Cover image for Statistical physics : an introductory course
Title:
Statistical physics : an introductory course
Author:
Amit, D. J., 1938-2007.
Personal Author:
Publication Information:
Singapore ; River Edge, N.J. : World Scientific, 1999.
Physical Description:
xii, 565 pages : illustrations ; 27 cm
General Note:
Includes index.
Language:
English
Subject Term:
Added Author:
ISBN:
9789810231927

9789810234768
Format :
Book

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Material Type
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Status
Central Library QC174.8 .A45 1999 Adult Non-Fiction Non-Fiction Area
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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

Prefacep. xi
Part I The Kinetic Theory of Gasesp. 1
Introductionp. 3
Chapter 1 Velocity and Position Distributions of Molecules in a Gasp. 6
1.1 Avogadro's law, or the equation of state of an ideal gas
1.2 Temperature and thermal equilibriump. 9
1.3 Equipartition of energy per molecule and its constituent parts--a fundamental problemp. 13
1.4 The density in an isothermal atmosphere--the Boltzmann factor in the potential energyp. 20
1.5 The Maxwell-Boltzmann distributionp. 24
1.6 Averages and distributionsp. 28
Chapter 2 Brownian Motionp. 32
2.1 Historical backgroundp. 32
2.2 Characteristic scales of Brownian motionp. 33
2.3 Random walkp. 35
2.4 Brownian motion, random force and friction: the Langevin equationp. 37
2.5 Solving the Langevin equation: approximations and orders of magnitudep. 41
2.6 Applications and implicationsp. 44
Chapter 3 Transport Coefficientsp. 49
3.1 Introductionp. 49
3.2 The mean free path and mean free timep. 50
3.3 Self-diffusionp. 56
3.4 The mobility coefficientp. 61
3.5 The connection between the diffusion coefficient and the mobilityp. 63
3.6 Viscosity and thermal conductivityp. 64
3.7 Appendix: a more detailed calculation of the diffusion coefficientp. 68
Self-assessment exercisesp. 71
Solutions to exercises in the textp. 74
Solutions to self-assessment exercisesp. 107
Part II Statistical Physics with Paramagnetsp. 119
Introductionp. 121
Chapter 0 Essential Background in Thermodynamicsp. 124
0.1 The first lawp. 124
0.2 The second law and the entropyp. 128
0.3 Thermodynamic potentialsp. 129
0.4 The third lawp. 133
Chapter 1 Thermodynamics with Magnetic Variablesp. 134
1.1 Introductionp. 134
1.2 The first law in magnetic variablesp. 136
Chapter 2 Microscopic States and Averagesp. 138
2.1 Magnetic states, angular momentum and paramagnetismp. 138
2.2 Microscopic states, observablesp. 141
2.3 Probabilities and averagesp. 143
Chapter 3 Isolated Paramagnet--Microcanonical Ensemblep. 147
3.1 Number of states and probabilitiesp. 147
3.2 Calculating averages and correlationsp. 149
3.3 Numerical examples and Stirling's formulap. 152
Chapter 4 Isolated Paramagnet--Subsystems and Temperaturep. 156
4.1 Microscopic states and thermodynamic equilibriump. 156
4.2 [beta] and the temperaturep. 157
4.3 Sharpness of the maximump. 158
4.4 Identification of temperature and entropyp. 161
4.5 Negative temperaturep. 163
4.6 Summaryp. 164
Chapter 5 Paramagnet at a Given Temperaturep. 165
5.1 The canonical ensemblep. 165
5.2 The partition function and thermodynamic quantitiesp. 167
5.3 Susceptibility and specific heat of a paramagnetp. 170
5.4 Paramagnet with J ] 1/2p. 173
Chapter 6 Order, Disorder and Entropyp. 174
Chapter 7 Comparison with Experimentp. 177
Summaryp. 178
Self-assessment exercisesp. 180
Solutions to exercises in the textp. 183
Solutions to self-assessment exercisesp. 213
Part III Statistical Physics and Thermodynamicsp. 223
Introductionp. 225
Chapter 1 The Canonical Ensemble and Thermodynamicsp. 226
1.1 The partition function and the internal energyp. 226
1.2 Thermodynamic workp. 228
1.3 Entropy, free energy, the first and second lawsp. 233
1.4 The paramagnet--revisitedp. 236
1.5 On the statistical meaning of the free energyp. 237
Chapter 2 Harmonic Oscillator and Einstein Solidp. 243
2.1 Microscopic statesp. 243
2.2 Partition function for oscillatorsp. 245
2.3 Einstein's solidp. 248
Chapter 3 Statistical Mechanics of Classical Systemsp. 253
3.1 Statistical mechanics of a single particlep. 253
3.2 Statistical mechanics of a classical gasp. 258
Chapter 4 Statistical Mechanics of an Ideal Gasp. 261
4.1 The ideal gasp. 261
4.2 Mixtures of ideal gases--Dalton's lawp. 263
4.3 Maxwell-Boltzmann distribution and equipartitionp. 265
4.4 Ideal gas of quantum particlesp. 268
Chapter 5 The Gibbs Paradox and the Third Lawp. 275
5.1 Two difficultiesp. 275
5.2 The Gibbs paradox and its resolutionp. 276
5.3 Remarks on the third law of thermodynamicsp. 281
5.4 Summaryp. 283
Chapter 6 Fluctuations and Thermodynamic Quantitiesp. 284
6.1 Paramagnet: fluctuations in the magnetizationp. 284
6.2 Energy fluctuations and the specific heatp. 286
6.3 Summaryp. 287
Self-assessment exercisesp. 288
Solutions to exercises in the textp. 292
Solutions to self-assessment exercisesp. 322
Part IV From Ideal Gas to Photon Gasp. 337
Introductionp. 339
Chapter 1 An Ideal Gas of Molecules with Internal Degrees of Freedomp. 340
1.1 Center of mass and internal motionsp. 340
1.2 Kinematics of a diatomic moleculep. 342
1.3 Gas of general composite moleculesp. 346
1.4 Diatomic gas: classical treatmentp. 352
1.5 Diatomic molecules: vibration and rotationp. 356
1.6 The equipartition principle and its violationp. 361
1.7 Diatomic gas--quantum calculationp. 363
Chapter 2 Gases in Chemical Reactionsp. 366
2.1 Conditions for chemical equilibriump. 366
2.2 The law of mass actionp. 368
2.3 Dissociation in a diatomic gasp. 373
Chapter 3 Phonon Gas and the Debye Modelp. 376
3.1 Sound waves in a crystalp. 376
3.2 Vibrational modes, phonons and enumeration of statesp. 379
3.3 The Debye modelp. 382
Chapter 4 Thermodynamics of Electromagnetic Radiationp. 385
4.1 General considerations of radiation at thermal equilibriump. 385
4.2 Radiation densityp. 387
4.3 Black body radiationp. 390
4.4 Absorption and emission of radiation--Kirchhoff's lawp. 394
4.5 Role of black body radiation in modern physicsp. 398
Appendix Calculation of Some Integralsp. 401
Self-assessment exercisesp. 403
Solutions to exercises in the textp. 406
Solutions to self-assessment exercisesp. 434
Part V Of Fermions and Bosonsp. 451
Introductionp. 453
Chapter 1 Grand Canonical Ensemblep. 454
1.1 Definitions and motivationp. 454
1.2 Connection to thermodynamicsp. 455
Chapter 2 Statistical Mechanics of Identical Quantum Particlesp. 458
2.1 Classification of states--occupation numbersp. 458
2.2 Quantum statistics--many-particle statesp. 460
2.3 Thermodynamics of fermions and bosonsp. 461
2.4 Average occupation numbersp. 463
Chapter 3 Electrical Conductivity in Metalsp. 466
3.1 The Drude modelp. 466
3.2 A critique of the Drude modelp. 470
3.3 The Sommerfeld modelp. 471
3.4 Electrons at high and low temperaturesp. 474
3.5 Metals at room temperaturep. 478
3.6 Thermodynamics of the Sommerfeld modelp. 479
Chapter 4 Boson Gasp. 485
4.1 Bose-Einstein distributionp. 485
4.2 Chemical potential at low temperaturesp. 486
4.3 Bose-Einstein condensationp. 488
4.4 Superfluidityp. 490
4.5 Bose-Einstein condensation in heliump. 493
4.6 Viscosity of a superfluidp. 497
4.7 Fermi liquid and superconductivityp. 503
Appendix Calculation of Some Integralsp. 509
Self-assessment exercisesp. 512
Solutions to exercises in the textp. 514
Solutions to self-assessment exercisesp. 536
Indexp. 547

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