Introduction To Statistical Physics

Title Page......Page 1
Contents......Page 3
Preface......Page 7
1.1 The scope of statistical physics......Page 9
1.2 Description of the assemblies-phase space......Page 11
1.3 The average properties of an assembly......Page 13
1.4 Classical and.quantum assemblies......Page 15
2.1 Distribution over energies......Page 17
2.2 Weights of configurations......Page 20
2.3 The most probable configuration......Page 22
2.4 The sharpness of the configuration maximum......Page 25
2.5 The multiplier ß......Page 27
2.6 The multiplier α......Page 33
2.7 The Maxwell-Boltzmann Distribution......Page 34
3.1 Average properties of systems......Page 36
3.2 The classical perfect gas......Page 38
3.3 Mean and most probable velocities......Page 41
3.4 The Doppler broadening ofspectral lines......Page 43
3.5 Equipartition of energy......Page 45
3.6 The specific heats of gases......Page 48
3.7 The Einstein Diffusion Equation......Page 50
4 Bose-Einstein Statistics......Page 53
4.1 The Bose-Einstein Distribution......Page 54
4.2 The Bose-Einstein Gas......Page 57
4.3 Black-body radiation: the Photon Gas......Page 59
4.4 The specific heats of solids: the Phonon Gas......Page 63
5.1 The Fermi-Dirac Distribution......Page 68
5.2 The·Fermi-Dirac Gas......Page 71
5.3 The Electron Gas......Page 73
5.4 Pauli paramagnetism......Page 76
5.5 Thermionic emission......Page 78
6.1 The statistical concept of temperature......Page 83
6.2 Entropy......Page 85
6.3 The free energy......Page 90
7.1 The weight W_max for a classical perfect gas......Page 94
7.2 The Boltzmann Partition Function......Page 95
7.3 The Evaluation of the Classical Partition Function......Page 99
7.4 Gibbs\' paradox......Page 101
7.5 The semi-classical perfect gas......Page 103
7.6 Components of the Partition Function......Page 107
8.1 The paramagnetic gas......Page 114
8.2 The harmonic oscillator......Page 119
8.3 The diatomic molecule......Page 121
8.4 The two energy level system......Page 129
8.5 The disordered lattice......Page 132
9.1 Ensembles......Page 136
9.2 The constant temperature ensemble......Page 137
9.3 Thermodynamic properties of the canonicalensemble......Page 140
9.4 The evaluation of the Total Partition Function......Page 142
9.6 Application of the canonical ensemble toan imperfect gas......Page 147
9.7 Fluctuations of the assembly energy in a canonical ensemble......Page 152
9.8 The quantum mechanical density operator......Page 155
10 The Grand Canonical Ensemble......Page 159
10.1 Thermodynamic functions of an open assembly......Page 160
10.2 The Grand Partition Function......Page 162
10.3 Evaluation of the Grand Partition Function......Page 165
10.4 Fluctuations in the number of systems......Page 173
10.5 The chemical potentials in the equilibrium state......Page 175
Bibliography......Page 178
APPENDICES......Page 179
1 The Lagrange UndeterminedMultipliers......Page 181
2 Stirling\'s Approximation......Page 184
3 Derivation of the Distribution over Energies for a Classical Ensemble......Page 186
4 Equivalent Volumes Phase Space......Page 191
5 The Volume of a State in Phase Space......Page 193
6 The Γ-lntegrals......Page 197
6 Integrals Involving the Fermi Function......Page 200
Index......Page 209