## Thermal PhysicsSuitable for both undergraduates and graduates, this textbook provides an up-to-date, accessible introduction to thermal physics. The material provides a comprehensive understanding of thermodynamics, statistical mechanics, and kinetic theory, and has been extensively tested in the classroom by the author who is an experienced teacher. This book begins with a clear review of fundamental ideas and goes on to construct a conceptual foundation of four linked elements: entropy and the Second Law, the canonical probability distribution, the partition function, and the chemical potential. This foundation is used throughout the book to help explain new topics and exciting recent developments such as Bose-Einstein condensation and critical phenomena. The highlighting of key equations, summaries of essential ideas, and an extensive set of problems of varying degrees of difficulty will allow readers to fully grasp both the basic and current aspects of the subject. A solutions manual is available for instructors. This book is an invaluable textbook for students in physics and astronomy. |

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### Contents

Background | 1 |

12 Some dilute gas relationships | 4 |

13 The First Law of Thermodynamics | 8 |

14 Heat capacity | 11 |

15 An adiabatic process | 13 |

16 The meaning of words | 16 |

17 Essentials | 18 |

Further reading | 21 |

The Free Energies | 222 |

102 Helmholtz free energy | 225 |

103 More on understanding the chemical potential | 226 |

104 Gibbs free energy | 230 |

106 Why the phrase free energy? | 234 |

107 Miscellany | 236 |

108 Essentials | 238 |

Further reading | 239 |

The Second Law of Thermodynamics | 24 |

22 The Second Law of Thermodynamics | 28 |

23 The power of the Second Law | 29 |

24 Connecting multiplicity and energy transfer by heating | 31 |

25 Some examples | 35 |

26 Generalization | 39 |

27 Entropy and disorder | 44 |

28 Essentials | 45 |

Further reading | 46 |

Problems | 47 |

Entropy and Efficiency | 51 |

32 Maximum efficiency | 55 |

33 A practical consequence | 59 |

34 Rapid change | 60 |

35 The simplified Otto cycle | 62 |

36 More about reversibility | 67 |

37 Essentials | 69 |

Further reading | 70 |

Problems | 71 |

Entropy in Quantum Theory | 75 |

42 The quantum version of multiplicity | 80 |

44 Essentials | 86 |

Problems | 87 |

The Canonical Probability Distribution | 89 |

52 Probabilities when the temperature is fixed | 91 |

spin ½h paramagnetism | 94 |

54 The partition function technique | 96 |

55 The energy range ½E | 99 |

56 The ideal gas treated semiclassically | 101 |

57 Theoretical threads | 109 |

Further reading | 111 |

Problems | 112 |

Photons and Phonons | 116 |

62 Electromagnetic waves and photons | 118 |

63 Radiative flux | 123 |

64 Entropy and evolution optional | 128 |

65 Sound waves and phonons | 130 |

66 Essentials | 139 |

Further reading | 141 |

The Chemical Potential | 148 |

72 Minimum free energy | 155 |

73 A lemma for computing | 156 |

74 Adsorption | 157 |

75 Essentials | 160 |

Further reading | 161 |

Problems | 162 |

The Quantum Ideal Gas | 166 |

82 Occupation numbers | 168 |

classical and semiclassical | 173 |

85 The nearly classical ideal gas optional | 175 |

86 Essentials | 178 |

Further reading | 179 |

Problems | 180 |

Fermions and Bosons at Low Temperature | 182 |

92 Pauli paramagnetism optional | 192 |

93 White dwarf stars optional | 194 |

theory | 199 |

experiments | 205 |

96 A graphical comparison | 209 |

97 Essentials | 212 |

Further reading | 214 |

Problems | 215 |

Problems | 240 |

Chemical Equilibrium | 244 |

112 A consequence of minimum free energy | 246 |

113 The diatomic molecule | 250 |

114 Thermal ionization | 257 |

115 Another facet of chemical equilibrium | 260 |

116 Creation and annihilation | 262 |

117 Essentials | 264 |

Further reading | 266 |

Phase Equilibrium | 270 |

122 Latent heat | 273 |

123 Conditions for coexistence | 276 |

124 GibbsDuhem relation | 279 |

125 ClausiusClapeyron equation | 280 |

126 Cooling by adiabatic compression optional | 282 |

127 Gibbsphase rule optional | 290 |

128 Isotherms | 291 |

129 Van der Waals equation of state | 293 |

1210 Essentials | 300 |

Further reading | 301 |

The Classical Limit | 306 |

132 The Maxwellian gas | 309 |

133 The equipartition theorem | 314 |

134 Heat capacity of diatomic molecules | 318 |

135 Essentials | 320 |

Further reading | 322 |

Approaching Zero | 327 |

142 Entropy in paramagnetism | 329 |

143 Cooling by adiabatic demagnetization | 331 |

144 The Third Law of Thermodynamics | 337 |

145 Some other consequences of the Third Law | 341 |

146 Negative absolute temperatures | 343 |

147 Temperature recapitulated | 347 |

148 Why heating increases the entropy Or does it? | 349 |

149 Essentials | 351 |

Further reading | 352 |

Problems | 353 |

Transport Processes | 356 |

152 Random walk | 360 |

viscosity | 362 |

154 Pipe flow | 366 |

thermal conduction | 367 |

156 Timedependent thermal conduction | 369 |

an example | 372 |

158 Refinements | 375 |

159 Essentials | 377 |

Further reading | 378 |

Critical Phenomena | 382 |

162 Critical exponents | 388 |

163 Ising model | 389 |

164 Mean field theory | 392 |

165 Renormalization group | 397 |

166 Firstorder versus continuous | 407 |

167 Universality | 409 |

168 Essentials | 414 |

Further reading | 415 |

Epilogue | 419 |

Physical and Mathematical Data | 420 |

Examples of Estimating Occupation Numbers | 426 |

The Framework of Probability Theory | 428 |

Qualitative Perspectives on the van der Waals Equation | 435 |

### Common terms and phrases

absolute zero adiabatic approximation atoms average behavior bosons calculation canonical probability distribution Carnot cycle chapter chemical potential classical ideal gas coefficient coexistence compute conduction electrons constant context cooling critical point Debye denotes dependence derivative diatomic molecule diffuse efficiency energy input entropy change equal estimate example exponent exponential expression external parameters factor fermions Figure flux frequency Gibbs free energy heat capacity helium Helmholtz free energy hence ideal gas law implies input by heating integral interaction Ising model isothermal kinetic energy lattice Law of Thermodynamics liquid logarithm low temperature macroscopic macrostate magnetic moment mass mean field theory molecular momentum multiplicity negative nuclei number density occupation numbers paramagnetic particles partition function phase photon potential energy pressure provides quantum radiation ratio relationship relative reservoir Second Law semi-classical single-particle solid spatial specified speed theory thermal equilibrium thermal physics vaporization curve variables velocity vibrational volume wavelength waves