Preface xiii
Part I Elements of Thermal Physics 1
1. Fundamentals 3
1.1 PVT Systems 3
1.2 Equilibrium States 6
1.3 Processes and Heat 10
1.4 Temperature 12
1.5 Size Dependence 13
1.6 Heat Capacity and Specific Heat 14
Problems 17
2. First Law of Thermodynamics 19
2.1 Work 19
2.2 Heat 21
2.3 The First Law 21
2.4 Applications 22
Problems 26
3. Properties and Partial Derivatives 27
3.1 Conventions 27
3.2 Equilibrium Properties 28
3.3 Relationships between Properties 34
3.4 Series Expansions 40
3.5 Summary 41
Problems 42
4. Processes in Gases 45
4.1 Ideal Gases 45
4.2 Temperature Change with Elevation 48
4.3 Cyclic Processes 50
4.4 Heat Engines 52
Problems 58
5. Phase Transitions 61
5.1 Solids, Liquids, and Gases 61
5.2 Latent Heats 65
5.3 Van der Waals Model 67
5.4 Classification of Phase Transitions 70
Problems 72
6. Reversible and Irreversible Processes 75
6.1 Idealization and Reversibility 75
6.2 Nonequilibrium Processes and Irreversibility 76
6.3 Electrical Systems 79
6.4 Heat Conduction 82
Problems 86
Part II Foundations of Thermodynamics 89
7. Second Law of Thermodynamics 91
7.1 Energy, Heat, and Reversibility 91
7.2 Cyclic Processes 93
7.3 Second Law of Thermodynamics 95
7.4 Carnot Cycles 98
7.5 Absolute Temperature 100
7.6 Applications 103
Problems 107
8. Temperature Scales and Absolute Zero 109
8.1 Temperature Scales 109
8.2 Uniform Scales and Absolute Zero 111
8.3 Other Temperature Scales 114
Problems 115
9. State Space and Differentials 117
9.1 Spaces 117
9.2 Differentials 121
9.3 Exact Versus Inexact Differentials 123
9.4 Integrating Differentials 127
9.5 Differentials in Thermodynamics 129
9.6 Discussion and Summary 134
Problems 136
10. Entropy 139
10.1 Definition of Entropy 139
10.2 Clausius? Theorem 142
10.3 Entropy Principle 145
10.4 Entropy and Irreversibility 148
10.5 Useful Energy 151
10.6 The Third Law 155
10.7 Unattainability of Absolute Zero 156
Problems 158
Appendix 10.A. Entropy Statement of the Second Law 158
11. Consequences of Existence of Entropy 165
11.1 Differentials of Entropy and Energy 165
11.2 Ideal Gases 167
11.3 Relationships Between CV, CP, BT , BS, and ?V 170
11.4 Clapeyron?s Equation 172
11.5 Maximum Entropy, Equilibrium, and Stability 174
11.6 Mixing 178
Problems 184
12. Thermodynamic Potentials 185
12.1 Internal Energy 185
12.2 Free Energies 186
12.3 Properties From Potentials 188
12.4 Systems in Contact with a Heat Reservoir 193
12.5 Minimum Free Energy 194
Problems 197
Appendix 12.A. Derivatives of Potentials 197
13. Phase Transitions and Open Systems 201
13.1 Two-Phase Equilibrium 201
13.2 Chemical Potential 206
13.3 Multi-Component Systems 211
13.4 Gibbs Phase Rule 214
13.5 Chemical Reactions 215
Problems 217
14. Dielectric and Magnetic Systems 219
14.1 Dielectrics 219
14.2 Magnetic Materials 224
14.3 Critical Phenomena 229
Problems 233
Part III Statistical Thermodynamics 235
15. Molecular Models 237
15.1 Microscopic Descriptions 237
15.2 Gas Pressure 238
15.3 Equipartition of Energy 243
15.4 Internal Energy of Solids 246
15.5 Inactive Degrees of Freedom 247
15.6 Microscopic Significance of Heat 248
Problems 253
16. Kinetic Theory of Gases 255
16.1 Velocity Distribution 255
16.2 Combinatorics 256
16.3 Method of Undetermined Multipliers 258
16.4 Maxwell Distribution 260
16.5 Mean-Free-Path 265
Problems 267
Appendix 16.A. Quantum Distributions 267
17. Microscopic Significance of Entropy 273
17.1 Boltzmann Entropy 273
17.2 Ideal Gas 274
17.3 Statistical Interpretation 278
17.4 Thermodynamic Properties 279
17.5 Boltzmann Factors 284
Problems 286
Appendix 17.A. Evaluation of I3N 286
Part IV Statistical Mechanics I 289
18. Ensembles 291
18.1 Probabilities and Averages 291
18.2 Two-Level Systems 293
18.3 Information Theory 295
18.4 Equilibrium Ensembles 298
18.5 Canonical Thermodynamics 302
18.6 Composite Systems 305
Problems 308
Appendix 18.A. Uniqueness Theorem 308
19. Partition Function 311
19.1 Hamiltonians and Phase Space 311
19.2 Model Hamiltonians 312
19.3 Classical Canonical Ensemble 316
19.4 Thermodynamic Properties and Averages 318
19.5 Ideal Gases 322
19.6 Harmonic Solids 326
Problems 328
20. Quantum Systems 331
20.1 Energy Eigenstates 331
20.2 Quantum Canonical Ensemble 333
20.3 Ideal Gases 334
20.4 Einstein Model 337
20.5 Classical Approximation 341
Problems 344
Appendix 20.A. Ideal Gas Eigenstates 344
21. Independent Particles and Paramagnetism 349
21.1 Averages 349
21.2 Statistical Independence 351
21.3 Classical Systems 353
21.4 Paramagnetism 357
21.5 Spin Systems 360
21.6 Classical Dipoles 365
Problems 367
Appendix 21.A. Negative Temperature 367
22. Fluctuations and Energy Distributions 371
22.1 Standard Deviation 371
22.2 Energy Fluctuations 375
22.3 Gibbs Paradox 376
22.4 Microcanonical Ensemble 380
22.5 Comparison of Ensembles 386
Problems 391
23. Generalizations and Diatomic Gases 393
23.1 Generalized Coordinates 393
23.2 Diatomic Gases 397
23.3 Quantum Effects 402
23.4 Density Matrices 405
23.5 Canonical Ensemble 408
Problems 410
Appendix 23.A. Classical Approximation 410
Part V Statistical Mechanics II 415
24. Photons and Phonons 417
24.1 Plane Wave Eigenstates 417
24.2 Photons 421
24.3 Harmonic Approximation 425
24.4 Phonons 429
Problems 434
25. Grand Canonical Ensemble 435
25.1 Thermodynamics of Open Systems 435
25.2 Grand Canonical Ensemble 437
25.3 Properties and Fluctuations 438
25.4 Ideal Gases 441
Problems 443
26. Fermions and Bosons 445
26.1 Identical Particles 445
26.2 Exchange Symmetry 447
26.3 Fermi?Dirac and Bose?Einstein Statistics
452
Problems 456
Appendix 26.A. Fermions in the Canonical Ensemble 457
27. Fermi and Bose Gases 461
27.1 Ideal Gases 461
27.2 Fermi Gases 465
27.3 Low Temperature Heat Capacity 466
27.4 Bose Gases 469
Problems 472
28. Interacting Systems 475
28.1 Ising Model 475
28.2 Nonideal Gases 481
Problems 487
29. Computer Simulations 489
29.1 Averages 489
29.2 Virial Formula for Pressure 490
29.3 Simulation Algorithms 496
A. Mathematical Relations, Constants, and Properties
501
A.1 Partial Derivatives 501
A.2 Integrals and Series 501
A.3 Taylor Series 502
A.4 Hyperbolic Functions 502
A.5 Fundamental Constants 503
A.6 Conversion Factors 503
A.7 Useful Formulas 503
A.8 Properties of Water 504
A.9 Properties of Materials 504
Answers to Problems 505
Index 509
