  the  jacket-loss  would  not  result  in  its  conversion 
into  work.  The  jacket  would  act  to  bring  the  expansion  line 
lower  than  an  adiabatic  on  the  pv  plane.  If,  however,  the 
phenomenon  of  retarded  combustion  be  in  action,  the  expan- 
sion pressure  would  be  increased;  and  while  perhaps  a  less 
temperature  would  be  attained,  a  greater  value  for  the 
entropy  change  might  be  made  to  result.  That  is,  if,  instead 
of  having  the  maximum  temperature  represented  by  2 
reached  by  the  ignition  (Fig.  169),  a  temperature  of  7  only 


!N     *         R! 


^- >|  b 

I 

Fig.  168. 

is  reached  by  the  ignition  at  the  beginning  of  the  working 
stroke,  then  the  retarded  combustion  traces  a  path  such  as 
1-7-8  during  the  expansion  whose  latter  part  only  is 
adiabatic.  If  the  area  of  heat  represented  by  the  area 
whose  upper  boundary  is  1-7-8  is  the  same  as  that  bounded 
by  the  line  1-7-2,  then  the  combustion  is  completed  before 
the  exhaust  opens  and  no  waste  of  gas  occurs.  If  less,  then 
the  retarded  combustion  has  been  so  noticeable  as  to  cause  a 
waste  of  unburned  gas. 

296.  Compound  Gas-engines. — It  will  have  been  observ- 
able from  most  of  the  indicator-diagrams  of  gas-engines  that 


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INTERNAL-COMBUSTION  ENGINES.  44^ 

the  exhaust  opens  while  a  considerable  pressure  remains  upon 
the  piston.  This  may  be  as  much  as  30  to  40  pounds  above 
the  atmosphere  at  the  beginning,  and  the  coughing  noise  of 
such  exhaust  is  a  great  objection  to  this  type  of  engine  for 
many  locations,  apart  from  the  apparent  waste  of  available 
energy. 

The  problem  may  be  stated  generally,  by  saying  that  it 
is  desired  to  expand  the  compressed  charge  during  the 
working  stroke  to  a  volume  greater  than  that  which  the 
charge  occupied  before  compression.  This  cannot  be  done 
in  the  single  cylinder  of  the  Otto  cycle-engine,  and  the 
attempts  to  secure  continuous  expansion  in  more  than  one 
cylinder  have  not  been  successful  as  yet.  In  some  two- 
cylinder  engines  one  has  had  a  larger  volume  than  the  other, 
either  by  different  areas  or  different  length  of  stroke,  but 
the  two  cylinders  have  received  their  charge  simultaneously 
and  not  in  succession  as  a  continuous  process.  Clerk  has 
suggested  that  in  small  engines  it  is  to  be  questioned  whether 
an  increase  in  the  expansion  beyond  the  volume  of  the 
charge  before  compression  may  not  so  far  reduce  the  volume 
of  mixture  dealt  with  at  each  stroke  as  to  increase  the  relative 
loss  of  heat  to  the  jacketed  cylinder-walls  to  a  point  where 
the  gain  from  greater  expansion  will  be  more  than  neutralized. 
In  larger  engines  dealing  with  larger  volumes  of  gas  and  with 
their  slower  transfer  of  heat  to  met^l  walls,  the  gain  from 
successful  compounding  will  be  realized  when  further  investi- 
gation shall  have  revealed  some  principles  as  yet  not 
mastered. 

297.  The  Oil-engine,  using  Kerosene  or  Non-volatile 
Oils. — It  will  be  at  once  apparent  that  if  the  object  in  the 
gas-engine  is  to  burn  the  fuel  supplying  heat  directly  in  the 
working  cylinder,  this  same  object  can  also  be  secured  by 
injecting  a  liquid  fuel  in  a  finely  divided  state,  or  a  state  of 
vesicular  vapor,  mixed  with  the  air  which  it  requires  for  its 
combustion.     Hence  it  was  early  proposed  and  tried  to  use 


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442  HEAT  AND   HEAT-ENGINES. 

petroleum  and  its  derivative  oils,  so  as  to  make  this  type  of 
motor  available  where  municipal  or  private  gas  companies 
were  not  at  hand,  or  where  the  manufacture  of  gas  by 
producer  methods  was  not  convenient  or  practicable.  The 
first  practical  petroleum  engine  was  that  of  Julius  Hock  of 
Vienna  (1870),  and  the  early  Brayton  engines  of  1873  were 
planned  for  oil.  If  the  more  volatile  derivatives  of  petroleum 
are  used,  such  as  naphtha  or  gasoline,  a  current  of  air  passing 
over  or  through  them  will  absorb  hydrocarbons  to  such  an 
extent  as  to  become  an  illuminating-gas,  and  can  be  used  as 
such  in  an  engine  (§  47).  But,  as  a  rule,  the  dangers  con- 
nected with  the  use  of  these  lighter  oils,  and  particularly  with 
their  storage  in  any  quantity,  have  precluded  their  use  on  any 
large  scale.  On  the  other  hand,  the  use  of  crude  petroleum 
is  attended  with  difficulty  from  the  presence  of  its  heavier 
and  less  inflammable  constituents,  whereby  it  becomes  difficult 
to  burn  it  completely  and  to  ignite  it  promptly.  There  are 
troublesome  residues  also,  which  leave  a  deposit  in  the 
cylinder  (§  49).  In  many  places,  furthermore,  the  use  of  crude 
oil  is  prohibited  by  ordinance  by  reason  of  its  offensive  odor, 
and  from  the  danger  connected  with  the  presence  in  it  of  its 
volatile  elements.  Hence  the  usual  oil-engine  burns  oil  of 
the  grade  known  as  burning  oil,  or  kerosene  (§  43),  which  is 
safe  and  efficient. 

The  use  of  a  liquid  fuel  suggests  that  it  should  be  first 
finely  subdivided  or  made  into  a  spray  or  mist  by  the  action 
of  a  current  of  compressed  air,  and  then  afterwards  the  true 
vaporization  of  the  liquid  oil  shall  take  place  by  heat.  In 
certain  successful  oil-engines,  however,  the  spraying  process 
is  omitted,  and  the  oil  injected  in  its  liquid  state.  Oil- 
engines may  therefore  be  classified  into  groups: 

1.  The  oil  is  atomized  or  sprayed,  and  then  vaporized. 

2.  The  oil  enters  the  working  cylinder  as  a  liquid,  and 
is  there  vaporized. 


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INTERNAL-COMBUSTION  ENGINES.  443 

3.  The  oil  is  vaporized  in  a  separate  vessel,  from  which 
it  passes  to  the  working  cylinder  as  a  gas. 

As  in  the  case  of  gas-engines, .  the  methods  for  igniting 
the  mixture  of  air  and  oil-vapor  will  distinguish  oil-engines 
from  each  other. 

The  mixture  may  be  fired  by  (i)  an  electric  spark;  (2)  by 
passing  through  an  incandescent  tube;  (3)  by  heat  of  the  in- 
ternal surfaces,  combined  with  the  heat  of  compression. 

The  Priestman  engine  will  serve  as  a  type  of  the  first 
group;  the  Hornsby-Akroyd  of  the  second;  and  of  the  third 
group  the  best  known  examples  are  the  British  designs  of 
Crossley  and  of  Fielding  and  Piatt. 

In  the  Priestman  engine  the  air-supply  is  passed  through 
a  heating-chamber,  which  is  surrounded  by  the  hot  exhaust- 
gases.  If  the  latter  are  at  600°  F.,  the  chamber  will  be  at 
nearly  300°  F.  The  oil  is  injected  into  this  chamber  by  a  small 
jet  of  air,  and  changes  from  spray  to  oil-vapor  by  evaporation, 
and  passes  into  the  cylinder  upon  the  aspirating  stroke.  The 
compression  of  the  preheated  air  brings  it  to  a  high  tempera- 
ture, above  that  to  be  met  in  the  gas-engine,  thus  lowering 
the  weight  of  charge  present  in  the  engine  at  each  stroke, 
and  reducing  the  average  available  pressure.  The  high 
temperature  renders  the  mixture  liable  also  to  premature 
ignitions.  The  presence  of  the  charge  in  the  vaporizing 
chamber  in  the  event  of  a  back  explosion  from  the  working 
cylinder  constitutes  a  menace  to  the  safety  of  the  whole 
machine.  •  The  necessity  for  keeping  the  vaporizing  chamber 
hot  by  means  of  exhaust-gases  makes  it  necessary  to  use 
some  oil  at  every  stroke,  even  at  light  loads,  so  that  govern- 
ing forms  a  difficulty  with  the  design,  and  the  consumption  of 
oil  is  not  proportionately  diminished  as  the  load  diminishes. 

In  the  Hornsby-Akroyd  engine  the  vaporizer  is  a  cast- 
iron  non-jacketed  chamber  behind  the  working  cylinder,  to 
which  it  is  connected  by  a  narrow  neck.  The  heat  due  to 
each   ignition   keeps  this  chamber  hot  enough    so  that    oil 


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444  HEAT  AND   HEAT-ENGINES.  ^ 

injected  into  it  is  vaporized,  and  the  completion  of  the  com- 
pression stroke,  forcing  in  a  charge  of  fresh  air  from  A^ithout, 
raises  the  mixture  to  the  point  of  ignition,  and  it  ignites 
without  outside  means  to  effect  it.  The  vaporizer  is  heated 
by  gas  or  by  a  blast  oil-lamp  outside  of  it  to  start  the  engine. 
Governing  is  effected  by  causing  the  oil-pump  to  send  its 
charge  back  into  the  suction  by  a  by-pass,  instead  of  into^ 
the  vaporizer,  but,  as  in  the  previous  case,  the  vaporizer  must 
not  be  allowed  to  cool  off  too  mi;ch  at  light  loads,  else 
ignition  fails. 

This  type  suffers  also  from  the  lower  average  pressure 
than  is  secured  with  gas,  because  the  mixture  of  oil,  gas,  and 
air  is  less  likely  to  be  thorough,  and  an  excess  of  air  is  there- 
fore usual  to  secure  perfect  combustion.  The  engine  must 
furthermore  be  massive  to  meet  the  possibility  and  likelihood 
of  double  charges,  when  for  any  cause  an  ignition  has  been 
missed  on  one  stroke,  and  twice  the  normal  quantity  of  oil  is 
fired  at  the  next  ignition. 

In  the  third  group  the  typical  engine  has  the  oil  and  a 
small  volume  of  air  injected  into  a  heated  vaporizer  consisting 
of  tubes  or  passages  kept  hot  by  waste  heat  from  the  blast- 
lamp  which  heats  the  ignition-tube.  A  second  volume  of  air^ 
heated  before  it  enters,  joins  the  oil  in  the  vaporizer  and 
completes  the  vaporization.  The  main  charge  of  air  for  the 
mixture  is  not  preheated,  but  enters  through  a  separate 
valve,  mixing  with  the  oil-vapor  and  being  ignited  by  an 
incandescent  tube.  The  use  of  cool  air  permits  higher  [com- 
pression, and  hence  higher  mean  pressures,  with  the  attendant 
advantages.  The  exterior  lamp  with  its  heat  and  noise  are 
objections,  however,  and  the  simplicity  of  the  Hornsby- 
Akroyd  design  has  much  to  commend  it. 

298.  The  Oil-engine  using  Gasoline  or  Light  Volatile 
Oils. — The  difficulties  from  legal  restrictions  and  city  ordi- 
nances attaching  to  the  storage  and  use  of  the  volatile  oils 
have    been    already  referred   to   in  a  preceding   paragraph. 


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INTERNAL-COMBUSTION  ENGINES.  445 

Their  lightness  in  weight,  and  the  lightness  of  the  fuel-supply 
in  tanks  for  a  given  traverse,  have  made  this  type  popular  on 
the  continent  of  Europe  for  motor-carriages  or  automobile 
use.  By  reason  of  the  volatile  character  of  the  liquid  fuel,  it 
is  only  necessary  to  force  air  through  and  over  it,  for  the 
former  to  take  up  hydrocarbon  vapor  in  quantities  to  make 
an  ignitible  gas.  The  mixture  is  easily  ignited  by  passing  it 
through  incandescent  tubes  heated  by  a  shunt  oil-circuit 
which  supplies  a  lamp  beneath  them,  burning  with  a  Bunsen 
flame.  Electric  igniters  are  not  used  for  motor-carriages  by 
reason  of  the  weight  of  the  necessary  battery. 

The  best  known  gasoline-motor  in  Europe  is  the  Daimler. 
The  usual  form  has  two  cylinders,  closed  at  both  ends.  The 
back  ends  behind  the  pistons  operate  on  the  usual  Otto 
cycle,  the  front  ends  acting  as  air-pumps,  so  that  an  addi- 
tional pressure  of  a  few  pounds  is  secured  before  ignition  with 
a  surcharge  of  air  from  the  front  ends.  The  compressed  air 
from  the  front  effects  the  carbonization  of  the  working  charge, 
and  also  operates  the  lamp  of  the  ignition-tubes.  These 
are  two  platinum  tubes.  The  two  cylinders  incline  to  each 
other  at  an  angle  of  about  30**,  with  their  connecting-rods 
acting  on  a  common  crank-pin.  In  motor-carriages  the  main 
shaft  runs  at  a  constant  speed  and  in  one  direction,  so  that 
speed  changes  and  reversing  is  effected  by  gears  and  clutches. 

The  naphtha-engine,  as  used  extensively  in  launches,  is 
not  a  direct-combustion  engine,  but  uses  the  volatile  liquid 
in  a  closed  vapor  cycle  as  steam  is  used  in  the  condensing 
engine.     This  will  be  referred  to  under  "  Vapor-engines." 

299.  The  Diesel  Petroleum-motor. — A  most  interesting 
development  of  the  principles  of  the  heat-engine  has  been 
made  in  Germany  during  the  years  1893-97  by  a  Mr.  Rudolf 
Diesel.  The  fundamental  peculiarity  of  his  engine  lies  in  the 
same  lines  as  those  of  the  Hornsby-Akroyd.  The  idea  is  to 
compress  the  air  to  a  point  at  which  its  temperature  due  to 
the  compression  (§  182)  shall  be  above  the  point  of  ignition 
of  the  fuel  to  be  used.     If  the  latter  is  petroleum,  crude  or 


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44^  ITEA  T  AND   HRA  T-ENGINES. 

refined,  a  measured  quantity  of  it  as  controlled  by  a  governor 
is  injected  into  the  highly  heated  air.     It  enters  as  a  vapor 
by  being  sprayed  by  air  from  a  small  auxiliary  pump,  and  by 
being  forced  also  through  a  close-mesh  wire  gauze.     If  the 
compression  has  been  carried  (as  is  expected)  to  a  pressure 
of  500  pounds  per  square  inch  or  over,  the  finely  divided  oil 
ignites,  and  supplies  to  the  expanding  air  the  heat  equivalent 
to  the  work  it  is  doing  in  expanding,  realizing  (to  the  extent 
that  it  secures  this  result)  the  ideal  Carnot  theorem  of  having 
the  heat  supplied  isothermally  during  expansion  or  at  the  con- 
stant highest  temperature  of  the  cycle  instead  of  having  the 
supply  occur  along  a  line  of  falling  temperature.     It  would 
be  obviously  possible  to  supply  fuel  enough  to  do  all  the  work 
of  the  stroke  without  drop  of  temperature,  but  this  would 
consume  more  oil  in  the  first  place,  and  in  the  second  place 
would  leave  the  gases  when  ready  to  exhaust  at  a  temperature 
unnecessarily  and  wastefully  high.     Hence  the  charge  of  oil 
is  proportioned  so  as  to  keep  up  the  expanding  gases  to  7\ 
during  a  part  only  of  the  stroke,  which  results  in  there  being 
always  an  excess  of  air  so  as  to  secure  complete  combustion. 
When  the  oil-charge  is  completely  burned  at  an  early  period 
of  the  working  stroke  and  can  furnish  no  more  heat  to  the 
expanding  air,   cooling  begins  by  the  adiabatic   expansion, 
which  then  sets  in,  and  which  continues  till  the  end  of  the 
stroke,  leaving  the  gases  to  exhaust  at  a  lower  temperature, 
and  without  causing  so  much  heat  to  pass  out  by  way  of  the 
jackets.     The  latter  are  retained,  however,  for  the  sake  of 
uniformity  of  temperature  in  valves  and   pistons.     A  new 
charge  is  again  drawn  in  on  an  aspirating  stroke,  and  com- 
pressed on  the  return  stroke  as  in  the  Otto  cycle. 

The  injection  of  the  fuel  after  compression  is  complete 
eliminates  the  danger  of  premature  ignition  and  explosion; 
governing  is  also  much  simplified;  and  what  is  more  impor- 
tant than  all,  a  practically  perfect  combustion  is  secured, 
without  carbon  loss  in  smoke  or  in  lamp-black  deposit. 

Starting  is  effected  by  a  few  strokes  by  a  hand  oil-pump, 


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INTERNAL-COMBUSTION  ENGINES.  AA7 

to  throw  a  preliminary  fuel-supply  into  the  casing  of  the 
fuel-valve;  from  a  storage  of  compressed  air  at  high  tension 
from  a  previous  run  a  charge  of  cold  air  is  admitted  by  a 
starting-valve  to  the  working  cylinder,  sufficient  to  turn  the 
fly-wheel  through  two  revolutions,  or  past  one  compressing 
stroke.  This  is  done  with  the  valve-cams  out  of  gear,  but  at 
the  close  of  the  first  revolution  the  cams  are  thrown  into  gear 
automatically,  and  the'engine  will  then  start  off.  The  high 
temperatures  used  enable  this  engine  to  work  on  low-grade 
oils,  or  even  upon  powdered  solid  fuel,  as  well  as  with 
kerosene,  alcohol,  or  gas.  Governing  is  done  by  by-passing 
the  charge  or  injection  from  the  oil-pump,  which  is  propor- 
tioned for  the  maximum  supply  to  be  required. 

By  applying  the  temperature-entropy  diagram  to  the 
cycle  of  the  Diesel  motor,  it  will  be  apparent  that  when  the 
proper  practical  conditions  are  secured  for  it,  it  approaches 
more  nearly  to  the  ideal  Carnot  conception  than  any  of  the 
preceding  motors,  and  therefore  the  ratio  of  heat  utilized  to 
heat  supplied  or  its  efficiency  should  be  by  so  much  greater 
as  this  approach  is  more  close.  Tests  show  an  efficiency 
of  38  per  cent  for  the  Diesel  engine,  as  compared  with  25  to 
30  in  ordinary  gas  engines.  Fig.  170  illustrates  the  engine 
in  section,  and  Fig.  171  is  a  reproduction  of  one  of  its  cards. 

300.  Performance  and  Economy  of  Direct-combustion 
Engines. — Any  comparison  or  critical  discussion  of  different 
types  of  direct-combustion  engine  when  stated  in  consump- 
tion of  fuel  per  H.P.  must  be  unsatisfactory  and  unreliable 
to  the  extent  that  the  heat-units  per  unit  of  fuel,  or  from  the 
analysis  of  the  fuel,  are  unknown  or  unstated.  The  figures 
following  are  therefore  given  only  as  guides,  and  as  points  in 
a  reconnaissance  survey,  by  reason  of  the  lack  of  such  deter- 
mining data,  and  because  also  the  sizes  of  the  engine  are  not 
given.  Large  engines  burn  less  gas  per  H.P.  than  small 
ones. 

With  the  ordinary  city  illuminating-gas  to  be  met  in  Great 
Britain  and  the  United  States  an  average  ranging  from  20  to 


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448 


HEAT  AND   HEAT-ENGINES. 


Fw.171. 


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INTERNAL-COMBUSTION  ENGINES.  449 

24  cubic  feet  per  indicated  horse-power  may  be  expected, 
which  corresponds  to  a  net,  or  brake,  horse-power  consump- 
tion of  24  to  30  cubic  feet  per  hour.  Record  consumptions 
run  as  low  as  13^  to  15  cubic  feet  per  I.H.P.  per  hour,  or  18 
to  20  cubic  feet  per  brake  horse-power, 

The  largest  gas-engines  of  Europe  and  probably  in  the 
world  are  of  400  H.P. ;  the  highest  number  of  revolutions  per 
minute  is  400. 

When  gas  can  be  secured  from  producers  of  the  Dowson 
or  Taylor  or  other  economical  type  the  lower  calorific  power 
per  cubic  foot  increases  the  consumption  in  cubic  feet,  but 
not  the  consumption  per  pound  of  coal  or  of  carbon.  For 
example,  in  a  town  in  Connecticut  where  electric  lighting  is 
supplied  by  gas-engines  operating  on  producer-gas  the  gas 
has  only  153  B.T.U.  per  cubic  foot,  and  99  cubic  feet  are 
required  by  brake  horse-power  per  hour.  This  corresponds, 
however,  to  a  consumption  of  1.075  pounds  of  carbon  per 
brake  horse-power  per  hour.  English  and  Continental  records 
are  1.3 1  to  1.34  pounds  of  coal  per  I.H.P.  per  hour  on  small 
engines,  and  an  opinion  has  been  expressed  that  with  engines 
of  over  100  H.P.  the  consumption  should  drop  to  one  pound. 

With  oil  of  the  grade  of  kerosene  the  consumption  in 
pounds  per  I.H.P.  per  hour  ranges  from  0.75  to  1.25,  corre- 
sponding to  a  consumption  per  brake  horse-power  ranging 
from  0.82  to  1.68  pounds.  The  Diesel  motor  has  an  authen- 
ticated record  of  240  grams  of  kerosene  oil  per  brake  horse- 
power per  hour,  equivalent  to  0.531  pound,  which,  when 
reduced  on  the  basis  of  a  price  of  2^  to  3  cents  per  gallon 
for  fuel-oil,  results  in  a  calculated  consumption  of  15  cents* 
worth  of  such  oil  per  horse-power  per  hour  in  engines  of 
100  H.P. 

301.  Advantages  of  the  Gas-  or  Oil-engine. — The  prin- 
ciple of  direct  combustion,  or  the  liberation  of  the  heat 
energy  directly  in  the  working  cylinder,  as  contrasted  with  the 
indirect  method  of  imparting  this  heat  energy  to  the  heat 


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450  HEAT  AND   HEAT-ENGINES. 

medium  in  a  separate  vessel,  offers  some  inherent  advantages; 
and  certain  others  attach  to  the  methods  used  to  avail  of  this 
principle  or  are  incidental  to  it.  That  is,  there  are  some 
advantages  attaching  intrinsically  to  the  use  of  gas  or  oil  as  a 
source  of  heat  energy  (§§  42-56)  apart  from  the  principle  of 
direct  combustion  as  a  means  of  utilizing  that  energy. 

Attaching  to  the  direct-combustion  principle  may  be 
noted : 

(i)  The  direct  utilization  of  heat  energy  to  drive  the 
piston  in  a  single  apparatus. 

(2)  Resulting  from  this  an  economy  of  combustible  per 
horse-power  per  hour  because  heat  is  not  wasted  in  a  furnace 
or  chimney,  or  in  doing  work  upon  a  heat  medium  which  is 
not  utilized  in  the  engine. 

(3)  No  fuel  is  consumed  wastefully  to  start  up  the  motor, 
nor  is  any  wasted  after  the  engine  stops.  The  losses  in 
banking  fires  under  a  boiler  which  runs  intermittently  are 
avoided,  and  the  losses  of  fuel  in  the  grates  from  cleaning 
Anc'  when  the  run  is  over. 

^^4)  The  engine  is  ready  to  start  on  the  instant,  without 
delay  caused  by  getting  up  steam  or  starting  the  fire. 

(5)  By  direct  use  of  gas  or  oil  in  engines  the  advantages 
of  storage  of  energy  are  reaped.  Gas  can  be  made  when 
convenient,  and  stored  in  holders  for  use  after  working-hours 
or  when  the  generating-plant  is  not  running. 

(6)  Incident  to  this  is  the  advantage  of  subdividing 
power  units  in  a  large  plant,  each  of  which  may  receive  its 
supply  of  motor  energy  through  pipes  without  loss,  and  which 
can  be  run  independently  of  each  other  as  to  time,  soeed, 
capacity,  and  the  like,  as  long  as  the  store  of  gas  or  oil  holds 
out. 

(7)  Storage  of  energy  in  the  form  of  gas  under  pressure 
enables  great  power  to  be  stored  in  small  bulk  and  with  small 
weight,  to  be  expended  in  motors  as  required.  The  auto- 
mobile and   the    experimental    flying-machine  avail  of   this 


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INTERNAL-COMBUSTION  ENGINES.  45  ' 

feature.     So  also  might  street-cars  where  electricity  or  com- 
pressed air  is  not  available  or  preferable. 

(8)  The  absence  of  the  boiler  and  its  furnace  and  chimney 
make  the  plant  compact  when  the  gas  generation  and  holders 
are  provided  for  elsewhere.  The  oil-engine  is  portable  from 
the  same  causes,  and  convenient  for  temporary  erection. 

(9)  The  absence  of  the  boiler  (when  not  oflFset  by  the 
presence  of  the  producer  or  the  gas-holder)  lowers  the  insur- 
ance risk,  and  the  owner  avoids  the  expense  of  licensed 
attendants  upon  the  steam-generating  plant.  At  least  this 
is  the  case  where  local  legislation  is  in  force  on  these  points, 
as  in  most  cities. 

(10)  The  absence  of  the  boiler,  with  its  furnace  and 
chimney,  avoids  the  repair  and  maintenance  expenses  which 
attach  to  these  features  of  a  power  plant,  as  well  as  the  labor 
to  operate  them,  and  their  first  cost. 

The  gas-  or  oil-engine  furthermore  attaches  to  itself  the 
advantages  of  mechanical  stoking  and  of  oil  or  gas  used  as 
fuel.     Such  are: 

(11)  Combustion  practically  perfect  and  smokeless, 

(12)  No  human  labor  for  handling  fuel  into  the  heat 
apparatus  nor  for  disposing  of  the  ashes,  with  attendant  cost. 

(13)  No  dust  nor  sparks  nor  soot,  except  at  the  central 
gas-generator  plant.     With  oil  there  is  none  anywhere. 

302.  Disadvantages  of  the  Gas-  or  Oil-engine. — As  in 
the  foregoing  paragraph,  some  of  the  following  objections  are 
inherent,  and  others  attach  only  to  certain  solutions  of  the 
problem.  An  engine  is  excellent  to  the  extent  that  it  avoids 
these  difficulties. 

(i)  Gas-engines  are  usually  single-acting,  if  not  acting  on 
only  one  stroke  in  four.  This  makes  them  more  bulky  than 
the  double-acting  steam-engine  using  the  same  mean  pressure. 

(2)  It  is  difficult  to  command  a  high  mean  pressure. 

(3)  The  effort  is  irregular,  and  hence  a  disproportionately 
heavy  fly-wheel  is  demanded  to  secure  steadinesso 


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452  HEAT  AND  HEAT-ENGINES, 

(4)  Where  governing  is  done  by  missing  a  charge,  the 
speed  must  vary  widely.  Many  types  do  not  govern  well 
nor  closely. 

(5)  Most  require  an  auxiliary  of  some  sort  to  start  them 
from  rest. 

(6)  There  is  no  way  of  increasing  the  power  of  the  engine 
beyond  the  maximum  for  which  it  is  proportioned,  to  meet 
short  demands  for  greater  power. 

(7)  It  is  not  usually  arranged  to  run  in  both  directions, 
or  is  not  easily  reversible. 

(8)  An  unpleasant  odor  of  partly  burned  or  of  unconsumed 
gas  belongs  to  many  examples.     Leakage  seems  unavoidable. 

(9)  The  high  tension  of  the  contents  of  the  cylinder  at  the 
end  of  expansion  makes  the  exhaust  noisy,  or  like  a  succes- 
sion of  coughs,  and  there  is  a  loss  of  heat  in  such  hot  gases. 

(10)  The  water-jacket  around  the  cylinder  is  necessary  to 
keep  it  and  the  valves  cool  enough  to  be  tight  and  prevent 
deformation  by  heat  and  wasting  from  oxidation.  The  heat 
which  goes  into  this  water-jacket  would  otherwise  go  into  the 
exhaust  (§  295),  and  could  not  be  saved  except  at  expense  in 
other  ways;  but  the  engine  must  be  supplied  with  the  water 
for  this  jacket,  and  with  provisions  for  the  water  to  cool  if  it 
is  too  valuable  to  be  wasted. 

(11)  If  the  water-jacket  is  ineffective,  and  often  where  it 
works  well,  the  lubrication  of  the  hot-piston  is  difficult. 
Packings  should  be  avoided,  or  should  be  metallic  when  they 
are  required. 

(12)  Explosions  of  some  violence  occur  in  the  exhaust- 
pipe.  The  fire  laws  of  New  York  compel  the.  metallic  ex- 
haust-pipe to  be  carried  to  free  air,  and  not  merely  to  enter 
a  brick  flue  leading  to  the  air.  Explosions  in  such  flues 
would  be  disastrous.  The  explosion  is  due  to  a  charge  which 
is  not  ignited  in  the  cylinder. 

(13)  Lamp-black  deposits,  the  result  of  imperfect  com- 
bustion, clog  and  defile  the  working  parts,  valves,  ports,  and 


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INTERNAL'COMBUSTJON  ENGINES. 


453 


the  like.  This  deposit  is  very  troublesome  between  the 
points  of  spark-igniters.  The  difficulty  can  only  be  avoided 
by  having  the  contacts  self-cleansing  by  sliding  upon  each 
other. 

303.  Conclusion. — The  gas-engine  has  been  much  more 
studied  in  England  and  the  Continent  than  in  the  United 
States.  In  most  places  it  is  cheaper  to  burn  city  gas  in  gas- 
engines  to  operate  dynamos  to  generate  electric  current  for 
incandescent  lighting  than  it  is  to  burn  the  gas  directly  in 
chandeliers.  Where  fuel-gas  can  be  made  in  producers  this 
plan  is  much  the  cheaper.  In  many  cities  the  insurance  rate 
upon  the  producer  plant  makes  its  cost  prohibitory.  The 
gas-engine  (or  oil-engine)  is  the  rival  which  the  steam-engine 
is  to  anticipate  in  the  next  few  years,  for  small  sizes  in  any 
case»  and  possibly  for  units  of  considerable  size  also. 

Fig.  173  shows  the  successive  positions  of  the  usual  form 
of  slide-valve  in  Otto  gas-engines,  and  should  be  studied  in 
connection  with  Fig.  144  on  page  414. 


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CHAPTER  XXI. 
VAPOR-ENGINES. 

305.  Introductory. — It  has  been  already  noted  (Chapter 
IX)  that  any  other  convenient  heat  media  could  be  used  to 
carry  the  heat  energy  from  the  furnace  or  source  of  heat  and 
make  it  available  for  doing  of  mechanical  work  in  the  engine- 
cylinder,  if  there  were  reasons  why  steam  or  air  should  not 
be  preferred.  It  was  further  suggested,  however,  that  there 
were  practical  reasons  why  the  effort  to  use  other  media  had 
not  as  yet  been  approved  by  commercial  success.  The  object 
of  this  chapter  is  to  go  more  fully  into  this  question  with 
respect  to  a  selected  series  of  heat-carriers,  and  to  show  the 
physical  and  theoretical  basis  for  the  disapproval  of  their 
claims  for  recognition  for  these  uses,  except  perhaps  in  a  few 
special  cases. 

Water  and  air  being  the  only  heat  media  found  in  a 
natural  state  in  unlimited  quantities,  all  the  others  are  manu- 
factured products  or  compounds  which  must  be  purchased. 
Hence  they  must  be  worked  in  a  closed  cycle,  and  not 
rejected  to  the  atmosphere  from  which  they  cannot  be 
regained.  They  will  therefore  be  operated  in  condensing 
engines,  and  will  be  used  as  vapors  to  be  condensed  from  the 
gaseous  to  the  liquid  state  after  working  in  their  cylinder. 
The  heat  will  be  applied  to  convert  them  into  gases,  becom- 
ing latent  in  the  process  of  increasing  their  entropy.  This 
heat  will  be  given  out  in  adiabatic  expansion  in  part,  and  in 
part  to  the  condensing  appliance,  as  discussed  in  §§  195  and 
2iS  et  seq,  of  Chapters  XIV  and  XV,  and  the  cycle  will  be 

454 


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VAPOR'ENCINES,  455 

closed  by  pumping  the  liquid  back  into  the  generator  to  be 
raised  in  temperature  and  entropy  to  the  high  initial  condi- 
tion again. 

The  attraction  to  the  more  volatile  vapors  of  certain 
liquids  comes  about  from  the  facts  of  their  physical  constitu- 
tion, whereby,  either  by  reason  of  a  lower  specific  heat  or  for 
molecular  reasons,  they  are  raised  to  a  higher  tension,  as 
registered  by  a  pressure-gauge,  by  a  smaller  amount  of  heat 
than  is  the  case  when  heat  is  applied  to  water  to  make  it  into 
steam.  If  gauge  pressure  meant  heat  energy  also,  then  there 
would  be  ho  question  as  to  the  thermal  superiority  of  these 
more  volatile  media.  It  will  be  the  object  of  the  succeeding 
paragraphs  to  show  how  insignificant  or  negative  these 
thermal  advantages  usually  are. 

The  problem  of  the  use  of  volatile  vapors  may  be 
approached  from  several  different  points  of  view.  It  may  be 
first  examined  from  the  assumption  that  the  competing  vapor 
is  to  be  worked  within  the  same  temperature  limits  as  the 
accepted  steam-engine,  disregarding  the  inconvenient  pres- 
sures which  result,  and  the  relation  of  work  done  to  heat 
supplied  can  be  deduced  under  these  conditions. 

Or,  secondly,  the  problem  of  keeping  the  pressures  within 
normal  limits  may  be  made  the  determining  one,  and  the 
temperatures  adjusted  to  the  condition  of  strength  of  cylin- 
ders and  other  parts  v/hich  must  resist  pressure  strain. 

Or,  thirdly,  a  set  of  conditions  advantageous  to  the  use 
of  the  vapors  may  be  assumed,  and  the  computations  directed 
to  show  whether  the  resulting  quantity  of  the  heat  medium  by 
weight  or  the  size  of  the  cylinder  by  volume  is  more  advan- 
tageous or  economical  of  fuel  than  in  the  case  of  the  steam- 
cylinder. 

306.  Formulae  for  the  Work  of  a  Vapor. — The  accepted 
formulae  for  the  work  of  a  vapor  which  expands  isothermally 
with  change  of  entropy  at  the  constant  temperature  7",,  as 
represented  by  the  line  AB  in  Fig.  175;  then  expands  adia- 


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4S6 


HEAT  AND   HEAT-ENGINES. 


batically  along  the  curve  BC  to  a  final  pressure  CG^  or  p^\ 
drops  to  a  back-pressure  GHy  or  /,,  and  is  then  worked  back 
by  isothermal  compression  and  finally  by  adiabatic  compres- 
sion to  the  origin  A^  has  been  deduced  by  Rankine,  Clausius, 
and  others  from  differential  equations,  and  appears  in  three 


Fig.  175. 

forms.     If  the  cubic  foot  is  used  as  the  unit,  then  the  work 
of  one  stroke  in  foot-pounds  will  be: 

Work  =/c,A  I  r.  -  r.(i  +  hyp.  logp-)  I 

in  which/  =  778,  the  mechanical  equivalent  of  one  B.T.U. ; 
C  =  the  specific  heat,  at  constant  pressure,   taken 
at  its  mean  value  between  7)  and  7",,  if  it  is 
variable ; 
Z?,  =  weight  in  pounds  of  one  cubic  foot  of  the  vapor 
at  the  temperature  7, ; 
y,  and   7",  =  absolute    temperatures    corresponding   to    the 
pressure  values  used ; 
Z,  =  the  latent  heat  of  evaporation  of  a  cubic  foot 
of  the  vapor  at  the  temperature  7, ; 


Digitized  by  VjOOQ IC 


VAPOR'ENGINES.  ^57 

/,  and  p^  =  the  pressures  at  the  end  of  adiabatic  expansion 
and  in  the  condenser,  respectively; 
r  =  the  ratio  of  expansion  to  reduce  the  tempera- 
ture of  the  vapor  from   7",   to   7",.     This  is 
given  by  Rankine  in  the  equation 


AB 

r  = 


EC 


=  £(778Ahyp.log^  +  ^), 


in  which  Z,  =  latent  heat  of  evaporation  of  a  cubic  foot  of 
vapor  at  the  final  temperature  7",. 

With  complete  expansion,  so  that  /,  equals  /, ,  the  last 
term  disappears,  or  the  area  will  be 

Work  =  J  CD,  I  r,  -  r.(i  +  hyp.  log  ^)  }  +^.  ^^^*. 

If  it  be  preferred  to  discuss  the  problem  from  the  point 
of  view  of  ^  pound  oi  the  vapor  instead  of  a  cubic  foot,  the 
expression  for  the  work  may  be  used  in  the  more  convenient 
of  the  two  forms  deduced  by  Rankine ;  that  is,  the  formula 
may  be,  when/,  is  equal  to  p^\ 

Work  =  ABCD  =  778  |  T,  ^  7.(i  +  hyp.  log^)  | 

T  —  T 

in  which  L^  is  the  latent  heat  of  evaporation  of  one  pound  of 
vapor  at  the  temperature  7,  and  is  given  by  a  formula 

i.  =  ^  +  *7., 
or 

A  =  ^+*7,  +  ^7A 

in  which  both  b  and  c  may  have  a  negative  value. 


Digitized  by  VjOOQ IC 


458  HEAT  AND   HEAT-ENGINES. 

When  there  is  a  difference  between  the  pressures  /,  and 
p^  the  formula  may  be  transformed  into 

Work  =  ABCHK  =  a  hyp.  log  -p  -  b{T,-^  7;)  +  rvip,  -/.)» 

in  which  v^  is  the  volume  occupied  by  one  pound  of  the  vapor 
at  the  pressure  corresponding  to  7",.  Instead  of  rt'„  the 
quantity  v^  could  be  used,  or  the  final  expanded  volume  which 
is  r  times  the  initial  volume  admitted. 

The  next  step  in  the  problem  is  the  demand  upon  the 
physicist  or  laboratory  experimenter  for  the  values  of  the 
factors  or  constants  which  enter  the  formulae. 

307.  Experimental  Data  for  a  Problem  in  Vapors  as 
Heat  Media. — The  data  of  density,  pressure  corresponding  to 
temperature,  latent  heat  at  different  temperatures,  and  specific 
heat  for  the  vapors,  have  in  most  cases  been  reduced  to 
formulae  with  constants  to  be  substituted,  and  these  constants 
or  factors  are  to  be  multiplied  by  the  variable  or  arbitrary 
temperature.  It  will  be  necessary,  therefore,  to  assume  a 
temperature  range  between  the  limits  of  which  the  vapor  is 
to  be  worked.  The  investigation,  along  these  lines,  whose 
completeness  has  made  it  almost  a  classic  among  American 
researches  in  this  field  is  identified  with  the  names  of  Messrs. 
Henry  L.  Gantt  and  D.  H.  Maury,  and  was.  first  made  in 
1883-84.  It  was  later  revised  by  Prof.  De  Volson  Wood. 
It  will  therefore  be  convenient  to  use  the  same  assumptions 
and  data  which  they  have  followed  as  respects  temperature 
and  the  like,  so  as  to  follow  a  similar  procedure. 

If  the  standard  steam-pressure  range  be  taken  as  a  start- 
ing-point to  determine  the  temperature  range,  it  may  be 
taken  as  between  125  pounds  per  square  inch  and  10  pounds 
per  square  inch — absolute  pressures  counted  from  vacuum  as 
a  zero.     This  gives  the  temperature  range 

t^  =  172°  C.  =  342°  Fahr.  =  802°  abs.  Fahr. ; 
/,  =     90°  C.  =:  194°  Fahr.  =  655°  abs.  Fahr. 


Digitized  by  VjOOQ IC 


VAPOR-ENGINES. 


459 


The   Rankine    formula    for  pressures  with  temperatures 
given  is(§  134) 

log/  =^  -  -^-  ^, 

in  which  A^  B,  and  C  are    constants  having  the  following 
values: 


log  i? 


IorC 


Steam 

Alcohol 

Carbon  disulpbide.  ... 

Chloroform 

Ammonia 


8.28203 

8.68170 

7.4263 

4.3807 

8.4079 


3.441474 

3.4721707 
3.3274293 
[This  B  is  3.288394  negative] 
3-341632 


5.583973 
5.4354446 
5.1344146 
6. I 89963 I 


Making   the   substitutions,   the    following  values  for  the 
pressures  result: 


Lbs.           q.  Ft.  Lbs.  per  Sq.  Ft. 

Steam 

17408 
36450 
36745 
24871 
468700 
55350 

1469 

3279 
7269 

5432 

II3IOO 

1440 

Alcohol ' 

Carbon  disulphide 

Chloroform 

Ammonia 

Ether  

The  specific  heat  at  constant  pressure  for  any  temperature 
/  for  such  vapors  is  given  by  a  formula  of  the  form  (§  139) 
G  =  ^  +  2i?/  +  3C/«. 

The  constants  will  be  for  the  various  vapors,  if  /  is  the 
temperature  in  degrees  F. : 


b 

c 

d 

Steam 

0.99957333 
0.50954300 
0.2323140 
0.2305470 

0.000002222 
0.00056407 

0.00004555 
0.00002817 

0.0000000926 
0.000000617284 
0.0000000000 
0  00000000 

Alcohol 

Carbon  disulphide 

Chloroform  . .  .■ 

Ammonia 

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460 


HEA  T  AND   HEA  T-ENGINES, 


Substituting  the  corresponding  values,  the  mean  value  of 
C^  between  7",  and  T^  becomes 


Steam. 
Cp=    I 


Alcohol. 
0.954 


Garb.  Dis. 
0.257 


Chloroform. 
0.245 


Ammonia. 
1.229 


The  general  formula  for  the  weight  of  a  cubic  meter  of  a 
saturated  vapor  of  the  class  under  consideration  (§  141)  is 
given  by  the  formula 

-0=1  =  —tl-^ 
"       ^\       36.2  i^r/ 

in  which  6  is  the  density  of  the  vapor  referred  to  that  of  air> 
and  has  been  observed  for  the  vapors  in  question  to  be: 


when  the  calculations  are  made  .for  Z?,  and  D^  by  substituting 
in  the  formula.     Or  the  following  method  may  be  used. 

The  latent  heats  of  evaporation  per  kilogram  (§    140)  at 
any  temperature  t  is  given  by  a  formula  of  the  form 

r  =  a  —  bt  —  ct\ 

in  which  a^  b^  and  c  are  constants  having  the  following  values 
(reduced  to  British  units  from  the  corresponding  metric  values 
determined  by  Regnault): 


( 


Steam 

Alcohol 

Carbon  disulphide 

Chloroform 

Ammonia. ....... 


1121.7 
524.07 

164.57 
123.6 

555.5 


0.6946 

0.92211 

0.0716 

0.093 

0.613 


0.00002222 
—  0.000679 
0.0002746 
0.000282 
0.000219 


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VAPOR-ENGINES. 


461 


By  substitution  of  the  values  of  the  constants  a  series  of 
values  for  t^  and  /,  result  and  which  give  the  tabular  values 
for  Z,  and  Z,  (the  latent  heat  per  pound)  when  these  are 
multiplied  by  the  weights  per  pound  and  by  the  symbol  778 
ory  to  reduce  heat-units  to  foot-pounds.      Hence 


Steam 

Alcohol 

Carbon  disulphide. ... 

Chloroform 

Ammonia 


'•i  I  '•1  I  ^\ 

(Thermal  Units.)  (Thermal  Units.)    (Foot-pounds.) 


873.59 
288.19 
108 . 07 
58.92 
320.54 


978.44 

370.73 

140.34 

94.94 

428.34 


(Foot-pounds.) 


679653 
224216 

84077 

45S43 

249383 


761226 

28S428 

109188 

73867 

333246 


The  weight  of  one  cubic  foot  of  saturated  vapor  is  the 
ratio  of  the  latent  heats  per  pound  (Z)  to  the  latent  heats 
per  cubic  foot  (/),  or 

/ 


w  = 


The  latent  heats  per  cubic  foot  in  foot-pounds  are: 


A 

^ 

Steam 

1S6905 
381359 
259844 
136930 
2954108 

20553 
43791 
64970 
53353 
873561 

Alcohol 

Carbon  disulphide  . .. 
Chloroform 

Ammonia. .  • 

Combining  these  with  the  values  for  Z  above, 


7(1, 

(Weight  in  i  cu.  ft.) 

7(.3 

(Weight  in  i  cu.  ft.) 

Steam 

Alcohol 

0.275 
1. 701 
3.091 
2.978 
11.842 

0.027 
O.151 
0.595 
0.722 
2.621 

Carbon  disulphide  ... 
Chloroform  ....... ... 

Ammonia 

Digitized  by  VjOOQ IC 


462 


HEAT  AND    HEAT-ENGINES, 


308.  Efficiency  of  a  Volatile  Vapor  between  g^ivett 
Temperature  Limits.  —  The  simplest  case  will  be  the 
hypothesis  of  Carnot,  that  all  heat  is  imparted  at  the  high 
temperature  /,  and  withdrawn  at  the  lower;  the  expansion 
and  the  compression  adiabatic.  To  make  the  case  general, 
suppose  the  heat  Z,  to  produce  a  volume  v^  which  is  not  the 
unit  volume  whose  weight  is  Z>,.  Then  the  work  of  expan- 
sion will  become 

w=jcD,v, I r. -  r.(i  +  hyp. log  J|) I  +  L-SlL,-Y^^,, 

and  the  work  of  compression  will  be 

W'=JCD,v,  I  T,  -  7;(i  +  hyp.  log  ^)  |  +  p,v,. 

The  effective  work  will  therefore  be  what  the  previous 
discussions  of  Chapters  XIV  to  XIX  would  have  led  to  ex- 
pect, or 

(r.  -  7-,)  X  ^-  =  (r.  -  r.)  x  (0.  -  0.). 

Substituting  in  these  equations  their  values,  the  following 
tabular  solution  results: 


Heat  Medium. 


Water 

Alcohol 

Ether  

Bisulphide  of  carbon 

Chloroform 

Ammonia 


Work  of 

Work  of 

Difference 

Expansion, 

Compression, 

Effective 

Heat  used. 

Foot-pounds. 

Foot-pounds. 

Work. 

50323 

15932 

34391 

186905 

61043 

26652 

34391 

186905 

II5000 

80609 

34391 

186905 

64538 

30147 

34391 

186905 

71S43 

37455 

34391 

186905 

72222 

37831 

34391 

186905 

Efficiency, 
Per  Cent. 


18.4 
1S.4 
18.4 
18.4 
1S.4 
18.4 


In  discussing  the  above  it  will  be  noted: 
(i)  That  the    thermal  efficiency  of  all  the  media  when 
operated  within  the  same  limits  of  temperature  is  the  same. 


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VAPOK'ENGINES. 


463 


This  might  have  been  foreseen,  since  the  formula  indicates 
that  the  efficiency  is  independent  of  the  medium  used. 

(2)  The  amount  of  heat  required  to    evaporate  a  cubic 


iF>Uu«. 

, 

1=*?°°? 

1 1  1 

r: 1 

^- 

N- 

--4^ 

§  MOUO 

1 

\ 

_, 

. 

_ 

if  i  1 

I 

1 

\ 

]551UU0 

1 

\ 

IMCOO 

\ 

' 

i 

48U00 

1 

\ 

Wi 

J 

1      1 

\ 

4pOUp 

1 

C- 

-V-- 

- 

- 

"T 

Al  fohol- 

1      1 

\j 

42000 

[ 

1 

- 

- 

'f' 

- 

-^ 

^ 

, 

. 

Si 

Ipl 

- 

1  1 

\ 

I 

"l"' 

awop 

\ 

-< 

eijoi  >fc 

somoo  • 

Avi 

nir 

on 

a  Sea 

C. 

■cdu« 

'd 

V 

acuob 

IT' 

an 

d  gJvrn  l;y  hea 

^tV^ 

urc9. 

- 

~ 

._, 

- 

- 

J 

r 

AnimonJ 

1    I 

» 

V 

\ 

■i  1 

:, 

V 

axw) 

\ 

\ 

1    1 

y\ 

V 

^ 

1     1 

\ 

200000 

-^ 

1 

^;^ 

1  1 

- 

•:im 

tn\ 

f       1 

W'- 

¥ 

- 

_ 

1 

1  1 

Tt 

\ 

1 

^ 

■^. 

':i\LiX' 

m 

1 

K 

1 

1 

1    1 

ISOOO 

\ 

\ 

' 

1 

A 

\ 

1 

^"V 

1 

15000 

>>.^ 

^ 

\ 

... 

— 

\r'.;nOT>1a 

- 

■^ 

100000 

-Jlfl- 

x\\ 

1 

I?WJO 

i 

:¥ 

i 

.sao 

\ 

\  i 

^ku 

«^ 

1   1 

)  * 

1 

\^ 

^ 

•^ 

1 

1 

1 

G-jOO 

\ 

s 

^K 

M 

^ 

1 

1 

\ 

\ 

AlobhoN. 

i=*^ 

■-^ 

'^^ 

^^=-==: 

fej= 

^ 

!th 

er; 

}oao 

\_ 

Wnter 

"■ 

^1 

1    ^ 

U-< 

fc^ 

-^ 

- 

- 

0 

1 

1 

■ 

" 

T 

- 

15- 

- 

«-- 

M^ 

dv' 

— 

U 

-r^ 

^ 

^  — 

S. 

u.. 

-t 

Mil    Vol 

im 

U4- 

M" 

4"V 

V, 

_ 

Fig.  176. 

meter  of  water  at  7",  degrees  absolute  is  less  than  that 
required  to  evaporate  the  other  vapors  at  that  temperature. 
Note  the  values  for  Z,. 

(3)  Note  also  the  values  for  Z,.     The  water  in  expanding 


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464  HEAT  AND   HEAT-ENGINES. 

has  given  up  more  of  its  heat  in  doing  work  down  to  the 
temperature  7",  than  has  been  given  by  the  others.  In  other 
words,  water  has  done  the  same  amount  of  effective  work  as 
the  others,  and  has  left  a  less  quantity  of  heat  to  be  taken 
care  of  by  the  condensing  water. 

(4)  The  pressure  of  the  vapor  of  water  at  the  temperature 
Zj  is  much  less  than  that  of  the  other  vapors.  Hence  the 
others  require  much  more  massive  castings  and  greater 
strength  in  all  parts  to  withstand  the  strain  than  are  needed 
for  the  steam-engine,  and  yet  they  do  no  more  effective  work 
in  the  same  range.  This  pressure  range  for  the  same  tem- 
perature range  is  shown  most  clearly  in  the  plotted  diagram 
(Fig.  176),  which  shows  equal  work  areas,  but  with  very 
different  values  for/^  and  v^. 

(5)  The  same  diagram  shows  also  the  inconvenient  losses 
from  excessive  back-pressures  with  the  vapors  other  than 
water,  which  back-pressures,  as  above,  can  only  be  mitigated 
by  a  use  of  inconvenient  volumes  of  condensing  water  at  a 
low  temperature,  as  will  be  referred  to  hereafter. 

(6)  The  component  works  of  expansion  and  compression 
differ  very  widely,  while  having  a  constant  total  difference. 
The  discussion  is  therefore  inconclusive  in  so  far  as  any  effect 
of  varying  interchange  of  heat  with  the  cylinder-walls  may  be 
introduced  by  these  differing  states  of  the  medium,  in  its 
cycle. 

(7)  The  diversity  in  pressure  range  for  the  same  tempera- 
ture range  turns  the  thoughts  to  the  possibility  of  a  species 
of  compounding  with  two  media  in  series.  This  will  be 
referred  to  again. 

309.  Efficiency  of  a  Volatile  Vapor  between  given 
Pressure  Limits. — The  difficulties  of  the  preceding  proposi- 
tions with  respect  to  pressure  make  it  desirable  to  examine 
the  action  of  volatile  vapors  when,  the  convenient  pressures 
which  would  prevail  in  an  ordinary  engine  are  set  as  the 
limits,  and  the  temperature  limits  are  determined  by  these 


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VAPOR-ENGINES, 


465 


limiting  pressures.  It  will  result  that  while  the  same  formulae 
will  apply  as  in  the  previous  paragraphs,  the  quantities  will 
differ  because  of  the  different  values  for  the  temperatures. 
Let  the  same  initial  temperature  be  chosen  corresponding  to 
120  pounds  pressure  for  steam,  and  the  terminal  pressure 
correspond  to  that  in  a  condenser  kept  at  10  pounds  above 
vacuum.  Making  the  computations  as  before  gives  the  fol- 
lowing tabular  result: 


Vapor. 


HaO 

CaH.O 

CS, 

CHCl. 

NH, I 

C4H,oO 


341.60 
286.34 
275.34 
295-34 
66.34 

66.34 
231.34 


T'l 


194.00 
158.34 
94-34 
125-34 
-  41.66 

39-34 
141.34 


104 
104 
104 
104 
104 

39-34 
104 


802.26 
747.00 
736.00 
756.00 
527.00 
527.00 
692.00 


654.66 
619.00 
565.00 
586.00 
419.00 
500.00 
602.00 


Vapor. 


H.O 

CH.O 

CSa , 

CHCl, 

NH, I 

<:4H.„o 


/l 

/t 

/• 

^1 

L^ 

'  17408 

1469 

152 

186905 

20553 

17408 

1469 

375 

199649 

20992 

17408 

1469 

1717 

135730 

15586 

17408 

1469 

920 

114109 

18786 

17408 

1469 

33020 

166700 

17726 

17408 

10406 

10406 

166700 

10648 

17408 

1469 

2530 

146542 

564.66 
564.66 
564.66 
564.66 

564 . 66 
500.00 
564.66 


1. 000 

0.859 
0.249 
0.242 
1. 000 
1. 000 
0.579 


Lbs.   Vapor    necessary 
to  produce  i  H.  P.  per 
Hour  between  120  lbs. 
and  10  lbs.  Pressure. 

Vapor. 

M 

w 

If 

E 

W 

HaO 

1. 000 

49084 
57222 
35109 
37617 
-254827 

8579 
29108 

237739 
31 1249 
182255 
186359 

-154483 
306812 

226734 

20.64^ 

18.38 

19-27 

20.13 

165.00 

2.87 

12.  84 

11.44 
30.48 
89.24 

78.15 

CaH.O 

cs, 

1. 193 
1.484 
1. 135 
-0.204 
1.033 
4.877 

CHC13 

NH, 1 

<:4H,oO 

90.30 

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466 


HEAT  AND   HEAT-ENGINES. 


The  figure  of  165  for  the  ammonia  vapor  is  the  result  of 
the  unpractical  assumption  which  makes  the  condenser  pres> 
sure  greater  than  that  of  the  boiler.  Hence  a  second  engine 
worked  by  the  condenser  will  be  required  to  operate  the 
engine  imagined,  and  the  figure  belongs' to  the  supplementary 
engine.  The  second  ammonia  line  belongs  to  the  supposi- 
titious case  of  an  engine  operated  with  condensing  water  at 
39""  F.  This  is  not  obtainable  except  by  climatic  accident  or 
by  use  of  mechanical  refrigeration. 

It  will  therefore  appear  from  the  above : 

(i)  The  rival  for  steam  in  theoretical  efficiency  is  chloro- 
form only,  which  requires  nearly  eight  times  the  weight  of 

PRESSURES. 
^^    ^^  c^' 

Sg  H  s§ 


Fig.  177. 

medium  per  horse-power  per  hour  and  must  be  operated  in  a 
cylinder  of  one  and  one-quarter  times  the  volume — both 
tending  to  obliterate  the  small  gain. 

(2)  This   comparison    is    distinctly   unfair   to   the   vapors 
other  than  steam,  and  makes  them  show  at  a  disadvantage- 


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VAPOR-ENGINES. 


467 


This  is  made  clear  by  plotting  the  work-diagram  for  the 
vapors  as  in  Fig.  177.  Both  ether  and  bisulphide  of  carbon 
are  expanded  below  the  line  of  back-pressure,  or  more  than 
completely. 

310.  Effect  on  Efficiency  of  Volatile  Vapors  from  Ad- 
justing Final  Pressure  and  Expansion  Ratio. — If  the  back- 
pressure be  fixed  by  a  convenient  adjustment  of  the  condens- 
ing water  in  amount  or  temperature,  a  more  favorable  pro- 
portioning of  the  ratio  of  expansion  may  be  made  for  certain 
of  the  vapors,  so  as  to  have  their  final  pressures  so  adjusted 
to  the  initial  pressure,  which  has  been  fixed  as  in  the 
preceding  case,  that  no  loop  occurs.  This  alters  the  final 
volume  of  the  expanded  vapor,  or  it  may  be  effected  by 
letting  the  final  pressure  be  increased  by  such  a  quantity  as 
will  obliterate  the  loop.  Keeping  then  the  same  initial 
pressures,  but  increasing  the  finals  (/,),  the  work  will  vary 
slightly,  without  a  variation  in  the  heat  expenditure,  and  a 
change  of  thermal  efficiency  will  follow.  The  values  in 
metric  units  as  presented  by  Gantt  and  Maury  for  this  case 
give: 


Medium. 


/l 

/« 

w 

H 

E 

84518 

7043 

267705 

1330639 

20.12 

84518 

7358 

262614 

1465207 

17.92 

84518 

I7I90 

162869 

1094722 

14.88 

84518 

15844 

162875 

878729 

18.53 

84518 

I02I4 

219200 

I I 36084 

19.29 

Vo 


olume. 


Water 

Alcohol 

Ether  

Carbon  bisulphide 
Chloroforra 


I 

I -035 
.845 
.756 
.944 


This  table  shows  steam  to  have  an  advantage  in  thermal 
efficiency  and  in  weight  per  horse-power  per  hour  over  all  the 
vapors,  but  not  in  cylinder  volume;  it  should  also  be  remem- 
bered that  the  less  efficiencies  in  this  case  as  compared  with 
that  of  the  preceding  paragraph  are  to  be  offset  against  the 
losses  from  the  higher  values  for  r  in  that  case.     Such  losses 


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468 


HEAT  AND   HEAT-ENGINES. 


are  probably  the  result  of  condensation  at  the  higher  ratios^ 
and  of  friction.  Fig.  177  shows  the  change  in  diagram  which 
results  when  the  foregoing  changes  of  condition  are  imposed 
and  a  more  eflfective  adjustment  of  condition  is  made. 

311.  Effect  on  Efficiency  of  Certain  Vapors  by  an  In- 
crease in  the  Pressure  Range. — Combining  the  results  of  the 
last  paragraph  with  the  computations  of  §  307,  so  that  the 
temperature  limits  of  a  condensing  engine  are  used  without 
a  complete  expansion  down  to  the  condenser  temperature 
with  the  attendant  heat-losses  from  the  cylinder-walls,  another 
set  of  values  are  derived.  This  may  be  done  first  with  con- 
ditions assumed  most  favorable  to  the  steam-engine,  as  in 
§  308,  and  then  with  respect  to  getting  more  favorable  con- 
ditions for  some  or  all  of  the  other  vapors,  as  in  §  309. 

The  first  alternative  will  be  applied  as  in  §  307,  with 
initial  temperatures  of  172°  C,  final  temperatures  of  90°  C, 
and  a  condenser  temperature  of  40°  C.  or  105®  F.,  which  is 
as  low  as  can  be  conveniently  secured  for  the  year  round  in 
the  temperate  zone.      For  this  case  the  final  results  are: 


Medium. 

Work. 

Heat. 

Efficiency. 

Kilograms 
perK.  P. 
per  Hour. 

Cylinder 
Volume. 

Water 

267705 
525086 
751821 
360878 
376517 

1330639 

2894904 
4447823 

1798275 
2002139 

20.12 
18.14 
16.90 
20.07 
18.81 

5.19 
13.13 
28.64 
34.41 
42.06 

J 

Alcohol 

.488 
.232 
.314 
.396 

Ether  

Carbon  disulphide 

Chloroform 

If  the  second  alternative  be  chosen,  and  the  conditions  so 
adjusted  to  the  qualities  and  properties  of  the  vapors  as  to 
reproduce  under  this  assumption  the  same  back-pressure 
values  as  were  used  in  §  309,  then  the  final  results  are 
further  improved  foi  the  volatile  vapors  as  given  in  the 
following  table : 


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VAPOK-ENGINES. 


469 


Medium. 

/i 

w 

// 

E 

F 

M 

Waiter 

Alcohol 

Ether 

84518 
'7043 
164600 

7358 
31S970 

267705 
62297S 
98S752 
428486 
462834 

1330639 
2894904 
4447823 

1798275 
2002139 

20.12 
21.52 
22.23 
23.83 
23.12 

5.19 
11.07 
21.78 
28.98 
34.21 

I 
.853 

Bisulphide  of  carbon 
Chloroform 

17190 
179230 

15844' 
145720 

10214 

•535 
.550 
.761 

PRESSURES. 

^H        a^i"        «rS 
osLj        if(->         uiV 

«a      '^S       0-2' 

i^   ii   U 

340,000-r 
380.000- 

soo.ooo-j 

.280,000 
200,000 
210.000 -j 
820.000 

aoo.ooo 

180.000 
100.000 1 
140,000 
120.000 1 
100.000 

80,000 

80,000 

40,000 

:!0.000t 


Fig.  178. 
The  indicator-diagram  for  this  set  of  conditions  is  shown 
in   Fig.  178  and  presents  the  same  pecuh'arities  as  to  exces- 
sively high  pressures  for  the  other  media  than  steam,  to  which 


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470 


HEA  r  AND   HEA  TENGJNES. 


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VA  POR  ENGINES,  47 1 

reference  has  already  been  made.  The  table  shows  the 
<iirection  in  which  efficiencies  superior  to  that  of  steam  are  to 
be  sought'  but  if  this  thoroughfare  is  closed,  then  the  volatile 
vapors  must  be  recommended  for  reasons  other  than  their 
superior  thermal  efficiency  or  their  economy  in  fuel  per  horse- 
power  per  hour. 

In  comment  on  the  figures  it  should  be  added  that  con- 
densation during  expansion  or  initial  condensation  (§  224) 
would  increase  the  weight  of  vapor,  except  where  it  was  used 
in  a  superheated  state 

If  the  steam  is  to  be  used  without  condensation,  as  in 
ordinary  non-condensing  engines  expanding  down  to  atmos- 
pheric pressure  only,  then  the  other  media  show  to  a  little 
better  advantage.  The  table  on  page  470  computed  by  Prof. 
D.  S.  Jacobus  presents  the  data  belonging  to  this  assumption : 

The  conclusion  safely  to  be  drawn  from  this  table  is  that 
if  the  comparison  made  with  steam  under  a  condition  least 
favorable  to  its  economy  shows  so  little  margin  of  advantage 
over  the  other  vapors,  there  must  be  great  advantages  for 
them  yet  to  be  revealed  if  they  are  to  be  considered  for  large- 
scale  work, 

312.  Usual  Vapor  Media.  Their  Disadvantages. — 
The  foregoing  paragraphs  have  enumerated  the  most  fre- 
quently tried  of  the  volatile  vapor  media.  A  list  which 
should  not  omit  some  available  ones  would  be  perhaps  hard 
to  make.     It  should  include,  however: 


Ammonia (NH$) 

Ether (C4H.0O) 

Carbon  disulphide..  (CSi) 

Chloroform (CHCl,) 

Naphtha (C,H,4-  C.Hia) 


Gasoline <  . . . .  (C.Hm—CtHi.) 

Carbonic  acid  gas . .  (COt) 

Acetone (CsH«0) 

Alcohol....- (CH.O) 

Tetrachloride  of  carbon  (CCI4) 


These  have  been  tried  or  proposed  separately,  or  in  com* 
bination  with  steam,  or  even  with  each  other. 

The  advantages  to  be  urged  for  them  are  those  consequent 
upon  the  lowered  intensity  of  the  source  of  heat  to  change 


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472  HE  A  T  AND   HE  A  T  ENGINES. 

them  into  vapors  with  considerable  tension.  It  therefore 
becomes  possible  to  use  a  species  of  retort  of  small  weight 
and  bulk,  within  which  a  small  weight  of  the  medium  can  be 
injected  at  each  stroke,  to  be  at  once  volatilized  and  raised 
in  tension,  and  to  be  worked  in  the  working  cylinder.  This 
cannot  well  be  done  with  steam,  because  the  high  temperature 
of  such  a  **  spray-boiler ' '  for  steam  would  result  in  its  rapid 
corrosion  and  failure  from  deterioration  of  structure.  There 
is  therefore  no  reservoir  of  accumulated  heat  energy  as  in  a 
steam-boiler,  and  its  weight  and  bulk  are  avoided.  Working 
pressure  is  promptly  secured. 

On  the  other  hand,  the  disadvantages  of  these  vapors, 
beside  those  already  enumerated  in  the  preceding  calculations, 
are  those  which  result  from  their  comparison  with  steam. 

(i)  They  have  to  be  bought  and  paid  for. 

(2)  They  require  to  be  operated  as  condensing  engines, 
and  demand  a  large  body  of  cooling  water. 

(3)  Some  are  inflammable,  and.  their  vapor  mixed  with  air 
is  explosive. 

(4)  Some  are  irrespirable,  or  produce  unpleasant  effects  if 
inhaled,  upon  the  human  frame. 

(5)  Some  have  an  odor,  pungent  or  even  offensive. 

(6)  Leakage  must  therefore  be  prevented  at  stuffing-boxes 
and  elsewhere,  by  the  use  of  a  double-chambered  construc- 
tion, which  is  costly  and  troublesome. 

(7)  Some  act  corrosively  upon  metals,  either  alone  or  in 
combination  with  air  or  water. 

An  interesting  computation  under  the  second  objection 
has  been  made  which  shows  that  with  most  of  the  vapors,  to 
maintain  a  back-pressure  of  one  atmosphere  only,  an  amount 
of  water  is  required  which  is  one  half  of  that  which  would 
maintain  a  27-inch  vacuum  with  steam.  So  that,  in  cities 
where  condensing  water  is  metered  and  taxed  at  a  rate  of 
$1.50  per  thousand  cubic  feet  required,  the  vapor-engine 
requires  an   expense   for  water  equal  to  that    for   its   fuel. 


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VAPOR-ENGINES.  47? 

Unless  the  saving  in  fuel  more  than  offsets  this  increased 
water  cost,  or  unless  the  vapor-engine  is  to  be  run  in  places 
where  condensing  water  is  available  without  cost,  the  steam 
will  show  commercially  at  an  advantage. 

313.  Naphtha  and  Gasoline-engines.  —  The  use  of 
naphtha  in  small  launches  instead  of  steam  has  been  of  con- 
sideiable  extent  and  interest  in  recent  naval  and  pleasure- 
boat  practice.  Liquid  naphtha  stored  in  bulkhead  tanks  in 
the  hull  of  the  boat  is  used  as  fuel  when  mixed  with  air  to 
heat  a  retort  within  which  the  pure  naphtha  liquid  is  vapor- 
ized, expanded,  and  brought  to  a  high  tension  by  the  external 
heat.  The  vapor  operates  then  in  the  engine,  and  is  exhausted 
into  a  keel  condenser,  a  coil  of  pipes  outside  the  hull,  and 
along  the  garboard  strakes  under  the  water.  The  machine 
starts  by  giving  a  few  strokes  to  a  hand  air-pump  to  generate 
the  naphtha-gas  in  the  furnace,  and  by  injecting  by  a  second 
pump  a  small  charge  into  the  retort  As  soon  as  the  pressure 
generated  in  the  retort  will  drive  the  engine  to  compress  the 
air  for  the  furnace-gas,  the  compression  of  the  air  and  the 
injection  of  liquid  naphtha  become  automatic,  and  the 
process  becomes  continuous.  The  valves  on  the  two  naphtha 
circuits  control  pressure  and  therefore  speed.  The  fuel- 
naphtha  is  the  only  supply  which  becomes  exhausted,  as  the 
motor  flu'd  operates  in  a  closed  circuit.  The  naphtha  motor 
weighs  but  100  pounds  per  horse-power  in  the  smaller  sizes, 
down  to  75  pounds  per  horse  power  in  the  larger,  which  is  to 
be  offset  against  the  combined  weight  of  engine  with  its 
boiler  and  contents  in  the  steam-yacht.  The  objection  is  the 
difficulty  from  having  no  reserve  of  energy  in  store  on  which 
to  draw  under  unfavorable  conditions  of  wind  or  waves. 
Fig,  179  shows  a  section  of  a  naphtha-launch  engine. 

Yarrow  &  Co.  state  that  the  volume  of  vapor  with  naphtha 
in  their  launches  produces  \  the  volume  which  would  be  given 
by  steam  at  atmospheric  pressure.  A  36-foot  launch  with 
8-foot  beam,  weighing  with  its  machinery  and  fuel-supply  one 


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474 


HEA  T  AND   HE  A  T- ENGINES. 


ton,  will  run  8  miles  per  hour  in  still  water  and  can  cany 
fuel  for  200  miles  if  necessary.  One  and  one  half  gallons  per 
hour,  or  one  third  gallon  per  horse-power  per  hour,  will  be 


Fig.  179. 

consumed  in  the  furnace,  and  allowance  for  leakage  and  waste 
must  be  added. 

314  Binary  Vapor-engines. — The  experimenters  with 
vapors  however,  have  usually  preferred  to  retain  the  steam- 
generator  or  boiler  as  a  means  for  the  convenient  transfer  of 
heat  to  the  volatile  vapor  they  were  to  use  as  a  motor  fluid. 
This  principle  has  been  used  with  the  ether-engine,  the 
ammonia-engine,  and  the  bisulphide-of-carbon  engine.  The 
scheme  is  illustrated  in  Fig.  180  as  applied  to  a  bisulphide 
engine.  5  is  the  ordinary  steam-boiler  supplying  heat 
through  the  pipe  P  to  the  generator  AB.     Condensed  steam 


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VA  POR'ENGINES. 


475 


from  this  generator  is  returned  by  a  small  feed-pump  /. 
Within  the  generator  ^5  is  the  closed  chamber  C  holding  the 
volatile  liquid,  ammonia,  ether,  or  whatever.  The  heat  of 
the  steam-jacket  vaporizes  the  volatile  motor  fluid,  which 
passes  through  the  pipe  E  to  the  motor-C5/linder  F.  Ex- 
hausting thence  into  the  surface  condenser  G  with  its  provi- 


•s^ 


Fig.  180. 

sions  for  circulating  water  through  pipes  or  tubes  within  it  to . 
bring  the  motor-vapor  back  to  a  liquid,  the  latter  is  returned 
to  C  by  the  feed-pump  h.     The  two  circuits  are  closed  and 
distinct   from   each   other.     No   additional   charge   of  either 
fluid  is  required  except  to  replace  leakage  losses. 

The  other  form  of  the  binary  plan  is  to  add  a  vapor 
motor-cylinder  to  the  steam  motor-cylinder  and  have  the 
two  cylinders  drive  the  shaft  as  in  the  compound  steam- 
engine.  The  difference,  however,  is  that  the  exhaust  from 
the  less  volatile  medium  is  made  to  pass  through  tubes  or 
between  thin  plate  surfaces  on  whose  other  side  is  the  more 
volatile  fluid.  The  tube  or  plate  surface  is  a  condenser  for 
the  hotter  fluid,  and  the  boiler  for  the  more  volatile  one. 
The  vapor  is  heated  by  the  heat  from  the  exhaust-steam  of 
the  first  cylinder,  and  acquires  tension  to  act  to  'drive  the 
piston  in  the  vapor-cylinder.  From  this  vapor-cylinder  the 
vapor  must  pass  to  a  condenser  with  abundance  of  cold  circu- 


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476  HEAT  AND   HEAT-ENGINES, 

lating  water,  to  be  from  thence  pumped  back  into  the 
generator  to  be  used  anew  in  circuit.  This  is  the  method 
used  by  Du  Trembley  (1842)  with  ether,  and  by  Ellis  (1872) 
with  carbon  bisulphide. 

By  the  first  plan  no  advantage  is  reaped  from  a  saving  of 
furnace-losses  in  the  boiler;  by  the  second  plan,  if  the  steam- 
engine  were  a  wasteful  one,  some  advantage  might  follow 
from  utilizing  its  wastes  to  evaporate  the  second  fluid.  If  it 
had  no  wastes,  there  should  not  be  heat  enough  available 
after  exhaust  to  make  the  subsequent  cylinder  worth  while, 
and  a  loss  in  transfer  of  heat  is  unavoidable,  since  the  im- 
parting body  must  be  hotter  than  the  recipient.  Nearly 
3000  horse-power  were  aggregated  in  vessels  on  the  Medi- 
terranean service  using  Du  Trembley*s  ether-engines  before 
the  introduction  of  the  compound  steam-engine,  but  no  care 
could  prevent  escape  of  the  vapor,  and  fire  and  other  dis- 
asters followed. 

315.  Wellington  Series  Vapor  Motor. — In  the  spring  of 
1897  announcement  was  made  that  the  late  Mr.  Arthur  M. 
Wellington  of  New  York  had  been  giving  earnest  study 
previous  to  his  death  in  1895  to  the  problem  of  extending  the 
Du  Trembley  principle  to  the  working  of  several  motors  in 
series  with  successively  more  easily  vaporizable  media  as  the 
lower  end  was  neared.  Starting  with  steam  as  having  the 
greatest  absorptive  capacity  for  heat  in  the  first  cylinder,  the 
exhaust  was  to  pass  into  a  special  chamber  of  thin  plate  cells, 
within  which  it  should  be  cooled  in  the  process  of  giving  its 
heat  to  the  next  medium,  which  was  to  be  found  on  the  other 
side  of  the  separating  metal  walls  of  the  chamber.  The 
cellular  chamber  was  therefore  a  boiler  or  heater  for  the 
second  medium,  while  a  condenser  for  the  first.  The  second 
cylinder,  operating  with  the  second  medium,  exhausted  into 
a  second  condenser-heater  for  the  third  medium,  and  so  on 
to  the  last  medium,  which  was  condensed  by  cold  water 
when  the  descent  down  temperature  had  gone  as  far  as  it 


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VAPOR  ENGINES. 


A77 


was  practicable  to  carry  it.  The  fundamental  idea  is  to  work 
«ach  medium  within  the  limits  of  temperature  range  for  which 
it  is  best  adapted,  and  to  transfer  the  heat  from  medium  to 
medium  by  most  effective  contact  methods  of  transfer.  The 
principle  is  that  of  compounding  by  temperature  but  not  by 
pressure,  since  the  media  are  isolated  in  separate  circuits,  and 
do  not  act  as  back-pressures  to  those  preceding  it.  The  cylin- 
der volumes  will  be  proportioned  for  the  pressure  range  belong- 
ing to  the  temperature  range  within  which  the  medium  works. 


c 

CONDENSERS 

Fig.  194. 

Fig.  194  will  illustrate  such  a  series  engine  both  in  the 
•continuous  system  for  one  or  a  few  media  and  in  the  succes- 
sive system  for  a  large  number  of  media  of  varying  properties. 

Mr.  Wellington  also  designed  and  patented  efficient  trans- 
ferring appliances  for  the  transfer  of  heat  between  the  media, 
but  his  engine  has  never  been  built  beyond  an  experimental 
stage.  It  is  open  to  the  practical  disadvantages  of  the  meciia 
which  it  uses,  and  it  is  further  fair  to  call  attention  to  the 
•difficulties  which  the  series  principle  involves. 


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47^  HEAT  AND  HEAT-ENGINES. 

The  object  of  the  series  plan  is  analogous  to  that  of 
compounding  below  the  low-pressure  cylinder  in  the  steann- 
engine.  To  enable  the  designer  to  use  a  warmer  temperature 
or  a  less  volume  of  condensing  water  or  a  less  bulk  of  con- 
denser, the  second  medium  is  intercalated  between  the 
medium  of  higher  heat  potential  and  the  condenser.  The 
purpose  is  to  diminish  the  inconveniences  attaching  to  con- 
siderable transfers  of  heat  in  a  short  interval  of  time.  On 
the  other  hand,  as  the  number  of  transfers  is  increased,  it 
must  be  remembered  that  there  is  a  loss  at  each  step  in  prac- 
tice, because  in  order  that  the  transfer  may  take  place  in 
reasonable  time,  or  with  reasonable  surface  and  weights  of 
metal,  there  has  to  be  a  difference  of  temperature  between 
the  hotter  and  cooler  body.  This  is  found  in  successive 
refrigerative  processes  to  be  conveniently  allowed  to  reach 
35°.  Hence  there  is  increased  loss  as  the  number  of  such 
transfers  is  increased.  Furthermore,  Fig.  i8i  shows  the  tem- 
perature-entropy diagram  of  a  four-series  engine  in  which  the 
line  15-16  is  fixed  by  the  coolest  available  condensing  water, 
and  the  area  of  heat  rejected  from  the  media  above  it  gives 
the  area  of  heat  energy  available  for  each  successive  medium. 
The  shaded  areas  are  separated  by  vertical  spaces  which 
represent  the  losses  in  transfer,  and  each  rectangle  is  made 
wider  as  the  succession  moves  down  temperature,  because 
with  less  value  for  T'the  factor  0  should  be  greater  to  pro- 
duce a  given  area.  While  each  medium  is  assumed  to  act  in 
a  Carnot  cycle,  yet  an  enveloping  line  which  would  give  a 
summation  of  the  areas  would  inclose  a  less  area  than  if  the 
hottest  medium  had  been  used  alone  within  the  same  tem- 
perature limits.  The  Carnot  standard  maximum  efficiency 
assumes  the  entropy  change  to  take  place  at  the  highest  and 
lowest  temperatures  respectively.  Hence  while  the  series 
principle  is  defensible  in  theory,  its  practical  difficulties  as  to 
size,  weight,  and  cost  of  transfer  apparatus  usually  more  than 
offset  the  possible  advantage. 


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VAPOR-ENGINES. 


479 


•a- 


Hi 


:Sflt 


J? 


Bi 


13 14 


p     E 


Fig.  181 


An  interesting  combination  of  the  series  principle  has  been 
suggested  wherein  a  gas-engine  and  a  steam-engine  are 
operated,  so  that  the  rejected  heat  from  the  gas-engine  shall 
be  used  to  make  steam  for  the 
second  cylinder.  It  is  a  ques- 
tion whether  the  gas-engine  re- 
jects heat  enough  to  make  this 
a  practically  utilizable  combina* 
tion  when  the  steam  cylinder  is 
to  be  of  any  size.  It  would 
form  an  interesting  computation 
for  which  there  is  no  present 
opportunity. 

The  commercial  obstacle  to 
the  series  principle  must  not 
be  overlooked.  The  bulk  and  weight  of  the  series  of  cylin- 
ders and  condensers  makes  an  interest  cost  for  the  plant  which 
causes  a  serious  inroad  into  its  possible  fuel  economy.  The 
Wellington  series  was  proposed  as  far  back  as  1872,  in  the 
Transactions  of  the  Polytechnic  Club  of  New  York  City,  by 
Mr.  T.  D.  Stetson. 

316.  Ammonia-vapor-engines. — Ammonia  is  employed 
usually  like  the  bisulphide  of  carbon  by  steam  vaporization  in 
a  closed  circuit.  It  can,  however,  be  used  in  a  sort  of  absorp- 
tion circuit,  by  causing  the  expanded  ammonia-gas  to  meet 
a  spray  of  ammoniacal  water  which,  when  cool,  will  absorb 
the  ammonia-vapor.  The  latter  can  be  separated  as  a  gas  on 
moderate  heating,  and  can  be  condensed  by  cooling,  or  by 
cooling  and  compression,  for  use  over  again.  This  latter  prin- 
ciple is  rather  along  the  line  of  the  convenient  storage  of  energy 
than  that  of  the  availability  of  ammonia  as  a  heat  medium. 
Where  ammonia  has  been  tried  as  a  medium  for  naval  uses 
it  has  been  found  to  offer  no  advantages  over  steam. 

317.  Combined-vapor-engines.  iEro-steam  Engines. — 
In  all  the  foregoing  discussion  of  volatile  heat  media  which 


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4^  HEAT  AND   HEAT-ENGINES, 

have  to  be  purchased  in  the  market  the  necessity  for  con- 
densation IS  rigorous,  and  the  consequent  presence  of  the 
necessary  cooling  water.  Where  the  facih'ties  for  condensa- 
tion cannot  be  had  it  has  been  proposed  to  combine  air  and 
steam,  and  lift  the  efficiency  of  the  latter  by  mixing  with  it 
the  air,  whose  efficiency  is  calculated  as  greater  than  that  of 
steam.  This  has  been  done  in  two  general  ways.  Air  under 
pressure  from  a  pump  has  been  forced  into  the  steam-pipe, 
so  that  the  cylinder-charge  was  of  nearly  equal  proportions  of 
steam  and  air  (Mont-Storm's  **Cloud  **  Engine,  1850-1881),  or 
'the  more  satisfactory  plan  may  be  followed  of  drawing  hot  air 
and  gases  from  the  flues  and  injecting  them  into  the*  steam- 
space  of  the  boiler  (Warsop's  and  Wethered's  methods). 
The  effect  of  the  hot  air  is  to  raise  the  temperature  of  the 
mixture  without  a  corresponding  rise  in  pressure,  producing 
the  equivalent  of  a  superheating  of  the  steam  and  lessening 
cylinder  condensation  (§§  132  and  229).  Some  loss  of  heat 
in  the  chimney-gases  is  also  prevented,  but  the  presence  of 
x:orrosives  in  the  products  of  combustion  with  most  fuels, 
made  active  by  the  reactions  with  hydrogen  and  at  high  tem- 
peratures, is  likely  to  attack  the  metal  of  the  engine. 

The  improved  economy  of  modern  steam-engines,  using  the 
higher  steam-pressures  and  the  principle  of  continuous  expan- 
sion, have  enabled  as  good  results  to  be  secured  with  steam 
alone  as  with  the  aero-steam  combination  as  it  has  been  used. 

318.  Storage  of  Energy  in  Liquefied  Vapors. — The  use, 
as  motor  fluids,  of  elastic  media  which  can  be  compressed  to 
liquids  by  mechanical  means  furnishes  a  compact  and  effective 
way  of  storing  such  energy  for  transport.  Carbonic  acid  has 
been  so  used  since  1823,  and  the  use  of  what  is  called  liquid 
air  is  now  proposed.  It  must  be  remembered,  however,  that 
there  is  to  be  derived  from  the  expansion  of  such  mechani- 
cally compressed  gases  only  the  energy  which  was  stored  in 
them,  less  the  heat  withdrawn  in  cooling  them  to  their  state 
of  stationary  temperature  in  accord  with  their  surroundings. 


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VAPOR-ENGINES.  4  8 1 

Unless  reheated  when  used,  their  expansion  and  vaporization 
withdraws  heat  from  their  surroundings  to  an  inconvenient 
extent,  and  in  the  case  of  carbonic  acid  or  other  gases  which 
have  a  cost  outside  of  the  labor  and  fuel  cost  of  compression, 
they  are  of  significance  only  where  expense  is  of  less  moment 
than  some  other  object  attained  by  their  use.  Compressed 
air  at  high  tensions  will  usually  meet  these  requirements  more 
satisfactorily  than  the  liquefied  gases. 

319.  Conclusion. — It  has  been  the  intention  that  the 
reader  and  student  shall  derive  from  this  chapter  the  conclu- 
sion that  the  vapor  of  water  is  the  most  effective  of  the 
various  heat  media  when  a  balance  is  struck  with  respect  to 
its  advantages  in  competition  with  the  others,  unless  certain 
extraordinary  conditions  are  imposed  as  to  weight  or  some 
other  feature.  It  was  intended  that  from  the  chapter  on  the 
gas-  or  oil-engine  the  conclusion  should  be  derived  that  the 
use  of  these  motors  will  extend  more  and  more  into  fields  now 
occupied  by  steam.  Hence  the  gas-  and  the  steam-engine 
are  the  two  most  important  motive-power  factors  where 
available  energy  from  falling  water  is  not  at  hand  by  electrical 
transmission  or  otherwise. 

With  the  completion  of  this  chapter  the  subject  of  heat 
and  heat-engines  as  laid  out  by  the  author  for  study  and  dis- 
cussion is  completed.  It  is  intended  that  this  treatment 
should  be  regarded  only  as  the  beginnings  of  the  subject, 
and  as  leading  to  the  mathematical  discussion  of  thermody- 
namics as  a  deductive  science  from  its  differential  equations. 
For  such  treatment  the  reader  is  referred  to  other  treatises. 
The  concluding  chapters  are  convenient  addenda  having  an 
obvious  connection  with  the  principal  purpose  of  the  book. 


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CHAPTER   XXII. 
MECHANICAL   REFRIGERATION. 

325,  Introductory. — In  the  preceding  chapters  the  object 
sought  has  been  to  liberate  heat  energy  from  fuel  or  other 
sources  of  heat,  and  to  utilize  this  energy  for  industrial  pur- 
poses in  the  form  of  mechanical  work.  The  purpose  of  the 
present  chapter  is  to  consider  the  converse  of  this.  Having  a 
store  or  supply  of  heat  energy  either  in  the  form  of  sensible 
or  observable  heat-units,  or  in  the  derived  form  of  mechanical 
energy,  it  is  sought  to  dispose  of  that  energy  in  both  forms, 
so  that  for  equalization  of  heat  condition  a  draft  shall  be 
made  upon  the  store  of  heat  energy  in  objects  or  places  under 
their  usual  conditions.  The  result  of  this  draft  or  lowering 
of  the  heat  condition  of  an  object  or  a  place  is  what  is 
generally  recognized  as  the  production  of  cold.  It  has  been 
most  aptly  called  a  process  of  **  heat-pumping.**  By  the 
expenditure  of  mechanical  energy  upon  a  convenient  and 
well-chosen  heat  medium  its  condition  as  to  temperature 
alone,  or  as  to  both  temperature  and  entropy  is  lowered 
towards  that  represented  by  the  absolute  zero  of  temperature, 
just  as  the  level  of  water  in  a  vessel  is  lowered  by  expending 
through  a  pump  the  energy  necessary  to  draw  water  out  of  it. 

The  process  of  expanding  a  heat  medium  in  an  engine 
from  a  high  temperature  T^  to  a  lower  one  T^  is  a  process  of 
mechanical  refrigeration.  It  is,  however,  only  when  this 
process  is  so  located  on  the  temperature  scale  that  the  drop 
down  the  scale  begins  at  the  normal  temperatures  and  pro- 
ceeds below  the   usual  limits  for  the  climate  and  the  zone 

482 


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MECHANICAL   REFRIGERATIOX. 


485- 


where  it  takes  plaice  that  the  term  refrigeration  is  properly 
used.  This  will  suggest,  however,  the  methods  which  are 
used  in  refrigerating  cycles. 

While  in  heat-engine  practice  the  medium  to  be  used  is 
chosen  with  a  view  to  its  heat-carrying  capacity,  in  refrigera- 
tion it  will  be  chosen  with  a  view  to  its  willingness  to  surren- 
der its  heat  energy  to  surrounding  objects.  The  vapors  have 
therefore  signal  significance  as  media  in  heat-pumping. 

326.  Analogy  between  the  Heat-engine  and  the  Ice- 
machine. — The  foregoing  analogy  may  be  made  more  appar- 
ent by  the  use  of  an  illustrative  diagram  (Fig.  185).  Let  the 
small  cylinder  on  the  left  be  the  compressing  or  feed-water- 


FEED  PUMP( 
OR 
COMPRESSOR. 


COOLER  OR  CONDENSER 

Tig.  185.    . 

pumping  cylinder  of  a  heat-engine  plant.  If  it  be  a  steam- 
engine,  the  current  will  pass  clockwise  or  upward  to  the  left 
from  C  through  Pto  B,  which  is  the  heater  (or  boiler).  In  the 
boiler  its  temperature  is  lifted  from  T^  to  7",.  Thence  it 
passes  to  the  working  cyliitder  A^  where  it  operates  by  its 
expansive  energy  to  drive  the  piston,  and  is  cooled  by  the 
supposedly  adiabatic  expansion  to  7",,  or  the  temperature  in 
the  cooler  or  condenser  (C),  which  withdraws  any  heat  which 
might  be  generated  by  the    species   of   compression    of  the 


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4^4  HEAT  AND   HEAT-ENGINES. 

medium  on  the  return  or  exhaust  stroke  of  the  working 
piston.  The  compressing  pump  P  draws  from  the  cooler  or 
condenser  and  completes  the  circuit. 

When  the  same  or  a  diflferent  medium  is  operated  as  a 
refrigerating  circuit  the  compressing  piston  in  P  receives 
mechanical  energy,  compressing  the  medium  and  raising  its 
temperature  an  amount  proportional  to  the  work  expended  in 
compressing  it.  The  current  moves  contraclockwise,  or  from 
the  compressor  downward  to  the  cooler  C.  Here  the  heat 
from  the  compression  is  withdrawn  by  a  circulation  of  cooling 
water  and  is  rejected  with  that  cooling  water,  so  that  the 
compressed  medium  leaves  the  condenser  at  the  tempera- 
ture T^,  From  the  cooler  the  medium  passes  to  the  working 
or  expansion  cylinder  A^  where  it  does  work  against  an 
exterior  resistance  (usually  that  of  compressing  the  medium 
in  Pvci  part),  and  by  such  adiabatic  expansion  is  cooled  below 
the  temperature  7",  of  the  condensing  water,  and  to  a  degree 
far  enough  below  the  surrounding  objects  to  be  anxious  to 
Avithdraw  heat  from  them.  From  A  the  cooled  and  expanded 
medium  passes  to  the  organ  By  which  is  a  heater  so  far  as  the 
medium  is  concerned,  while  it  appears  as  the  place  or  material 
to  be  refrigerated.  That  is,  it  supplies  its  heat  to  bring  up 
the  medium  to  its  own  heat  condition,  and  in  so  doing  i^ 
cooled  Itself.  From  this  refrigerating  chamber  or  heater  of 
the  medium  the  medium  passes  back  to  the  compressor  and 
repeats  the  cycle. 

It  is  apparent,  therefore,  that  in  the  heat-engine  there  is 
heat  supplied  from  without  at  the  heater  B  in  the  beginning 
of  the  cycle,  and  withdrawn  at  the  cooler  C  at  the  end ;  in 
the  refrigerating  cycle  heat  is  withdrawn  at  the  cooler  C  at 
the  beginning  of  the  cycle,  and  therefore  surrounding  objects 
must  supply  heat  a^  the  heater  B  to  the  medium  at  the  end 
of  the  cycle  to  close  it. 

327.  Refrig^eration  for  Ice-making  or  for  Cooling-cham- 
bers.    Brines. — The  heat  withdrawn  from  the  surroundings 


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MECHAiVICAL    REFRIGERATION.  485 

of  the  heater  B  in  the  preceding  paragraph,  to  warm  the 
medium  while  being  themselves  cooled  by  such  transfer,  is 
most  easily  transferred  from  a  liquid  to  the  medium  enclosed 
in  coils  of  pipes.  This  liquid  requires  to  be  one  which  shall 
not  be  too  liable  itself  to  freeze  by  the  cooling  process,  and 
is  therefore  a  solution  of  such  alkaline  salts  in  water  as  shall 
have  its  solidifying  point  lowered.  It  is  therefore  generically 
known  as  **  brine.'*  A  solution  of  Liverpool  salt  in  well- 
water,  of  a  degree  of  concentration  such  that  it  weighs  73 
pounds  per  cubic  foot  or  has  a  specific  gravity  of  1. 17,  will 
not  sensibly  thicken  or  congeal  at  zero  Fahrenheit.  American 
salt  brines  of  the  same  gravity  congeal  at  nearly  20°  F. 
Chloride  of  calcium  solution  or  chloride  of  magnesium  can  be 
used  instead  of  brine.     The  latter  remains  fluid  at  5^  F. 

When  artificial  ice  is  the  object  of  the  process  there  are 
two  usual  methods  which  are  followed.  The  cooled  brine 
surrounds  thin  metal  cans  within  which  is  enclosed  the  dis- 
tilled water  to  be  frozen  in  one  system,  which  is  therefore 
called  the  **  can  "  method;  or  the  cooled  brine  or  ammonia, 
itself  in  coils  circulates  between  hollow  plates,  perhaps  10  feet 
by  14  feet  in  area,  on  the  outside  of  which  the  ice  forms  in 
the  water-tank.  This  latter  is  called  the  plate  method.  In 
the  can  system  blocks  weighing  3CK>  pounds  will  be  frozen  in 
from  50  to  60  hours;  in  the  plate  system  the  ice  forms  14. 
inches  thick  over  their  area  in  from  9  to  14  days.  The  caa 
system  is  more  usual  for  ice-venders,  since  the  supply  of  ice- 
blocks  is  continuous,  but  the  product  of  the  plate  system 
costs  less,  although  the  plant  costs  more. 

When  cold-storage  chambers  or  cooling-chambers  in  fac- 
tories are  to  be  kept  at  low  temperatures  for  the  sake  of  their 
contents,  the  cooled  medium  can  be  circulated  in  coils  of 
pipes  about  the  walls  of  the  chambers,  or  a  cooled  brine  may 
be  similarly  circulated.  The  present  practice  tends  towards 
direct  expansion  except  in  special  cases,  as  likely  to  maintain 
a  more  uniform  mean  temperature  in  the  different  parts  of  the 


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486  HEAT  AND   HEAT-ENGINES, 

coils.  Or,  again,  air  which  is  cooled  by  passing  over  and 
through  a  brine  coil  may  be  circulated  in  the  chamber  by 
means  of  fans.  Such  air  will  deposit  its  moisture  in  the  form 
of  snow  upon  the  metal  of  the  coils,  and  a  dry  cool  air  only 
will  reach  the  stored  material,  and  condensation  thereon  will 
be  lessened  or  avoided.  Where  no  brine  is  used  the  system 
is  called  a  **  direct  expansion  "  system. 

328.  Media  for  Use  in  Refrigerating-machines.  Ad- 
vantages anfl  Disadvantages. — A  refrigerating  medium  may 
properly  be  expected  to  meet  as  many  as  possible  of  the 
following  requirements: 

(i)  If  it  is  a  vapor,  it  must  be  volatile  at  low  tempera- 
tures, but  at  pressures  not  too  far  below  that  of  atmosphere. 

(2)  At  high  temperatures  it  must  not  reach  high  pressures. 

(3)  It  must  be  stable  in  its  composition,  so  as  not  to  alter 
by  the  frequent  evaporations  which  it  must  undergo. 

Whether  a  vapor  or  a  permanent  gas : 

(4)  It  must  have  no  effect  on  metals  convenient  for  use  in 
machine-making. 

(5)  It  must  be  without  effect  on  convenient  lubricants 
such  as  will  have  to  be  used  in  cylinders. 

(6)  It  must  be  non-inflammable  if  leakage  occurs. 
.(7)  It  must  be  non-explosive. 

(8)  It  should  be  without  serious  physiological  effect  on 
-workers  around  the  machinery. 

(9)  It  should  not  be  too  costly  to  buy. 

The  discussion  of  vapors  as  heat  media  has  presented 
several  of  the  volatile  vapors  adapted  for  use  as  heat-carriers 
{§§  107-109  and  §  312).  For  the  uses  of  the  process  of  with- 
drawal of  heat,  while  some  of  the  same  media  will  serve,  there 
are  other  special  ones  which  have  been  tried.    The  list  includes : 

(i)  Water- vapor. 

(2)  Air. 

(3)  Ether  alone. 

(4)  Ether  mixed  with  SO,  (Du  Motay  binary  fluid). 


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MECHANICAL   REFRIGERATION,  4^7 

(5)  Anhydrous  sulphurous  acid  or  sulphur  dioxide  (SO,). 

(6)  Mixture  of  No.  5  with  carbonic  acid  (CO,),  '*  Pictet 
fluid." 

(7)  Ammonia  (NH,). 

(8)  Chymogene  or  other  volatile  derivatives  of  petroleum. 

Ether  is  practically  no  longer  in  use,  because  the  com- 
pressing cylinder  has  to  have  a  volume  six  times  that  required 
for  the  sulphur  dioxide  and  seventeen  times  that  for  an 
ammonia-machine.  This  follows  from  the  density  of  the 
ether- vapor.  It  has  also  to  be  worked  under  less  than  atmos- 
pheric pressure,  since  its  tension  at  2^^  F.  is  2  or  3  pounds 
per  square  inch,  and  the  tendency  of  air  to  leak  into  the 
machine  oxidizes  the  ether  to  a  less  volatile  compound. 
Ether  is  also  inflammable  and  acts  on  the  lubricants  to  dis- 
solve them.  Such  machines  as  used  in  India  appear  to  have 
made  6  pounds  of  ice  per  pound  of  fuel  consumed. 

Sulphur  dioxide  is  a  liquid  at  14°  F.,  and  at  60**  to 
65°  F.  has  a  tension  of  3  to  4  atmospheres.  It  is  without 
effect  on  grease  used  as  a  lubricant,  and  acts  like  one  itself 
to  keep  metallic  surfaces  from  contact.  It  is  not  inflammable 
and  is  stable,  but  is  irrespirable.  When  moisture  gets  to  it, 
the  active  acid  is  formed,  which  corrodes  metals. 

Carbonic  acid  (CO,)  used  alone  requires  so  high  a  range 
of  pressures  (800  pounds  per  square  inch  on  the  compressing 
side  and  300  pounds  on  the  suction  side)  that  it  is  not  prac- 
ticable. The  mixtures  of  Pictet  and  Du  Motay  have  been 
displaced  in  America  by  the  ammonia  systems,  on  account  of 
the  convenience  and  cheapness  of  the  medium  and  because 
capital  has  been  attracted  to  invest  itself  in  the  manufacture 
of  this  type  of  machinery. 

The  petroleum-vapors  are  explosive  and  dangerous  to  use, 
and  such  machines  are  only  experimental  as  yet. 

The  water-vapor  machine  uses  a  cheap  and  harmless 
medium,  but  the  cylinders  have  to  be  enormous  if  the  vapor 
operates  in  a  compression  cycle.    In  this  case  a  vacuum-chamber 


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488  HEAT  AND   HEAT-ENGINES. 

is  required,  in  which  by  a  pump  a  vacuum-pressure  of  about 
one  tenth  of  a  pound  per  square  inch  is  maintained.  A  part  of 
the  water  or  brine  injected  into  this  chamber  vaporizes,  and  the 
remainder  is  chilled  in  proportion  to  the  latent  heat  extracted 
from  it  for  the  vaporizing  of  the  first  portion.  The  water- 
vapor  thus  produced  may  be  handled  in  two  ways.  It  may 
be  passed  into  a  surface  condenser,  the  condensed  liquid 
pumped  out  to  waste,  and  the  remaining  vapor  compressed 
from  one  tenth  of  a  pound  to  one  and  one  half  pounds,  to  be 
worked  as  a  superheated  gas  in  a  cycle  similar  to  those  to  be 
discussed  presently;  or  the  absorption  principle  may  be  fol- 
lowed as  in  the  ammonia-machines  shortly  to  be  discussed, 
so  that  the  water-vapor  from  the  vaporization  in  the  vacuum- 
chamber  is  absorbed  by  sulphuric  acid  in  a  distilling  apparatus. 
From  the  acid,  which  has  a  great  affinity  for  water,  the  vapor 
is  expelled  by  gentle  heat,  and  after  condensation  is  removed 
by  the  air-pump  which  maintains  the  vacuum.  For  ice-mak- 
ing conditions  the  volume  of  water-vapor  would  have  to  be 
150  times  that  of  ammonia.  The  machine  is  not  in  use  in 
America  to  any  extent. 

The  air-  and  the  ammonia-machines  are  those  of  principal 
importance.  The  air-machine  is  principally  used  on  ship- 
board, where  pungent  vapors  from  any  leakage  would  be 
objectionable,  and  particularly  in  confined  or  ill-ventilated 
places. 

329.  Refrigerating-machines  using  Air  as  a  Medium. — 
The  discussion  of  the  air-engine  using  air  at  ordinary  tem- 
perature  at  admission  and  expanding  it  adiabatically  (§  260) 
should  have  made  it  clear  that  by  the  use  of  high  grades  of 
expansion  the  final  temperature  of  the  air  will  be  very  low. 
It  will  be  recalled  that 

II— I 

\vj    -\'pj   -  t: 

in  which  for  air  n  =  1. 41,  the  ratio  of  the  specific  heats  of 


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MECHANICAL   REFRIGERATION.  489 

air.     So  that  if  the  air  be  taken  in  at  68^  F.,  and  expanded 

so   that  the   ratio  ^  has  the  values  given  in  the   following 

table,  the  final  Fahrenheit  temperatures  will  be  those  given 
in  the  table  when  calculated  according  to  the  formula: 


/t 

Final  Temperature 
Fahrenheit. 

/a 

Final  Temperature 

Px' 

/r 

Fahrenheit. 

2 

-     28 

9 

—  180.5 

3 

-     75.9 

10 

—  188.9 

4 

-  106  6 

II 

-  196.3 

5 

-128.7 

12 

—  202.9 

6 

-145.7 

13 

—  20S.7 

7 

-  159-4 

14 

-214. 1 

8 

-  170.9 

15 

—  218.9 

The  same  truth  is  also  apparent  from  a  study  of  the  table 
in  §  182.  These  very  low  temperatures  cannot  be  secured 
unless  the  incoming  air  be  at  a  very  great  pressure,  and 
.moisture  in  the  air  and  the  conductivity  of  the  cylinder 
metal  limit  the  attainment  of  the  theoretical  figures.  It  is 
also  difficult  to  cool  the  air  in  bulk  to  atmospheric  tempera- 
ture, so  as  to  secure  a  cool  admission. 

The  air-machine  appears  in  two  general  forms.  The 
closed-cycle  machine,  represented  .  by  the  Allen  Dense-air 
Ice-machine,  and  the  open  cycle,  represented  by  the  Bell- 
Coleman  Machine  of  European  practice.  In  the  Allen 
machine,  and  others  on  the  same  principle,  there  are  three 
cylinders  taking  hold  upon  a  common  crank-shaft.  One  is  a 
steam-cylinder;  number  two  is  an  air-compressing  cylinder, 
taking  its  supply  of  air  from  the  closed  coil  of  the  refrigerat- 
ing-chamber,  and  compressing  it  to  200  pounds,  or  so,  to  the 
square  inch.  This  compressed  air  is  received  into  a  cooling- 
tank  or  surface  condenser,  where  the  heat  due  to  compression 
is  removed  so  far  as  possible  by  circulating  water,  and  the 
compressed  air  brought  as  nearly  to  the  temperature  of  that 
water  as  is  consistent  with  manageable  bulk  for  the  cooler. 


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<490 


HEAT  AND   HEAl^-ENGINES. 


Prom  this  cooling  reservoir  the  compressed  and  cooled  air 
icnters  number  three  cylinder,  in  which  it  acts  as  in  an  expan- 
sive air-engine,  doing  work  upon  the  driving-shaft  to  relieve 
the  duty  of  the  steam-cylinder.  The  exhaust  from  this  air- 
engine  cylinder  is  at  a  low  temperature,  as  indicated  by  the 
table  above,  and  is  led  into  the  cooling  coils  of  the  chamber 
or  brine,  which  latter  delivers  its  heat  to  the  pipes  enclosing 
the  exhaust  in  the  effort  to  equalize  the  differing  tempera- 
tures. 

The  open  cycle  of  the  Bell-Coleman  type  acts  as  in  the 
Joule  air-engine  reversed  (§  275).  It  draws  air  from  the  open 
-cooling-chamber  at  about  atmospheric  pressure;  compresses 
it  into  a  cooling  chamber  with  coils  of  pipes;  expands  it  in  a 
second  cylinder  to  the  pressure  of  the  open  chamber,  lower- 
ing its  temperature  by  such  expansion,  and  finally  exhausting 
the  cooled  air  into  the  refrigerating-chamber  again.  Fig. 
186  shows  a  diagram  of  the  organs  of  such  a  machine,  and 


ja: 


-^j 


TF" 


-^ 


^kiE 


COMPRESSOR 

Fig.  186. 


COLD 

STORAGE 

ROOM 


/^-^^^ 


Fig.  187  the  compression  and  expansion  diagrams.  The 
closed  curve  KadH'is  the  work  done  by  the  expansion-cylinder, 
while  CHKb  is  the  work  of  the  compressor,  leaving  the  differ- 


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MECHANICAL   REFRIGERATION. 


491 


ence   abed  to  be  provided   for  by  the  exterior  work  of  the 
steam-cylinder. 

The  standard  tests  of  the  performance  of  these  two  types 
of  machine  (expressing  them  in  heat-withdrawal  equivalent 
to  melting  pounds  of  ice  at  32°  F.  into  water  at  that  tem- 
perature, when  the  latent  heat  of  fusion  of  ice  is  142.2 
B.T.U.)  give  3  pounds  of  ice-melting  capacity  per  pound 
of  fuel  with  the  closed-cycle  machine  operating  between  39 
and  160  pounds  pressure;  and  for  the  open  cycle  3-4  pounds, 
assuming  the  engine  to  run  with  3  pounds  of  coal  per  horse- 


1^ 

*,              V, 

"  ^r- - 

— * 

K 

\ 

K 

\ 

1 
1 
1 

r 

\ 

\. 

1         1 

\ 
\ 

M 

1 

;      1 

\  r 

\ 

i 

1 

I                                                   1 

1 1 

1 

iN 

P                                          R 

V 

0 

*-- — -,_-, 

-.       I', 

^^ ,_,^^_^,* 

"Vjj-- — ■'- 

Fig.  187. 

power  per  hour.  The  advantages  which  they  offer  are  those 
from  the  cheapness  and  harmless  character  of  their  medium; 
their  drawbacks  proceed  from  the  bulk  and  size  of  the 
machine  and  the  proportionate  effect  of  the  frictional  resist- 
ances; the  effect  of  watery  vapor  in  the  air,  causing  snow  in 
the  pipes  and  connections;  and  the  effect  of  clearance  losses. 
If  high  pressures  are  used,  there  is  great  difficulty  in  making 
valves  which  will  keep  tight,  and  the  heat  from  the  com- 
pressor-cylinder is  sufficiently  conducted  to  other  parts  of  the 
machine  to  cause  a  loss  of  effectiveness.  With  high  tempera- 
tures glycerine  may  be  used  as  a  lubricant. 

330.  Ammonia  Refrigerating-machines.      Compression 
Type. — Reference    has   been    made   above    (§  328)    to    the 


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492  HEAT  AND   HEAT-ENGINES. 

American  prevalence  of  ammonia  as  a  medium  for  producing 
cold  mechanically.  This  results  from  the  commercial  accessi- 
bility of  ammonia  as  a  by-product  in  gas-making  or  coke- 
making,  and  the  comparative  ease  with  which  anhydrous 
ammonia  can  be  produced  from  ammonia-liquor  by  a  frac- 
tional distillation  process,  since  the  ammonia-gas  is  more 
volatile  than  the  steam-gas  from  water.     The  table  on  page 

493  computed  by  the  late  Prof.  De  Volson  Wood  gives  the 
properties  of  the  saturated  ammonia: 

From  this  table  the  convenient  adaptability  of  ammonia 
will  be  apparent  on  its  physical  side.  It  will  remain  a  liquid 
under  atmospheric  pressure  only  when  kept  at  the  tempera- 
ture of  30°  F.  below  zero  on  that  scale,  and  at  the  usual 
atmospheric  temperatures  in  this  climate  of  about  70**  it  will 
be  kept  a  liquid  only  by  maintaining  it  under  a  pressure  of 
115  pounds  above  the  atmosphere.  With  reduction  of 
pressure  the  liquid  becomes  a  vapor,  withdrawing  from  sur- 
rounding objects  the  heat  necessary  to  change  its  state.  This 
heat  of  vaporization  at  atmospheric  pressure  is  573  B.T.U.* 
as  compared  with  the  966  units  required  by  water. 

The  volatile  character  of  the  anhydrous  ammonia  makes 
it  unprofitable  to  use  ah  expansion-cylinder  in  its  cycle  as  is 
required  with  air,  since  the  gas  will  expand  of  itself  by  simply 
allowing  it  to  pass  from  a  higher  pressure  vessel  into  another 
at  lower  tension  and  temperature  through  a  regulating  cock 
or  valve,  and  in  the  change  of  state  by  such  expansion  the 
cooling  eiTect  is  so  much  greater  than  that  resulting  from  the 
exterior  work  done  in  an  expansion  cylinder,  that  the  latter 
becomes  negligible.  Such  separating-valve  is  called  an 
**  expansion-cock." 

In  using  ammonia  as  a  medium  there  are  two  principal 
systems,  the  compression  system  and  the  absorption  system. 

In  operating  a  refrigerating  plant  on  the  compression 
system  there  is  required  a  steam-engine  operating  an 
ammonia  compressor;  a  cooler  or  surface  condenser  in  whose 


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MECHANICAL   REFRIGERATION. 


493 


SATURATED    AMMONIA. 


Temperature. 


Pressure,/. 
(Absolute.) 


5^' 

I     I 

I 


2Ld 


I 


-  40 

-  35 

-  30 

-  25 

-  20 

-  15 

-  10 

-  5 
T  o 

+  5 

-h  10 

-f  15 

-f-  20 

-f  25 

+  30 

+  35 

+  40 

4-  45 

-f  50 

-f  55 

-f  60 

+  65 

4-  70 

+  75 

-f  80 

+  85 

+  90 

-f  95 

-|-  100 


420.66  1540 
425.66  1773 
430.661   2035 


I 


435-66 
440.66! 
445.66 

450.66 
455 -661 
460.661 


2329.5 
2656.4 
3022.5 

3428.0 
3968.0 
4373 


465.66]  4920.5 
470.661  5522  - 
475.66    6182 


480.66 
485.66 
490.66 

495.66 
500.66 
505.66 

510.66 
515.66 
520.66 

525.66 
530.66 
535-66 


6905.3 
7695.2 

8556.4 

9493-9 
10512 
11616 

12811 
1 4 102 
15494 

16994 
18606 
20339 


540.66  22192 
545-66  24172 
550.66  26295 


555-66 
560.66 


28566 
30980 


it 


10.69  579.67 

12.31  576.69 

14-13  573.69 

16.17  570. 68 

18.45  ^67.67 

20.99  564.64 


23-77 
27.57 
30.37 

34.17 
3S.55 
42.93 

47.95 
53.43 
59-41 

65.93 
73.00 
80.66 

88.96 

97.93 
107.60 

118.03 
129.21 
141.25 

154.11 
167.86 
182.80 

198.37 
215.14 


561.61 

558.56 
555.50 

552.43 
549.35 
546.26 

543-15 
540.03 
536.92 

533.78 
530.63 
527.47 

524.30 
521.12 
517.93 

515.33 
511.52 
508 . 29 

504.66 
501.81 
498.11 

495.29 
491.50 


(1} 


48.25 
48.35 
48.85 

49.16 
49.44 
49.74 

50.05 
50.44 
51.38 

50.84 
51.13 
51.33 

51.65 
51.81 
52.02 

52.22 
52.42 
52.62 

52.82 
53.01 
53-21 

53.40 
53.67 
53.76 

53-96 
54.15 
54.28 

54.41 
54.54 


•J  c 

**—  I 

•si 


531-42 
528.34 
524.84 

521.52 
518.23 
514.90 

511.56 
508.12 
504.12 

501.59 
498.22 

494.93 

491.50 
4S8.22 
484.90 

481.56 
478.21 
474.77 

471.44 
468 .  01 
464.76 

461.82 
457.95 
454.70 

450.75 
447-75 
443.70 

440.95 
437.35 


> 


24.38 

21.21 

18.67 

16.42 

14.48 
12.81 

11.36 
9-89 
9-14 

8.04 
7.20 
6.46 

5.82 
5.24 
4.73 

4.28 
3.88 
3.53 


o  o. 

> 


(•    -       1' 


j- 


.0234 
.0236 
•0237 

.0238 
.0240 
.0242 

.0243 

.0244 
.0246 

.0247 
.0249 
.0250 

.0252 
•0253 
.0254 

.0256 

.0257 
.0260 


3.21  .02601 
2.93  .02603 
2.671.0265 


2.45 
2.24 
2.05 

1.89 

1.74 
1. 61 


.0266 
.0268 
.0270 

.0272 

.0273 
.0274 

.0276 
.0277 


041 1 
0471 
0535 

0609 
0690 

0775 

0880 

lOII 
1094 

1243 
.1381 
.1547 

.1721 
.1908 


.2336 

.2577 
.2832 

.3115 
.3412 

.3745 

.4081 
.4664 

.4S78 

.5291 

.5747 
.6211 

.6756 
.7353 


coils  the  compressed  ammonia  may  be  cooled  by  the  with- 
drawal of  the  heat  due  to  the  compression,  which  is  made  up 
of  the  equivalent  of  the  mechanical  work  of  such  compression 


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494  HEAT  AND   HEAT-ENGINES, 

together  with  the  heat  necessary  to  produce  vaporization,  or 
the  latent  heat;  the  expansion-cock,  through  which  the  cooled 
and  liquified  ammonia  may  expand  into  a  gas,  withdrawing 
in  so  doing  the  heat  from  the  brine  which  surrounds  the  coil 
or  vessel  into  which  the  expansion  takes  place.  Subsidiary 
circulating-pumps  will  then  circulate  the  cooled  brine  in  the 
chambers  or  water  to  be  chilled.  Fig.  i88  illustrates  the 
organs  and  connections  for  such  a  brine  plant. 

If  the  direct-expansion  system  is  used,  the  expansion- 
valve  at  the  bottom  of  the  ammonia-receiver  is  replaced  by  a 
manifold  from  which  groups  of  expansion-valves  connect  with 
the  cooling-coils  in  the  cold  rooms  at  their  lower  ends.  The 
ammonia-gas  suction-pipe  is  connected  to  the  upper  or 
warmer  ends  of  these  cooling-coils  by  proper  valves,  and  the 
circulation  of  the  cooling  medium  is  thus  maintained. 

In  the  actual  operation  of  a  plant  the  suction  side  of  the 
compressor  is  connected  to  the  low-tension  side  of  the  vessel 
or  coil  controlled  by  the  expansion-cock,  and  a  suction- 
pressure  of  from  5  to  20  pounds  per  square  inch  above  atmos- 
phere is  maintained  there  by  regulating  the  speed  of  the 
compressor  and  the  opening  of  the  cock.  In  starting  with  a 
new  charge  of  anhydrous  ammonia,  it  is  introduced  into  this 
suction-chamber  from  the  exterior  vessel  in  which  it  has  been 
received  from  the  chemical  manufacturers.  Coming  into  the 
suction-chamber  or  coil  at  atmospheric  temperature,  the 
liquid  ammonia  volatilizes  under  the  reduced  pressure,  and  the 
proportion  to  be  volatilized  will  be  determined  by  the  tem- 
peratures surrounding  the  coil  or  suction-chamber.  Usually 
10  per  cent  so  volatilizes,  cooling  the  entire  mass  down  to  the 
temperature  of  ebullition  proper  to  the  suction-pressure. 
Then  the  remainder  of  the  liquid  ammonia  (or  90  per  cent) 
volatilizes  by  the  withdrawal  of  heat  from  the  surrounding^ 
coil  and  brine,  and  passes  as  a  gas  to  the  compressor-cylinder. 

The  compressing  stroke  raises  the  ammonia-pressure  to 
perhaps   150  pounds  and  70°  F.,  and  expels  the  gas  to  the 


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MECHANICAL   REFRIGERATION, 


495 


Fig.  188. 


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49^  HEAT  AND   HEAT-ENGINES. 

cooler  or  condenser,  where  the  heat  is  withdrawn  by  circula- 
tion of  water  and  submergence  in  it,  and  the  gas  condensed  to 
a  liquid  again  upon  the  high-pressure  side  of  the  expansion- 
cock  in  the  ammonia-receiver.  Upon  opening  the  latter,  the 
cycle  of  the  charging  process  is  repeated,  and  the  process 
goes  on  thereafter  continuously.  The  amount  of  ammonia 
charge  in  a  machine  will  vary  with  the  amount  of  piping  in 
the  circuit.  A  usual  allowance  averages  0.3  of  a  pound  per 
running  foot.  Leakage  or  wastage  ought  not  to  amount  to 
100  pounds  a  year  in  a  machine  of  50  to  75  tons  of  ice 
capacity  per  24  hours. 

It  will  be  apparent  that  the  temperature  of  the  cooling 
brine  will  be  determined  by  the  boiling-point  of  the  ammonia, 
and  that  this  will  be  determined  by  the  pressure  of  the  suc- 
tion side  of  the  compressor.  The  brine  is  usually  6°  colder 
than  the  space  it  cools,  and  about  as  much  warmer  than  the 
vaporizing  ammonia.  When,  therefore,  a  temperature  as  low 
as  0°  F.  is  required,  as  in  storage  of  fish,  the  suction- pressure 
is  kept  down  to  5  pounds;  for  brewery  work,  where  storage 
temperatures  of  34°  F.  are  low  enough,  a  suction-pressure  of 
28  pounds  will  suffice.  Cold-storage  chambers  for  fresh  meat 
can  be  maintained  at  25°  F.  with  24  pounds  suction-pressure. 

331.  Wet  or  Cold  and  Dry  or  Hot  Systems  of  Ammonia- 
compression. — If  the  regulation  of  the  supply  of  ammonia 
to  the  cooler  on  the  suction  side  of  the  compressor  is  so 
adjusted  to  the  pressure  that  vaporization  is  complete,  the 
machine  is  said  to  operate  dry,  or  to  belong  to  the  dry-com- 
pression system.  If,  on  the  other  hand,  some  liquid  ammonia 
is  allowed  to  remain  unvaporized,  or  if  some  liquid  ammonia 
is  injected  into  the  space  filled  with  vapor,  the  system  will 
be  known  as  the  wet  or  cold  compression  system.  Prof. 
Linde  introduced  the  first  wet  system,  which  is  often  known 
by  his  name,  and  Mr.  George  Richmond  the  second  or  injec- 
tion method.  The  difference  in  the  wet  and  dry  systems 
follows  from  the  presence  of  the  liquid  ammonia  in  the  corn- 


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MECHANICAL   REFRIGERATION,  49/ 

pressing  cylinder.  If  sufficient  liquid  is  brought  into  the 
compresser,  the  temperature  cannot  there  be  raised  higher 
than  the  boiling-point  corresponding  to  the  highest  tem- 
perature and  pressure  of  the  compression;  while  with  the 
<lry  saturated  gas  the  temperature  may  go  much  higher  than 
the  limit  set  by  the  other  system.  More  circulating  water, 
however,  will  be  required  in  the  latter  case  because  the 
compression-cylinder  must  be  water-jacketed,  which  is  not 
necessary  in  the  cold  system.  Tests  seem  to  show  the  two 
methods  to  give  about  equal  results  in  economy,  the  reactions 
of  the  hot  cylinder-walls  neutrah'zingthe  theoretical  advantage 
of  the  wet  system. 

332.  Ammonia  Refrigerating-machines.  Absorption 
Type. — In  the  absorption  system  of  ammonia  refrigerating- 
machines  advantage  is  taken  of  the  property  of  water  or  of  a 
weak  ammonia  hydrate,  whereby  it  shews  a  strong  avidity  to 
dissolve  in  itself  the  dry  ammonia-gas.  At  59°  F.  water  will 
absorb  727  times  its  volume  of  ammonia-vapor.  Hence  if  a 
pipe  leading  to  such  an  absorber  be  connected  to  the  lower 
tension  or  cool  side  of  the  expansion-cock,  the  anhydrous 
vapor  will  be  drawn  off  through  it  to  unite  with  the  weak 
liquor  in  the  absorber  at  a  rate  comparable  to  that  at  which 
the  suction-stroke  of  the  ammonia-compressor  acted  in  the 
compression  system.  The  liquor  in  the  absorber  is  drawn  off 
by  an  ammonia-pump  and  fed  into  a  still,  or  chamber,  within 
which  a  coil  of  hot  steam-pipes  will  vaporize  the  ammonia- 
gas,  and  crack  the  volatile  ammonia  from  the  less  volatile 
water.  The  ammonia-gas  may  be  at  the  same  pressure  and 
temperature  as  it  would  have  had  under  the  compression 
system,  and  is  led  into  a  condenser,  where  it  becomes  liquid 
anhydrous  ammonia,  to  be  worked  through  an  expansion- 
cock  as  in  the  other  system.  Hence  it  will  appear  that  the 
difference  in  the  two  systems  results  from  a  replacing  in  the 
absorption  system  of  the  compression-cylinder  and  its  driving- 
engine  by  a  vessel  called   the  absorber  with  an  ammonia- 


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498 


HEAT  AND   HEAT-ENGINES, 


liquor  pump  and  a  steam  still.  •  The  cooling  condenser,  the 
expansion-cock,  the  brine-cooling  appliance  and  its  pumps 
will  be  identical  for  both  systems.  It  usually  follows  that 
the  absorption  plant  will  be  somewhat  cheaper  to  install,  and 
in  many  places  it  is  convenient  to  avoid  the  running  of  the 
large  compressor  and  its  attendant  expense.  It  is  often  con- 
venient also  to  be  able  to  use  the  commercial  ammonia 
hydrate  of  62  per  cent  water  and  38  per  cent  ammonia  with 
a  specific  gravity  of  .880.  Fig.  189  shows  a  type  of  absorp- 
tion  plant  with  the  essential  organs. 


ABSORPTION  SYSTEM. 


=(^Wajjy^SuppV 


Hot  Weak  Uquor  Cooler 


•,r.:  .-.r  C  .-.i.-jeiafff;,  A* 


I  Adsorption 

I  Refrigerating  Apparatua. 


Vfwle  Cooling  Watw 


Fig.  189. 

333.  Refrigerating-machines  on  Pictet  System.  Car- 
bonic-acid Machines. — Previous  to  the  more  extensive  intro- 
duction of  the  ammonia-machines  into  America,  the  Pictet 
machine  was  the  most  extensively  employed.  It  is  still  in 
limited  use,  and  is  also  of  importance  in  Europe.  The 
medium  at  first  was  pure  sulphur  dioxide  (SOj),  but  is  now 
more  usually  the  so-called  Pictet  fluid  of  97  per  cent  of  SO, 
and  3  per  cent  of  CO,.  The  dilution  with  carbonic  acid 
enables  a  temperature   14°  F,  lower  to  be  secured  at  atmo- 


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MECHANICAL   REFRIGERATION. 


499 


spheric  pressure  than  can  be  attained  with  the  pure  sulphur 
dioxide.  The  Pictet  machine  requires  a  little  greater  bulk 
for  its  compressing  cylinder  than  the  amnrionia-machine,  but 
otherwise  they  should  be  of  equal  theoretical  efficiency. 

The  pure  carbonic-acid  machines  require  to  work  through 
a  range  of  pressures  higher  in  the  scale  than  the  foregoing, 
and  difficulties  from  leakage  and  from  the  tightness  of  valves 
have  stood  in  their  way.  To  operate  between  5°  F.  and  64** 
limits  of  temperature,  the  suction-pressure  has  to  be  300 
pounds  per  square  inch,  and  the  compression  over  800  pounds. 
The  compression-cylinder  will  be  of  one  quarter  the  volume 
of  the  equivalent  ammonia-machine,  and  this  fact  has  given 
interest  to  the  use  of  the  machine  for  yachts  and  similar 
marine  conditions,  where  room  and  weight  are  of  paramount 
importance.  The  carbonic  acid  is  more  effectively  worked  in 
an  expansion-cylinder  rather  than  through  an  expansion-cock. 


Fig.  190. 


334.  Temperature-entropy  Diagram  of  Refrigeratioir 
Cycle. — The  discussions  which  have  preceded  should  have 
made  easy  the  graphic  representation  of  the  useful  efifect  by 
the  use  of  the  temperature-entropy  diagram  (Fig.  190).     The 


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500  HEAT  AND    HEAT-ENGINES. 

expansion  of  a  permanent  gas  medium  in  an  expansion- 
cylinder  is  practically  adiabatic.  Starting,  therefore,  from 
the  upper  right-hand  corner  and  moving  towards  the  left, 
a  line  ab  is  described  which  is  a  curve  of  constant  pressure 
and  decreasing  temperature  caused  by  the  cooling  by  the 
condenser-water  to  the  point  b.  Here  adiabatic  expansion 
down  temperature  takes  place  through  the  expansion- 
cylinder  to  the  point  c.  The  brine  heats  the  medium  and 
increases  its  entropy  and  temperature  along  the  constant 
volume  line  cd^  and  at  d  the  compression  raises  the  tempera- 
ture without  change  of  entropy  from  ^to  a.  If  the  medium 
used  is  liquefiable  gas,  the  changes  of  entropy  occur  at  con- 
stant temperature  and  the  lines  ab  and  cd  are  horizontal* 
giving  the  Carnot  cycle  diagram  of  Fig.  80. 

In  direct-refrigerating  or  open  systems  (§  327),  using  air 
for  example,  where  the  cooled  medium  is  exhausted  into  the 
space  to  be  cooled,  it  will  usually  happen  that  the  line  cd  will 
not  be  a  continuous  one,  since  the  refrigerating-chamber  will 
not  raise  the  temperature  of  the  medium  to  that  correspond- 
ing to  d.  If  h,  for  example,  represents  some  such  tempera- 
ture level  T^ ,  then  the  line  through  h  represents  a  loss 
between  the  medium  and  the  compressing  cylinder  due  to  the 
warm  metal  walls  of  the  latter,  and  for  which  no  refrigerating 
eflfect  is  produced.  If  the  cylinder  could  be  kept  cool  enough 
to  have  adiabatic  compression  on  the  second  or  succeeding 
strokes  begin  at  //  and  describe  an  adiabatic  vertical  through 
A,  it  would  appear  that  by  successive  withdrawals  from  the 
continuously  cooling  refrigerator  a  continuous  lowering  of  T^ 
could  be  made  to  follow.  The  practical  limit  is  soon  reached, 
however,  from  the  impossibility  of  carrying  the  cylinder-metal 
temperature  down  as  the  process  goes  on. 

If,  however,  the  object  of  prime  interest  be  the  securing 
of  a  low  temperature,  the  principle  of  the  regenerator  may  be 
introduced  which  was  discussed  for  the  reverse  process  under 
Hot-air  Engines  (§  268).     The  regenerator  in  a  refrigerating- 


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MECHAXICAL   KEFRIGEJRATION, 


5or 


machine  is  usually  called  an  interchanger,  and  is  applied  to 
restore  the  heat  to  the  medium  which  is  called  for  by  the  gap 
between  //  and  d.  This  lowering  of  the  interchanger  tempera- 
ture   may    be    used    to    cool    the    medium    below    the    first 


1 


/                      y^ 

\ 

JL 

7 

\ 

)  ' 

'   '     ■-.■■,■■  "■.■■;■;■. 

-Tk 

a      J 

i-'. 

, 

^   *   f  ^   f  » 


Fig.   191. 


temperature  corresponding  to  d,  so  that  a  lower  entropy 
ordinate  is  reached  down  which  the  adiabatic  expansion 
occurs  (such  as  /^,  for  example).     This  lower  range  can  be 


Fig.  192. 


utilized  on  the  next  circuit  to  carry  the  cycle  still  lower,  the 
effect  being  cumulative  as  long  as  the  expansion-cylinder  can 
have  its  temperature  lowered  at  the  same  pace.  This  latter 
imposes  the  practical  limit. 


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S02 


HEAT  AND   HEAT-ENGINES. 


Figs.  191  to  193,  reduced  from  a  very  complete  paper  by 
Mr.  George  Richmond  (see  Appendix),  present  the  tempera- 
ture-entropy diagrams  of  ammonia,' SO,CO,,  and  ether  when 
these  media  are  operated  by  using  a  compression  and  an  ex- 
pansion cylinder  through  the  Carnot  cycle.  Fig.  192  shows  the 
diagrams  which  result  when  the  expansion-cylinder  is  omitted, 
and  the  media  are  operated  with  some  of  the  liquid  present 


TABULAR    DATA    FOR    CONSTRUCTION    OF    DIAGRAM    FIG.    19I. 

(l  lb.  of  each.) 


T, 

T. 

/. 

♦.=it 

-'¥. 

Ammonia 

580.56    543.03 
170.82    156.76 
121.50     67.93 
170.99  1  166. 14 

I. 2501 
.3678 
.2616 
.3682 

1.0367 

.2993 

.1297 

1         .3172 

Sulphur  dioxide 

Carbonic  acid 

Ether 

464.4 

523.8 

Represented     on     dia- 
gram by 

ah 

J): 

rectg.  bd  rectg.  hf 

be 

!    '" 

-1^"  -1:;- 

C             T,-T,.f^ 

Ammonia 

1 

60.10                    -T^Tfi 

—  .0918 

—  .0248 

—  .0171 

-f  .0188 

1 
.5084           627.47 
.1544           156.00 
.2         ;       570.5 

.475             . 

Sulphur  dioxide 

Carbonic  acid 

Ether 

21.59 
56.72 

31-47 

.0437 
.1148 
.0698 

Represented     on     dia- 
gram by 

area  abg/ 

be 

kc 

1 

SO  as  to  prevent  superheating  and  so  as  to  give  the  wet  or 
cold  system.  Additional  work  is  required  as  represented  by 
the  area  bge^  but  the  heat  removed  is  reduced  by  the  same 
amount,  because  the  heat  is  not  removed  from  the  liquid  as 
in  the  other  set  cf  conditions,  and  reducing  the  area  of 
refrigeration  by  the  area  ef,  equivalent  to  bge.      When   the 


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MECHANICAL   REFKIGERATION, 


503 


media  are  used  in  the  dry  system  there  will  be  a  rise  in 
temperature  and  entropy  after  the  point  //  is  reached,  and 
additional  work  will  be  done  as  represented  by  the  area  of 
khjc  (Fig.  193).  Refrigeration  is  also  increased  by  the  area 
of  the  rectangle  kd. 


MAUorf 
I  IT.— DOTTBD  L1RB8.  FIO.  M :  PRACTICAL  CTGLSr-SnPEBBSATBD  AOBRT 

;<;■»■  ftp*  -f  Vkjt  ■«■  Q/'e' 

Fig.  193. 


335.  Efficiency  in  a  Refrigerating  Cycle. — The  tempera- 
ture-entropy diagram  also  makes  apparent  to  the  eye  the 
meaning  of  the  expression  for  the  efficiency  in  a  refrigerating 
cycle.  In  the  heat-engine  cycle  or  the  direct  cycle  under  the 
Carnot  hypothesis,  the  high  temperature  of  the  source  of  heat 
is  the  starting-point,  and  the  heat  energy  flows  downward 
through  the  heat-engine,  which  utilizes  it,  and  that  which  is 
not  available  for  work  is  transferred  to  the  refrigerator  or 
condenser.  The  efficiency  is  then  the  fraction  whose  denomi- 
nator is  the  maximum  heat  energy  available,  and  whose 
numerator  is  that  part  of  it  which  is  transformed  into  work. 


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504  HEAT  AND   HEAT-ENGIXES. 

The  heat  rejected  will  measure  the  excess  of  the  denominator 
as  compared  with  the  numerator. 

In  the  refrigerating  cycle,  which  is  the  reverse  of  the  direct 
cycle,  the  problem  is  to  withdraw  heat  energy  from  the 
refrigerator  and  transfer  it  to  the  heater.  Universal  experi- 
ence and  the  dictum  of  the  second  law  of  thermodynamics 
indicate  that  this  can  only  be  done  by  the  expenditure  of 
mechanical  energy,  or  by  a  process  analogous  to  pumping. 
The  object  will  therefore  be  to  remove  the  greatest  quantity 
of  heat  energy  by  the  expenditure  of  the  least  mechanical 
energy  possible  to  accomplish  this  result.  Efficiency  of  such 
heat-pumping  will  therefore  be  measured  by  a  fraction  whose 
denominator  will  be  the  mechanical  work  required,  and  whose 
numerator  will  be  the  entire  amount  of  heat  pumped  out  of 
the  refrigerator.  The  difference  between  the  total  heat 
discharged  into  the  condenser,  and  the  heat  pumped  out  of 
the  refrigerator  will  be  the  equivalent  of  the  work  expended, 
and  it  will  be  obvious  that  the  less  heat  converted  into  work, 
the  more  cooling  is  done  and  the  more  efficient  the  apparatus 
as  a  refrigerating  device. 

Referring  then  to  the  temperature-entropy  diagrams,  it 
will  be  apparent  that  the  total  heat  energy  of  the  cycle  will 
be  the  product  of  the  upper  temperature  value  into  the 
entropy  range.  Calh'ng  this  upper  value  T^  and  the  entropy 
range  0,  we  have 

Heat  energy  obtained  from  refrigerator  =  07",. 

The  work  of  the  compressor  and  expander  is  to  take  the 
medium  used  and  operate  with  it  between  the  larger  value 
T^  and  the  lower  value  7",.  The  work  done  will  therefore  be 
7780(7;  —  r,)  in  foot-pounds  or  0(7;  -  7,)  in  beat-units. 

Hence  the  efficiency  by  definition  will  be 

Efficiency  ^""""^y  ^'^^"'"^^   -        ^^'         -        ^' 


Energy  expended       <K.T^  -  T,)       T,  -  T/ 


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MECHANICAL   REFRIGERATION.  505 

which  is  obviously  an  expression  in  the  form  of  the  reciprocal 

of  the  efficiency  of  a  heat-engine.     The  peculiarity  of  this 

expression  is  that  its  value  is  greater  than  unity.     This  is  due 

to  the  peculiar  negative  unit  which  it  presupposes  when  the 

object    is  the  pumping  down   of  heat  energy  as  a  positive 

operation.     Where    the    energy   obtained   is  a    part    of   the 

energy  expended,  as  is  the  usual  case,  this  apparent  difficulty 

is  avoided.      For  this  reason  many  engineers  prefer  to  use  the 

relation  between  the  heat  actually  withdrawn  as  heat  to  the 

work    expended    in     the    heat-pumping    and    call    this   the 

efficiency.     That  is, 

^^  .  Cooling  effect 

Efficiency  =  r^^ — -. , — ^^ ; :-. 

Work  required  to  produce  it 

This  may  become  unity  when  equal  areas  of  the  temperature- 
entropy  diagram  are  formed  by  the  position  of  the  line 
through  7",.  As  the  work  area  grows  less  than  one  half  the 
total  heat-energy  area,  the  efficiency  is  greater  and  transcends 
unity. 

.  In  either  use,  however,  an  important  pair  of  conclusions 
is  to  be  drawn : 

1st.  The  efficiency  increases  as  the  temperature  of  the 
refrigerating-room  increases; 

2d.  The  efficiency  increases  as  the  temperature  of  the 
condenser  or  cooler  is  lowered. 

The  practical  use  of  the  efficiency  results  from  the  fact 
that  it  gives  the  number  of  thermal  units  removed  per  778 
foot-pounds  expended.  If  the  latent  heat  of  fusion  of  ice  be 
called  142.2  B.T.U.  per  pound,  there  will  be  required  per 
ton  of  2000  pounds  made  per  24  hours  an  amount  of  heat 
represented  by 

142.2  X  2000  =  284400.0  heat-units. 

Each  horse-power  per  24  hours  will  be  represented  by 

33000  X  60  X  24       ^ 

^ ^  =  61070  heat-units. 

778  ^^ 


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5c6 


HEAT  AND   HEAT-ENGINES. 


Hence  the  number  of  tons  of  ice  made  from  water  at  32°  F, 
per  horse-power  per  day  of  24  hours  will  be 


£X 


61079  __  Heat 
284400  ~  Work 


X  .214  =  E  X  .214, 


in  which  the  heat  and  work  values  can  be  scaled  from  the 
temperature-entropy  diagram. 

336.  Refrigeration  by  a  Series  Process.  The  Step-by- 
step  Method. — It  is  obviously  possible  in  refrigeration  also 
to  make  use  of  a  succession  of  media  for  producing  a  low 
degree  of  temperature  just  as  in  the  series  heat-engine  it  was 
sought  to  widen  the  range  of  pressures  within  a  given  tem- 
perature range  (§  315).  The  advantage  secured  is  that  by 
using  a  series  each  agent  selected  may  be  best  adapted  to 
the  particular  range  of  temperature  through  which  it  is  used. 

If  the  Carnot  cycle  be  assumed  for  each  medium  in  the 


Rs 


Ri 


Fig.  195. 

series,  the  operation  as  presented  by  the  temperature-entropy 
diagram  will  be  conducted  in  a  series  of  steps  as  shown  in 
F^g-  195-  The  medium  adapted  for  the  top  of  the  range 
may  act  upon  the  material  to  be  cooled  by  lowering  its  tem- 
perature from  T^  to  7",  by  the  adiabatic  expansion  of  the 
medium  down  temperature  through  this  range.  The  body 
to  be  cooled  may  then  come  into  the  second  machine  operat- 
ing with  a  medium  adapted  for  the  lower  range  between  T^ 


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MECHANICAL  REFRIGERATION.  SO7 

and  7^,,  and  by  a  similar  expansion  process  may  have  its  tem- 
perature lowered  to  7", ,  and  a  third  step  with  a  third  medium 
may  drop  its  final  temperature  to  T^.  Using  again  the 
analogy  of  heat-pumping,  the  action  may  be  compared  to  a 
discharge  of  heat  energy  by  each  machine  of  the  series  into 
the  suction  or  refrigerator  of  that  above  it,  so  that  the  work 
is  done  in  three  (or  more)  steps  instead  of  doing  it  by  the 
one  step  which  might  be  difficult  and  even  impossible.  This 
method  is  used  in  liquefying  some  of  the  more  difficult  gases, 
and  when  used  alone  or  in  combination  with  free  expansion 
methods  can  produce  the  lowest  known  limits  of  temperature. 
337.  Design  of  a  Refrigerating-machine. — It  would  be 
manifestly  impossible  within  the  limits  imposed  by  this  dis- 
cussion to  refer  exhaustively  to  all  possible  machines  and 
combinations.  The  treatment  of  the  air-compressor  (Chapter 
XIII)  and  of  the  air-engine  (Chapter  XVIII)  furnish  all 
necessary  formulae  for  an  air-machine,  or  one  using  a  compres- 
sion and  an  expansion  cylinder.  The  heat  to  be  withdrawn 
from  the  cold-storage  room  will  be  for  each  pound  of  air 
passing  through  the  refrigerating-machine 

when  /,  corresponds  to  /„  the  pressure  at  which  the  air  enters 
the  compression-cylinder,  and  /^ ,  corresponding  to  p^,  is  the 
temperature  in  the  cold  chamber.  If  the  amount  of  heat  to 
be  removed  is  given  in  units  as  well  as  the  range,  then  the 
heat  withdrawn  will  be 

Q  =  MClt,  -  0» 

when  M  is  the  number  of  units  of  weight  of  air  to  be  taken 
care  of  per  minute.  Q  is  usually  given  in  terms  of  pounds  of 
ice  made  or  melted  in  a  given  time.  If,  for  example,  it  be 
400  pounds  of  ice  per  hour,  then 

Q  142.2  X  400 


Mz^ 


Cp{t,^t,)      60  X  o.2375(/,-/,)' 


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508  HEAT  AND   HEAT-ENGINES, 

The  work  of  compressing  M  units  without  account  of  clear- 
ance will  be 

as  shown  in  §  i8i,  which  may  be  written 


smce 


and     CV  —  C»  =  AR  =  Cp- 


The  work  in  the  expansion-cylinder  (§  254)  will  in  like- 
manner  be 

when  /,  corresponds  to  the/,  at  the  point  of  cut-off  in  that 
cylinder,  and  t^  corresponds  to  the  final  pressure  supposed  ta