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HN MRIA $
HARVARD ENGINEERING SCHOOL
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Digitized by VjOOQ IC
Digitized by VjOOQ IC jf
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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.
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KF I'/i ^ ^
ru^TUL Jiu^X.
-Ha-
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
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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
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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.
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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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TABLE OF CONTENTS. Xlll
»\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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XIV TABLE OF CONTENTS,
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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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TABLE OF CONTENTS, XV
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.
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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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36
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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FUELS.
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,
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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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40
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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42
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,
43
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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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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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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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.
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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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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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fUELS.
65
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.
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£. 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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72
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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j6
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
Digitized by
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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
'^uvB\noyeo
idMOd 3t|lJO|V3
O M M Q «n
-^ M m en «
OO OO OO CO oo
O OO OO e«
t>>0 O OO
OO OO GO OO
?5
2R
r^ 1- O^
5-83
r^ C OO
m tn t>«
0» M O
t^OO OO
q«V pu« iai^AV
ifuipnpxd
'j9MOc{'3y|JOlB3
\r> Mi CO u^ O
CO OO GO OO 00
O f ^ t>.
m m r^ »r»
O QO moo
GO OO OO GO
00 00 OO
•r r>.
S5
GO Q en
« O O
OO N O*
1- ^ m
8fj
'psAjasqo
jdMOd 3g!JO|C3
•f CO GO o «n
00 vO w U-. 1^
rf t" GO 00 r>»
t>. t>. r* r^ r^
en rr o «^
OO GO OO OO
O O w
M r>.o
« GO r>.
OO r* r^
OO en
\0 u>
1^ O e
\n r>.oo
Sao w
r>. r^ t^
■qsv po« J»l«A\
jo aAi8npx9
-«[Oy^ jO 1U»D J3J
8»/^ o o* o
r>. w i-i O
en w »f> envo
•qsv
o o »^ o o
O* -r "^ ^ en
in ^ m in\0
9ld098
-OipXH
O Q Q »r) O
^ r^oo r* r*
•038
-OJlIJiJ puB
'uaJHAxQ
O^O en Q r^
C4 C« M tnvO
uaJBojpXH
in r>. «n N vO
O^O en C^ •-«
C^ en t>»oo O^
M iM M M C«
•uoqj«3
vO "i-O 00 o
mo I- c« f
^ m r>» o* r*
O »n <
\n w <
envO »
OO O «-• N
en ^nO en
en w 1^ -r
•^ m »n in
o o
in m
en O O
m m «
en t^ O*
888
C4 O vO
en enco
C* r^ m
M l-l O
O 1-
O O »i^
b O en
\n m 04
en C^
O O
en r*
o g o
GO o* en
r>. en c*
O^ mO
N OO f
vO »n M
rt en in
-r enoo
1-nO o
rf> r- -t ^^ I (in ti «
r-^ en m ^ ^ co -*
Tf o^ h- in -r M n.
U
c
^ 6.N
g § rt
«2 o o o
6 6 « « «
o o.ti.-.ti
U Wi u u u
'^^^^ rt rt rt
5 5 G G G
2 2 c« e« e«
^ ^ -i •= -s
s c s 6 e
*^ 4) « 4>
GU3
"5 .a
G C
<< c o
2 2 6 8
S S o o
O O u wi
G G«*- **^
a E
O 3
6 622
3 6
•2 6^
au S
ea-i
rt 5 «
o o c
V V §
to w bo
00&
1- r*
r>* « vo
« GO en
r>. m O
p o
tAbO
•o
'eS
S 2S
*^u 6
G^ O
U ^ 3
O c o
_1 w
g 3 c1
o c .2
wi b :«
g2^
«•- >»
C ^ tf)
6 C G
o S «
u SJcu
oT oT J
J!< Jtf Jl«
o o o
UUU
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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
Digitized by VjOOQ IC
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
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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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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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J^ATE OF COMBUSTION, DRAFT. II5
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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HEAT AND HEAT-ENGINES.
CJMilETIvr-
Fio. 20.
Fio. 22.
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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ii8
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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RATE OF COMBUSTION, DRAFT.
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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RATE OF COMBUSTION. DRAFT
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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126
HEAT AND HEAT-ENGINES.
iij|iHi|ii[lilii||i|;iy|ji'lTi..*
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RATE OF COMBUSTION. DRAFT.
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128
HEAT AND HEAT-ENGINES.
'% «
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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.
"
*
"
"
" "
"
'
"
"
" "
"
"
"
" '
" "
" "
"
"
"
"
"
"
"
* "
"
"
" "
.
■
"
"
"
"
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"
\ 3
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.
. ,
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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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.
Digitized by VjOOQ IC
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**
f\
^
1
! 1 1 ! .
I
197.8'
i 1 , ■ 1
r -
^S^-' , ] ! : ,
1
N
^1..
1
--
1
\
7679'
1
-
1
! iN
■ 1 i ' 1
1
1
1 \l70,l' ' 1 1
1
1
i
1 \ 1 ' ' '
i
1
1 i >
kl62
3^ 1 1
1
1 X""'
m*
n^'V
146»
140«
136«
130**
1 ! ' \,...,
r
' 1 ; _ A
1
^ 1 , iV
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,
Digitized by
^oo^z
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/)*.
Digitized by VjOOQ IC
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
Digitized by
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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^
■>«'<»• coo
< 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
CO CO w « 0
rN. rn f>, i>H r^
0 0
M M
=
°s
0^ t CO
-) N u-> M
^ CO f>. 0
> •-• M Cl
CO CO N « 0
0 »r> ^ M r^
N COCO 0* 0*
CI 04 CI M C4
»n »-i c« CO M
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
00 n
0 00
CO CO
•
Heat
Equiv.
of
External
Work.
778
2
u
^oo o» N 00
00 r^O 0 ^
r>. 0 ^ mco
0 « -to u^
to 0
I 00 •-• 1- »n
-> mo 0 0
0 0 r^ r* r^
M d C4 CI C«
!>. 1^ rn r^ t>.
CO CO CO CO Tf
r^ r^ !■>. rN. r^
JCft
Heat
Equiv.
of
Internal
Work.
o>
1- 0^ m
TfM 1-co »o
^ m coo 0
0 CO w 0 in
00
%%\l%
00 in CO « 0
0* 0* 0\ 0^ Ov
00 GO CO CO CO
!>. 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
©so
4 QO coo »n
0000
rN. Q 0^ »n c«
Q Q i^ r^ r^
0 0 o> 0* 0^
C rN. m m d
^ 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
U??
C4 COO 0 f>.
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^
«n N ►- 0 ^
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
r^QO CO CO 00
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
o> c^ o> o» c^
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
Digitized by
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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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a
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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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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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.
Digitized by VjOOQ IC
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
Digitized by VjOOQ IC
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.
Digitized by VjOOQ IC
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
100
~^
1 i 1
909
\
CO
\
1
180
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80
V
1
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A.D.1TS0 1700 1770 1780 1790 ISOO ISIO r'^) ].s.'}o 1840 1850 liJ€0 1870 U90 1890 19Q0
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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Fig. 98.
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80000
85
85000
40
40000
45
49000
Fio. 94.
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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-
uu
■
/?
f
A
//
/
f
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4f
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ao
ao
10
80
40 90 GO
Fig. 95.
80
90
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.
Digitized by VjOOQ IC
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
^20?
1 1 !
200"
N
f^-»: 1 1
196"
IW
186»
180»
175*
170»
\l!>»-«'
-
1 1
N.».
r 1
1
1
1 1^
IS2.S
^
1
J
1 i 1"^
,«..,- 1
1 1 1
1 \l70> .
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180*
1 1
T' 1 ri\
f
158*
1
j 1 1 1
>
IW*
1
1
'Ml
l\
Itf*
140»
1 1
\
\\U
7
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~
-
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i3
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U5*
1
1
\
\
IW
106«
100*
!
\
1
! ' ' !
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
^
TU|0
>
11
1
ItflO
N
>^r
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omo
1 1
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m'*
ao*
W
iW
U0»
170»
1 ,
\
l«50.
v..
1 1
i
i
r
-
! 1
1 '
-
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-
1 1
1 1
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1
y
1„
193i2
, ,
[ 1
1
Y
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' 1
MO-
140*
130«
WO"
U0»
100»
J
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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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.
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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.
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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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HEAT AND HEAT-ENGINES.
Pig. 14«6.
Fig. 147.
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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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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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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
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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, ;
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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.
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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.
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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
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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«.
,
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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
Digitized by VjOOQ iC
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 :
Digitized by VjOOQ IC
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.
Q
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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