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

Super text! A methodical and scientific material with indisputable values in content, analysis, application. Scientific publications realized up to the 90s are the greatest value of the training of specialists and scientists.

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Hi

Page no. 13 is white.

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