Statistical Physics

An Introductory Course

By: Daniel J Amit, Yosef Verbin, Open University Of Israel The

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Paperback | 7 December 1999

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580 Pages

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26 x 18.5 x 3

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This invaluable textbook is an introduction to statistical physics that has been written primarily for self-study. It provides a comprehensive approach to the main ideas of statistical physics at the level of an introductory course, starting from the kinetic theory of gases and proceeding all the way to Bose-Einstein and Fermi-Dirac statistics. Each idea is brought out with ample motivation and clear, step-by-step, deductive exposition. The key points and methods are presented and discussed on the basis of concrete representative systems, such as the paramagnet, Einstein''s solid, the diatomic gas, black body radiation, electric conductivity in metals and superfluidity.The book is written in a stimulating style and is accompanied by a large number of exercises appropriately placed within the text and by self-assessment problems at the end of each chapter. Detailed solutions of all the exercises are provided.

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Preface	p. xi
The Kinetic Theory of Gases	p. 1
Introduction	p. 3
Velocity and Position Distributions of Molecules in a Gas	p. 6
Avogadro's law, or the equation of state of an ideal gas
Temperature and thermal equilibrium	p. 9
Equipartition of energy per molecule and its constituent parts--a fundamental problem	p. 13
The density in an isothermal atmosphere--the Boltzmann factor in the potential energy	p. 20
The Maxwell-Boltzmann distribution	p. 24
Averages and distributions	p. 28
Brownian Motion	p. 32
Historical background	p. 32
Characteristic scales of Brownian motion	p. 33
Random walk	p. 35
Brownian motion, random force and friction: the Langevin equation	p. 37
Solving the Langevin equation: approximations and orders of magnitude	p. 41
Applications and implications	p. 44
Transport Coefficients	p. 49
Introduction	p. 49
The mean free path and mean free time	p. 50
Self-diffusion	p. 56
The mobility coefficient	p. 61
The connection between the diffusion coefficient and the mobility	p. 63
Viscosity and thermal conductivity	p. 64
Appendix: a more detailed calculation of the diffusion coefficient	p. 68
Self-assessment exercises	p. 71
Solutions to exercises in the text	p. 74
Solutions to self-assessment exercises	p. 107
Statistical Physics with Paramagnets	p. 119
Introduction	p. 121
Essential Background in Thermodynamics	p. 124
The first law	p. 124
The second law and the entropy	p. 128
Thermodynamic potentials	p. 129
The third law	p. 133
Thermodynamics with Magnetic Variables	p. 134
Introduction	p. 134
The first law in magnetic variables	p. 136
Microscopic States and Averages	p. 138
Magnetic states, angular momentum and paramagnetism	p. 138
Microscopic states, observables	p. 141
Probabilities and averages	p. 143
Isolated Paramagnet--Microcanonical Ensemble	p. 147
Number of states and probabilities	p. 147
Calculating averages and correlations	p. 149
Numerical examples and Stirling's formula	p. 152
Isolated Paramagnet--Subsystems and Temperature	p. 156
Microscopic states and thermodynamic equilibrium	p. 156
[beta] and the temperature	p. 157
Sharpness of the maximum	p. 158
Identification of temperature and entropy	p. 161
Negative temperature	p. 163
Summary	p. 164
Paramagnet at a Given Temperature	p. 165
The canonical ensemble	p. 165
The partition function and thermodynamic quantities	p. 167
Susceptibility and specific heat of a paramagnet	p. 170
Paramagnet with J ] 1/2	p. 173
Order, Disorder and Entropy	p. 174
Comparison with Experiment	p. 177
Summary	p. 178
Self-assessment exercises	p. 180
Solutions to exercises in the text	p. 183
Solutions to self-assessment exercises	p. 213
Statistical Physics and Thermodynamics	p. 223
Introduction	p. 225
The Canonical Ensemble and Thermodynamics	p. 226
The partition function and the internal energy	p. 226
Thermodynamic work	p. 228
Entropy, free energy, the first and second laws	p. 233
The paramagnet--revisited	p. 236
On the statistical meaning of the free energy	p. 237
Harmonic Oscillator and Einstein Solid	p. 243
Microscopic states	p. 243
Partition function for oscillators	p. 245
Einstein's solid	p. 248
Statistical Mechanics of Classical Systems	p. 253
Statistical mechanics of a single particle	p. 253
Statistical mechanics of a classical gas	p. 258
Statistical Mechanics of an Ideal Gas	p. 261
The ideal gas	p. 261
Mixtures of ideal gases--Dalton's law	p. 263
Maxwell-Boltzmann distribution and equipartition	p. 265
Ideal gas of quantum particles	p. 268
The Gibbs Paradox and the Third Law	p. 275
Two difficulties	p. 275
The Gibbs paradox and its resolution	p. 276
Remarks on the third law of thermodynamics	p. 281
Summary	p. 283
Fluctuations and Thermodynamic Quantities	p. 284
Paramagnet: fluctuations in the magnetization	p. 284
Energy fluctuations and the specific heat	p. 286
Summary	p. 287
Self-assessment exercises	p. 288
Solutions to exercises in the text	p. 292
Solutions to self-assessment exercises	p. 322
From Ideal Gas to Photon Gas	p. 337
Introduction	p. 339
An Ideal Gas of Molecules with Internal Degrees of Freedom	p. 340
Center of mass and internal motions	p. 340
Kinematics of a diatomic molecule	p. 342
Gas of general composite molecules	p. 346
Diatomic gas: classical treatment	p. 352
Diatomic molecules: vibration and rotation	p. 356
The equipartition principle and its violation	p. 361
Diatomic gas--quantum calculation	p. 363
Gases in Chemical Reactions	p. 366
Conditions for chemical equilibrium	p. 366
The law of mass action	p. 368
Dissociation in a diatomic gas	p. 373
Phonon Gas and the Debye Model	p. 376
Sound waves in a crystal	p. 376
Vibrational modes, phonons and enumeration of states	p. 379
The Debye model	p. 382
Thermodynamics of Electromagnetic Radiation	p. 385
General considerations of radiation at thermal equilibrium	p. 385
Radiation density	p. 387
Black body radiation	p. 390
Absorption and emission of radiation--Kirchhoff's law	p. 394
Role of black body radiation in modern physics	p. 398
Calculation of Some Integrals	p. 401
Self-assessment exercises	p. 403
Solutions to exercises in the text	p. 406
Solutions to self-assessment exercises	p. 434
Of Fermions and Bosons	p. 451
Introduction	p. 453
Grand Canonical Ensemble	p. 454
Definitions and motivation	p. 454
Connection to thermodynamics	p. 455
Statistical Mechanics of Identical Quantum Particles	p. 458
Classification of states--occupation numbers	p. 458
Quantum statistics--many-particle states	p. 460
Thermodynamics of fermions and bosons	p. 461
Average occupation numbers	p. 463
Electrical Conductivity in Metals	p. 466
The Drude model	p. 466
A critique of the Drude model	p. 470
The Sommerfeld model	p. 471
Electrons at high and low temperatures	p. 474
Metals at room temperature	p. 478
Thermodynamics of the Sommerfeld model	p. 479
Boson Gas	p. 485
Bose-Einstein distribution	p. 485
Chemical potential at low temperatures	p. 486
Bose-Einstein condensation	p. 488
Superfluidity	p. 490
Bose-Einstein condensation in helium	p. 493
Viscosity of a superfluid	p. 497
Fermi liquid and superconductivity	p. 503
Calculation of Some Integrals	p. 509
Self-assessment exercises	p. 512
Solutions to exercises in the text	p. 514
Solutions to self-assessment exercises	p. 536
Index	p. 547
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