Statistical Physics

Cover......Page 1
Statistical Physics, Second Revised and Enlarged Edition......Page 4
1402059744......Page 5
Table of contents......Page 6
Preface......Page 10
1.1 THE MACROSTATE......Page 14
1.2 MICROSTATES......Page 15
1.3 THE AVERAGING POSTULATE......Page 16
1.4 DISTRIBUTIONS......Page 17
1.5.2 Possible distributions......Page 19
1.6.1 A simple assembly......Page 20
1.6.2 A composite assembly......Page 22
1.7 STATISTICAL ENTROPY AND MICROSTATES......Page 23
1.8 SUMMARY......Page 24
2 Distinguishable particles......Page 26
2.1.4 The average distribution......Page 27
2.1.5 The most probable distribution......Page 28
2.2.2 β and energy......Page 30
2.3.1 β and temperature......Page 31
2.3.2 Temperature and entropy......Page 33
2.4 THE BOLTZMANN DISTRIBUTION AND THE PARTITION FUNCTION......Page 34
2.5 CALCULATION OF THERMODYNAMIC FUNCTIONS......Page 35
2.6 SUMMARY......Page 36
3.1.1 An assembly of particles with two states......Page 38
3.1.2 Magnetic solids......Page 42
3.1.3 Cooling by adiabatic demagnetization......Page 43
3.1.4 Magnetization and thermometry......Page 47
3.2.1 The thermal properties......Page 49
3.2.2 The extreme quantum and the classical limits......Page 52
3.3 SUMMARY......Page 53
4.1 FITTING WAVES INTO BOXES......Page 56
4.2.1 Quantum states are k-states plus......Page 60
4.3 AN EXAMPLE – HELIUM GAS......Page 61
4.4 SUMMARY......Page 62
5.1 DISTRIBUTION IN GROUPS......Page 64
5.2 IDENTICAL PARTICLES – FERMIONS AND BOSONS......Page 66
5.3.1 Fermions......Page 68
5.3.2 Bosons......Page 69
5.3.3 Dilute gases......Page 70
5.4.1 Fermi–Dirac statistics......Page 71
5.4.2 Bose–Einstein statistics......Page 72
5.4.3 Maxwell–Boltzmann statistics......Page 73
5.5 SUMMARY......Page 74
6.1 THE VALIDITY OF THE MAXWELL–BOLTZMANN LIMIT......Page 76
6.2 THE MAXWELL–BOLTZMANN DISTRIBUTION OF SPEEDS......Page 78
6.3.2 Entropy......Page 81
6.3.3 Free energy and pressure......Page 83
6.4 SUMMARY......Page 84
7.1 ENERGY CONTRIBUTIONS IN DIATOMIC GASES......Page 86
7.2.2 Electronic contribution......Page 88
7.2.4 Rotational contribution......Page 89
7.3 THE HEAT CAPACITY OF HYDROGEN......Page 91
7.3.1 The onset of rotation......Page 92
7.4 SUMMARY......Page 94
8 Fermi–Dirac gases......Page 96
8.1.1 The Fermi–Dirac distribution......Page 97
8.1.2 The Fermi energy......Page 98
8.1.3 The thermodynamic functions......Page 101
8.2 APPLICATION TO METALS......Page 104
8.3 APPLICATION TO HELIUM-3......Page 105
8.4 SUMMARY......Page 108
9.1.1 The Bose–Einstein distribution......Page 110
9.1.2 The Bose–Einstein condensation......Page 112
9.2 APPLICATION TO HELIUM-4......Page 114
9.3.1 Photons and black-body radiation......Page 117
9.3.2 Phonons and lattice vibrations......Page 120
9.5 SUMMARY......Page 122
10.1.1 Isotopic disorder......Page 124
10.1.2 Localized particles......Page 125
10.2 AN ASSEMBLYAT FIXED TEMPERATURE......Page 127
10.2.1 Distinguishable particles revisited......Page 128
10.3 VACANCIES IN SOLIDS......Page 129
11.1 TYPES OF PHASE TRANSITION......Page 132
11.2 FERROMAGNETISM OF A SPIN -1/2 SOLID......Page 133
11.2.1 The spontaneous magnetization (method 1)......Page 134
11.2.2 The spontaneous magnetization (method 2)......Page 136
11.2.3 The thermal properties......Page 137
11.2.4 The paramagnetic region......Page 138
11.3 REAL FERROMAGNETIC MATERIALS......Page 139
11.4 ORDER–DISORDER TRANSFORMATIONS IN ALLOYS......Page 140
12.1.1 Matter and radiation in equilibrium......Page 142
12.1.2 Transitions with electrons......Page 144
12.2 ENSEMBLES – A LARGER VIEW......Page 145
13.1 CHEMICAL POTENTIAL REVISITED......Page 150
13.2.1 The new method......Page 152
13.2.2 The connection to thermodynamics......Page 153
13.3.1 Determination of the grand partition function......Page 154
13.3.2 Derivation of the distributions......Page 156
13.3.3 Thermodynamics of an ideal MB gas......Page 158
13.4.1 Free energy of a many-component assembly......Page 159
13.4.2 Mixed ideal gases......Page 160
13.4.3 Equilibrium in chemical reactions......Page 161
13.4.4 The law of mass action......Page 162
13.4.5 Reaction rates......Page 163
14 Dealing with interactions......Page 166
14.1 ELECTRONS IN METALS......Page 167
14.2.1 Landau Fermi liquid theory......Page 171
14.2.2 Application to liquid ^3He......Page 174
14.3 LIQUID HELIUM-4: A BOSE LIQUID?......Page 176
14.4 REAL IMPERFECT GASES......Page 177
14.4.1 Classical statistical mechanics......Page 178
14.4.2 Imperfect gases......Page 179
15.1 SUPERFLUID STATES IN FERMI–DIRAC SYSTEMS......Page 182
15.1.1 Superconductivity......Page 183
15.1.2 Superfluid ^3He......Page 185
15.2 STATISTICS IN ASTROPHYSICAL SYSTEMS......Page 187
15.2.1 After the big bang......Page 188
15.2.2 The stability of stars......Page 189
Appendix A Some elementary counting problems......Page 194
1 STIRLING’S APPROXIMATION......Page 196
2 APROBLEM WITH PENNIES......Page 197
1 MAXWELL–BOLTZMANN INTEGRALS......Page 200
2 FERMI–DIRAC INTEGRALS......Page 201
Appendix D Some useful constants......Page 204
Appendix E Exercises......Page 206
Appendix F Answers to exercises......Page 212
Index......Page 214