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Central Library | QC174.8 .A45 1999 | Adult Non-Fiction | Non-Fiction Area | Searching... |

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### Summary

### Summary

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.

### Table of Contents

Preface | p. xi |

Part I The Kinetic Theory of Gases | p. 1 |

Introduction | p. 3 |

Chapter 1 Velocity and Position Distributions of Molecules in a Gas | p. 6 |

1.1 Avogadro's law, or the equation of state of an ideal gas | |

1.2 Temperature and thermal equilibrium | p. 9 |

1.3 Equipartition of energy per molecule and its constituent parts--a fundamental problem | p. 13 |

1.4 The density in an isothermal atmosphere--the Boltzmann factor in the potential energy | p. 20 |

1.5 The Maxwell-Boltzmann distribution | p. 24 |

1.6 Averages and distributions | p. 28 |

Chapter 2 Brownian Motion | p. 32 |

2.1 Historical background | p. 32 |

2.2 Characteristic scales of Brownian motion | p. 33 |

2.3 Random walk | p. 35 |

2.4 Brownian motion, random force and friction: the Langevin equation | p. 37 |

2.5 Solving the Langevin equation: approximations and orders of magnitude | p. 41 |

2.6 Applications and implications | p. 44 |

Chapter 3 Transport Coefficients | p. 49 |

3.1 Introduction | p. 49 |

3.2 The mean free path and mean free time | p. 50 |

3.3 Self-diffusion | p. 56 |

3.4 The mobility coefficient | p. 61 |

3.5 The connection between the diffusion coefficient and the mobility | p. 63 |

3.6 Viscosity and thermal conductivity | p. 64 |

3.7 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 |

Part II Statistical Physics with Paramagnets | p. 119 |

Introduction | p. 121 |

Chapter 0 Essential Background in Thermodynamics | p. 124 |

0.1 The first law | p. 124 |

0.2 The second law and the entropy | p. 128 |

0.3 Thermodynamic potentials | p. 129 |

0.4 The third law | p. 133 |

Chapter 1 Thermodynamics with Magnetic Variables | p. 134 |

1.1 Introduction | p. 134 |

1.2 The first law in magnetic variables | p. 136 |

Chapter 2 Microscopic States and Averages | p. 138 |

2.1 Magnetic states, angular momentum and paramagnetism | p. 138 |

2.2 Microscopic states, observables | p. 141 |

2.3 Probabilities and averages | p. 143 |

Chapter 3 Isolated Paramagnet--Microcanonical Ensemble | p. 147 |

3.1 Number of states and probabilities | p. 147 |

3.2 Calculating averages and correlations | p. 149 |

3.3 Numerical examples and Stirling's formula | p. 152 |

Chapter 4 Isolated Paramagnet--Subsystems and Temperature | p. 156 |

4.1 Microscopic states and thermodynamic equilibrium | p. 156 |

4.2 [beta] and the temperature | p. 157 |

4.3 Sharpness of the maximum | p. 158 |

4.4 Identification of temperature and entropy | p. 161 |

4.5 Negative temperature | p. 163 |

4.6 Summary | p. 164 |

Chapter 5 Paramagnet at a Given Temperature | p. 165 |

5.1 The canonical ensemble | p. 165 |

5.2 The partition function and thermodynamic quantities | p. 167 |

5.3 Susceptibility and specific heat of a paramagnet | p. 170 |

5.4 Paramagnet with J ] 1/2 | p. 173 |

Chapter 6 Order, Disorder and Entropy | p. 174 |

Chapter 7 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 |

Part III Statistical Physics and Thermodynamics | p. 223 |

Introduction | p. 225 |

Chapter 1 The Canonical Ensemble and Thermodynamics | p. 226 |

1.1 The partition function and the internal energy | p. 226 |

1.2 Thermodynamic work | p. 228 |

1.3 Entropy, free energy, the first and second laws | p. 233 |

1.4 The paramagnet--revisited | p. 236 |

1.5 On the statistical meaning of the free energy | p. 237 |

Chapter 2 Harmonic Oscillator and Einstein Solid | p. 243 |

2.1 Microscopic states | p. 243 |

2.2 Partition function for oscillators | p. 245 |

2.3 Einstein's solid | p. 248 |

Chapter 3 Statistical Mechanics of Classical Systems | p. 253 |

3.1 Statistical mechanics of a single particle | p. 253 |

3.2 Statistical mechanics of a classical gas | p. 258 |

Chapter 4 Statistical Mechanics of an Ideal Gas | p. 261 |

4.1 The ideal gas | p. 261 |

4.2 Mixtures of ideal gases--Dalton's law | p. 263 |

4.3 Maxwell-Boltzmann distribution and equipartition | p. 265 |

4.4 Ideal gas of quantum particles | p. 268 |

Chapter 5 The Gibbs Paradox and the Third Law | p. 275 |

5.1 Two difficulties | p. 275 |

5.2 The Gibbs paradox and its resolution | p. 276 |

5.3 Remarks on the third law of thermodynamics | p. 281 |

5.4 Summary | p. 283 |

Chapter 6 Fluctuations and Thermodynamic Quantities | p. 284 |

6.1 Paramagnet: fluctuations in the magnetization | p. 284 |

6.2 Energy fluctuations and the specific heat | p. 286 |

6.3 Summary | p. 287 |

Self-assessment exercises | p. 288 |

Solutions to exercises in the text | p. 292 |

Solutions to self-assessment exercises | p. 322 |

Part IV From Ideal Gas to Photon Gas | p. 337 |

Introduction | p. 339 |

Chapter 1 An Ideal Gas of Molecules with Internal Degrees of Freedom | p. 340 |

1.1 Center of mass and internal motions | p. 340 |

1.2 Kinematics of a diatomic molecule | p. 342 |

1.3 Gas of general composite molecules | p. 346 |

1.4 Diatomic gas: classical treatment | p. 352 |

1.5 Diatomic molecules: vibration and rotation | p. 356 |

1.6 The equipartition principle and its violation | p. 361 |

1.7 Diatomic gas--quantum calculation | p. 363 |

Chapter 2 Gases in Chemical Reactions | p. 366 |

2.1 Conditions for chemical equilibrium | p. 366 |

2.2 The law of mass action | p. 368 |

2.3 Dissociation in a diatomic gas | p. 373 |

Chapter 3 Phonon Gas and the Debye Model | p. 376 |

3.1 Sound waves in a crystal | p. 376 |

3.2 Vibrational modes, phonons and enumeration of states | p. 379 |

3.3 The Debye model | p. 382 |

Chapter 4 Thermodynamics of Electromagnetic Radiation | p. 385 |

4.1 General considerations of radiation at thermal equilibrium | p. 385 |

4.2 Radiation density | p. 387 |

4.3 Black body radiation | p. 390 |

4.4 Absorption and emission of radiation--Kirchhoff's law | p. 394 |

4.5 Role of black body radiation in modern physics | p. 398 |

Appendix 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 |

Part V Of Fermions and Bosons | p. 451 |

Introduction | p. 453 |

Chapter 1 Grand Canonical Ensemble | p. 454 |

1.1 Definitions and motivation | p. 454 |

1.2 Connection to thermodynamics | p. 455 |

Chapter 2 Statistical Mechanics of Identical Quantum Particles | p. 458 |

2.1 Classification of states--occupation numbers | p. 458 |

2.2 Quantum statistics--many-particle states | p. 460 |

2.3 Thermodynamics of fermions and bosons | p. 461 |

2.4 Average occupation numbers | p. 463 |

Chapter 3 Electrical Conductivity in Metals | p. 466 |

3.1 The Drude model | p. 466 |

3.2 A critique of the Drude model | p. 470 |

3.3 The Sommerfeld model | p. 471 |

3.4 Electrons at high and low temperatures | p. 474 |

3.5 Metals at room temperature | p. 478 |

3.6 Thermodynamics of the Sommerfeld model | p. 479 |

Chapter 4 Boson Gas | p. 485 |

4.1 Bose-Einstein distribution | p. 485 |

4.2 Chemical potential at low temperatures | p. 486 |

4.3 Bose-Einstein condensation | p. 488 |

4.4 Superfluidity | p. 490 |

4.5 Bose-Einstein condensation in helium | p. 493 |

4.6 Viscosity of a superfluid | p. 497 |

4.7 Fermi liquid and superconductivity | p. 503 |

Appendix 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 |