Thermodynamics and Statistical Mechanics

Landsberg P.T.Thermodynamics and Statistical Mechanics(OUP,1978)(ISBN 0198511426)(600dpi)(475p) ......Page 3
Copyright ......Page 4
Preface v ......Page 5
Contents ix ......Page 9
A. THERMODYNAMICS xiii ......Page 13
1 NATURE OF AND SCOPE OF THERMODYNAMICS 1 ......Page 14
2.2. Adiabatic processes 5 ......Page 18
2.3. The laws of thermodynamics 7 ......Page 20
3.1. Fluids 11......Page 24
3.2. Other simple systems 15 ......Page 28
3.3. The velocity of sound 17 ......Page 30
3.4. Homogeneity of extensivity 20 ......Page 33
*3.5. The identification of mv and mp 22 ......Page 35
Problems 24......Page 37
*4.1. Condition for exactness of dfF 26 ......Page 39
*4.2. Condition for dfF = 0 to have an integrating factor 27......Page 40
*4.3. The equation dfF = 0 in two variables has always an integrating factor 28......Page 41
*4.4. Another condition for d'F = 0 to have an inregrating factor 30......Page 43
*4.5. Example for the absence of an integrating factor when n = 3 31 ......Page 44
4.6. Summary 32 ......Page 45
Problems 33 ......Page 46
5.1. Some qualitative formulations of the law 34 ......Page 47
5.2. Plausibility argument for the existence of an entropy function 36 ......Page 49
*5.3, The existence of an absolute temperature and an absolute entropy 40 ......Page 53
5.4. Mathematical formulations of the second law 47 ......Page 60
5.5. The intuitive meaning of entropy 50 ......Page 63
*5.6. An integrating factor for d'Q through equivalence relations 54 ......Page 67
*5.7. Discussion of equation (5.12) 56 ......Page 69
Problems 57 ......Page 70
6.1.A general connection between the two scales 61......Page 74
6.2.Application to the van der Waals gas and the ideal classical gas 64......Page 77
6.3.Various forms of the third law of thermodynamics 67......Page 80
Problems 73......Page 86
7.1. Extensive and intensive variables 77 ......Page 90
7.2. The meaning of chemical potential 80 ......Page 93
7.3. The Gibbs free energy and the Gibbs-Duhem relation 82 ......Page 95
7.4. Equilibrium conditions and the phase rule 84 ......Page 97
7.5. Changes internal to a system 90 ......Page 103
*7.6. Internal stability of a phase kept at given p and T 93 ......Page 106
*7.7. Stability of equilibrium of two parts of an isolated system 99 ......Page 112
*7.8. The van der Waals (first-order) transition 102 ......Page 115
*7.9. The ferromagnetic (second-order) transition 104 ......Page 117
*7.10. Chemical reactions and phase transitions 105 ......Page 118
*7.11. Generalizations and critical exponents 106 ......Page 119
Problems 109 ......Page 122
8 THE MASS ACTION LAW AND THE EQUILIBRIUM CONSTANTS 115 ......Page 128
Problems 120 ......Page 133
B. STATISTICAL MECHANICS 121......Page 134
9.1 . The first equation 123 ......Page 136
9.2. The second equation 131 ......Page 144
9.3. Some special distributions 135 ......Page 148
*9.4. Remarks on the foundations of statistical mechanics 138 ......Page 151
*9.5. The fine-grained entropy is constant in time 141 ......Page 154
Problems 147 ......Page 160
10.1. Mean occupation numbers 154 ......Page 167
10.2. Low-and high-temperature limits 158 ......Page 171
10.3. Occupation numbers for localized spins 160 ......Page 173
10.4. Negative temperatures 164 ......Page 177
*10.5. Phase-space structure for a paramagnet 166 ......Page 179
*10.6. Heat engines and heat pumps at positive and negative absolute temperatures 169 ......Page 182
Problems 177 ......Page 190
11.1. The general procedure 181 ......Page 194
11.2. Significance of the mean total number of particles: the canonical distribution 182 ......Page 195
11.3. Properties of the Fermi and Bose integrals I(c,s,±) 183 ......Page 196
11.4. Verification that the statistical model specifies a class of ideal quantum gases 184 ......Page 197
11.6. The classical approximation 186 ......Page 199
11.7. Classical statistical mechanics: the equi- partition theorem 189 ......Page 202
*11.8. An interpretation of the formula ZN = Z(N,1)/N! 191 ......Page 204
Problems 193 ......Page 206
12 THE DENSITY OF STATES FUNCTIONS 195 ......Page 208
Problems 204 ......Page 217
13.1. Temperature and black-body radiation 208 ......Page 221
13.2. The thermodynamic properties as obtained from statistical mechanics 209 ......Page 222
13.3. The distribution law for photons 212 ......Page 225
13.4. Matter and radiation in the universe 214 ......Page 227
13.5. The early universe 221 ......Page 234
13.6. Radiation in equilibrium with black holes and other systems 224 ......Page 237
13.7. The number of photons emitted by a black body per unit time per unit area 228 ......Page 241
*13.8. Thermodynamics of energy conversion 232 ......Page 245
*13.9. The effective temperature concept 237 ......Page 250
*13.10. The entropy of pencils of radiation 246 ......Page 259
Problems 251 ......Page 264
14.1. The statistical thermodynamics of oscillator systems 254 ......Page 267
14.2. Debyefs theory of the specific heats of solids 257 ......Page 270
14.3. The phonon gas 259 ......Page 272
14.4. The statistical thermodynamics of a Debye solid 263 ......Page 276
14.5. The heat capacities of some other systems 265 ......Page 278
Problems 270 ......Page 283
15.1. The statistical thermodynamics of an ideal quantum gas whose particles have non-zero rest mass 273 ......Page 286
15.2. A Fermi gas at absolute zero (electrons in metals) 274 ......Page 287
15.3. A Fermi gas at low temperatures (electrons in metals) 275 ......Page 288
15.4. Electrons and holes in semiconductors 280 ......Page 293
15.5. Defects in semiconductors 283 ......Page 296
15.6. Mass action laws from statistical mechanics 285 ......Page 298
15.7. Gravitational collapse of Fermi systems to black holes 288 ......Page 301
*15.8. Black-hole thermodynamics 293 ......Page 306
*15.9. A connection between Bose and Fermi statistics: population inversion and lasers 299 ......Page 312
Problems 301 ......Page 314
16.1. Variance and standard deviation 304 ......Page 317
16.2. Normal variates 306 ......Page 319
*16.3. Oscillators and modes of vibration 308 ......Page 321
*16.4. Discrete energy levels without quantization 310 ......Page 323
16.5. Particle number fluctuations 312 ......Page 325
*16.6. Bose-Einstein condensation 314 ......Page 327
16.7. Einstein1s formula for the fluctuation probability 317 ......Page 330
Problems 319 ......Page 332
17.2. The electrochemical potential 320 ......Page 333
17.3. The current densities 321 ......Page 334
17.4. Band edges, electrostatic potential, and energy scales 322 ......Page 335
17.5. The Fermi level is the electrochemical potential 324 ......Page 337
17.6. Einstein relations 326 ......Page 339
17.7. The connection between current density, electrochemical potential, and Einstein relation 328 ......Page 341
Problems 329 ......Page 342
18 OUTLOOK 332 ......Page 345
18.2. Interacting systems and the virial theorem 331 ......Page 344
18.3. Exact results in statistical mechanics 338 ......Page 351
18.4. Solar cell efficiencies 341 ......Page 354
18.5. Special relativistic effects 343 ......Page 356
18.6. General relativistic effects 349 ......Page 362
18.7. A maximum temperature? 354 ......Page 367
18.8. Symmetries in thermodynamics and statistical mechanics 355 ......Page 368
18.9. Order from fluctuations and growth 357 ......Page 370
Problems 358 ......Page 371
C. APPENDICES 359 ......Page 372
APPENDIX I INFORMATION THEORY 361 ......Page 374
APPENDIX II THE ALGEBRA OF LAGRANGIAN MULTIPLIERS 368 ......Page 381
APPENDIX III SOLID ANGLES 370 ......Page 383
APPENDIX IV SPECIAL RELATIVISTIC THERMODYNAMICS: SOME ADDITIONAL TOPICS 373 ......Page 386
D. SOLUTIONS OF PROBLEMS 381 ......Page 394
E. ADDITIONAL MATERIAL 425......Page 438
SUMMARY OF KEY RESULTS 427 ......Page 440
USEFUL MATHEMATICAL AND PHYSICAL DATA 435 ......Page 448
ADDITIONAL READING 439 ......Page 452
BIBLIOGRAPHICAL NOTES 441 ......Page 454
AUTHOR INDEX 453 ......Page 466
SUBJECT INDEX 455 ......Page 468
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