In this post, we will see the book Thermodynamics, Statistical Physics, and Kinetics by Yu. B. Rumer and M. Sh. Ryvkin

About the book

This book is intended for readers taking up the study of thermo­dynamics, statistical physics and kinetics. Accordingly, readers are assumed to have a knowledge of elementary physics, higher mathematics and quantum mechanics.

The sections marked by asterisks require a deeper knowledge and can be omitted on the first reading.

The book aims to gradually familiarize readers with methods used in thermodynamics, statistical physics and kinetics, to show how the concrete problems should be solved and to bring readers as soon as possible to a level which enables them to tackle more specialized books and papers. It has therefore proved necessary to include some matter, perhaps too simple for some, as well as problems that may be too difficult for others.

The book was translated from Russian by S. Semyonov and was published in 1980 by Mir.

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You can get the book here.

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Contents

Preface 5
Introduction 11

PART ONE THERMODYNAMICS 13

Chapter I. General Laws of Thermodynamics 13

1. Equilibrium states and equilibrium processes 14
2. Temperature. The temperature principle 16
3. Entropy. The entropy princip 18
4. Absolute temperature and absolute entropy 20
5. Work 23
6. Adiabatic and isothermal potentials 25
7. The energy principle. Supply and removal of heat 28
8. Heat capacity of gases 31
9. Cyclic processes. The Carnot cycle 33
10. Axiomatics of thermodynamics. Generalization of the concept of entropy to arbitrary thermodynamic systems. Nernst’s heat theorem 38
11. Thermodynamic coefficients. Polytropic processes 43
12. Thermodynamics of the van der Waals gas 52
13. Gas cooling methods. Gay-Lussac and Joule-Thomson processes 61
14. Thermodynamics of rods 67
15. Thermodynamics of magnetics 72
16. Thermodynamics of dielectrics 80
17. Thermodynamics of radiation 85
18. Thermodynamics of water 91
19. The thermodynamic potential. Method of thermodynamic functions 96
20. Thermodynamics of plasma 102
21. Polyvariant systems. Magnetostriction and the piezomagnetic effect 104

Chapter II. Systems with Variable Amount of Matter. Phase Transitions 110

22. Systems with variable amount of matter. The chemical potential 110
23.The increase in entropy in equalization processes. The Gibbs paradox 113
24. Extrema of thermodynamic functions 121
25. Thermodynamic inequalities 128
26. Phase equilibrium. First-order phase transitions 130
27. Three-phase equilibrium. Superheating and supercooling 141
28. Second-order phase transitions 148
29. Thermodynamics of superconductors 150
30. Multicomponent systems. Phase rule 155
31. Chemical equilibrium in a homogeneous system. The mass action law 158

PART TWO STATISTICAL PHYSICS

Chapter III. Statistical Distributions for Ideal Gases 165

32. Statistical regularities. Distributions, most probable distributions 165
33. 𝜇-Space. Boxes and cells 170
34. Bose-Einstein and Fermi-Dirac distributions 173
35. The Boltzmann principle 180
36. The Maxwell-Boltzmann distribution 186
37. Transition to continuously varying energy. Degeneracy conditions for ideal gases 190
38. The 𝛺-potential of Bose and Fermi gases 194
39. Energy quantization. The Nernst theorem 197

Chapter IV. The Maxwell-Boltzmann Gas 202

40. The Maxwell-Boltzmann monoatomic gas in the classical approximation. Phase volume of a cell and the zero point entropy 202
41. The’ Maxwell distribution 205
42. Spatial distribution of molecules 209
43. Polyatomic gases (classical theory). The equipartition theorem 210
44. The Maxwell-Boltzmann gas with two energy levels 214
45. Quantization of translational motion 216
46. Diatomic gas. Rotational degrees of freedom 219
47. Molecules consisting of identical atoms. Ortho- and paramodifications 225
48. Vibrational degrees of freedom 230
49. Thermal ionization of atoms 234
50. Thermal dissociation of molecules 239
51. Paramagnetic gas in a magnetic field 242

Chapter V. Degenerate Gases 246

52. Equilibrium thermal radiation. Photon gas 246
53. Thermal motion in crystals. Phonon gas 253
54. A degenerate Bose gas in the absence of a field. The Bose-Einstein condensation 262
55. The Bose gas in an external field 270
56. An electron in a periodic field 273
57. Degenerate Fermi gas. Electron gas in metals 276
58. Electrons in a semiconductor 283
59. Magnetism of an electron gas 286

Chapter VI. Systems of Interacting Particles. The Gibbs Method 297

60. 𝛤-space. Liouville’s theorem 297
61. Microcanonical and canonical distributions 302
62. T-V-𝜇 and T-P-N distributions 306
63. Another derivation of the T-V-N, T-V-𝜇 and T-V-N distribution
Thermodynamic corollaries 309
64. Derivation of the Bose-Einstein and Fermi-Dirac distributions with the aid of a grand canonical ensemble 322
65. Nonideal gases 325
66. Plasma. Debye’s screening 335
67. Extreme and negative temperatures 337
68. Second quantization 345
69. Superfluidity. Bogoliubov’s theory 359
70. Superconductivity 366

Chapter VII. Theory of Fluctuations 384

71. Fluctuations in energy, volume and number of particles 384
72. Fluctuations in main thermodynamic quantities 388
73. Fluctuations in occupation numbers in idéal gases 391
74. Fluctuation limit of sensitivity of measuring instruments. Nyquist’s
theorem 393

Chapter VIII. Phase Transitions 398

75. The Lee-Yang theory 398
76. Critical exponents and phenomenological inequalities for them 403
77. Critical point for the van der Waals gas 405
78. Phase transition in ferromagnetic materials. Molecular field method and the Bragg0Williams approximation 409
79. The Landau theory of second-order phase transitions 418
80. Review of results. Comparison with experiment. Models with exact
solutions 427
81. Fluctuations and phase transitions. The Ornstein-Zernike theory. Similarity hypothesis 435

PART THREE ELEMENTS OF KINETICS AND NON-EQUILIBRIUM THERMODYNAMICS

Chapter IX. Kinetics

82. The Smoluchowski equation. The principle of detailed balancing 444
83. The Fokker-Planck equation. Brownian motion 454
84. Kinetic balance equation. Einstein’s derivation of Planck’s formula 448
85. The Boltzmann kinetic equation 459
86. The Bogoliubov equations 465
87. Evolution stages for a non-equilibrium system. Bogoliubov’s derivation of Boltzmann’s equation 472
88. Dimensionless form of Bogoliubov’s equations. Factorization and the correlation functions. Free-molecule flow 483
89. Equation of a self-consistent field. Collisionless plasma 487
90. Oscillations of electron plasma 489
91. The Laws of conservation and the entropy increase law 495
92. Local equilibrium 501
93. The kinetic equation for plasma 505
94. Equations of gas dynamics 511
95. Methods of solution for Boltzmann’s equation 521
96. Irreversibility of macroscopic processes 531
97. Density matrix and its variation with time. The Cubo method 542

Chapter X. Elements of Non-Equilibrium Thermodynamics 549

98. Balance equations for mass, momentum, energy and entropy 549
99. Small deviations from equilibrium. Onsager’s principle 557
100. Corollaries of Onsager’s reciprocal relations. Theorem on the minimum production of entropy for stationary states. Examples 562
101. Far-from-equilibrium states 566

MATHEMATICAL APPENDIX

I. Jacobians (functional determinants) 570
II. Stirling’s formula 573
III. Lagrange’s method of finding the conditional extremum 574
IV. Integrals Jn 575
V. Probability function erf(x) 576
VI. Properties of function (x) = 576
VII. Integrals Kn and K’n 577
VIII. Dirac’s delta-function (x) and step function c (x) 579
IX. Integrals Ln 581
X. Integral M 581
XI. The Laplace transform 583
XII. Integrals for section 59 585
XIII. n-Dimensional sphere 586
XIV. The Gauss distribution for one and two variables 587

References 589
Name Index 591
Subject Index 593