Statistical and Thermal Physics: Fundamentals and Applications

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ISBN: 9781568811963 | 1568811969
Cover: Hardcover
Copyright: 9/24/2003

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This book provides a rigorous, self-contained introduction that is suited for teaching and self-study. In the first half of the book, the author introduces the subject inductively but rigorously, proceeding from the concrete and specific to the abstract and general. In clear physical language, the book explains the key concepts, such as temperature, heat, entropy, free energy, chemical potential, and distributions, both classical and quantum. In the second half, the author applies these concepts to a wide variety of phenomena, including perfect gases, electrons in metals and semi- conductors, phase transitions, heat engines, and transport processes.

Preface

xiii

1 Introduction

(4)

2 Temperature, Work, and Heat

(26)

2.1 Thermal Equilibrium and the Zero'th Law of Thermodynamics

(1)

2.2 Empirical Temperature

(6)

2.3 Work and Heat; the First Law of Thermodynamics

(5)

2.4 Reversible and Irreversible Processes

(1)

2.5 Magnetic Work

(4)

2.6 Enthalpy

(1)

2.7 Heat Capacity

(2)

2.8 Envoi

(1)

2.9 Problems

(5)

3 Macrostates and Microstates

(14)

3.1 Macrosystems, Microsystems, and Multiplicity

(2)

3.2 The Spin 1/2 Magnet

(6)

3.3 Multiplicity and Disorder

(3)

3.4 Envoi: Multiplicity in Other Systems

(1)

3.5 Problems

(3)

4 Entropy, Free Energy, and the Second Law of Thermodynamics

4.1 The Condition for Thermal Equilibrium

(2)

4.2 Entropy and the Second Law

(2)

4.3 Absolute Temperature

(2)

4.4 Negative Temperature

(1)

4.5 Entropy and Heat: Isentropic and Isothermal Processes

(3)

4.6 Entropy of Mixing

(1)

4.7 Free Energy

(3)

4.8 The Gibbs-Helmholtz Equation

(1)

4.9 Free Enthalpy (Gibbs Free Energy)

(3)

4.10 Adiabatic Processes

(1)

4.11 Irreversible Adiathermal Processes

(3)

4.12 The Third Law of Thermodynamics

(1)

4.13 Envoi

(1)

4.14 Problems

5 The Canonical Distribution: The Boltzmann Factor and the Partition Function

(94)

5.1 A System in Contact with a Heat Bath

(1)

5.2 The Boltzmann Factor and the Canonical Distribution

(2)

5.3 The Partition Function

(2)

5.4 The Many-Particle Partition Function

(2)

5.5 Examples of the Use of the Canonical Distribution

(6)

5.6 Fluctuations

(2)

5.7 Obtaining the Entropy and Free Energy from the Partition Function

(2)

5.8 Scaling of Energy and Temperature

(1)

5.9 Free Energy and Equilibrium

(6)

5.10 Thermally Activated Processes: Arrhenius' Law

(3)

5.11 Envoi

(1)

5.12 Problems

(8)

6 Continuous Energy Levels, the Density of States, and Equipartition

107

(32)

6.1 Density of States and the Partition Function for a Continuum

107

(2)

6.2 Density of States for a Single Free Particle: One Dimension

109

(1)

6.3 Density of States for a Single Particle: Two and Three Dimensions

110

(4)

6.4 Dimensional Derivation of the Density of States

114

(2)

6.5 Effect of Intermolecular Collisions

116

(1)

6.6 Energy and Partition Function of a Free Particle in Three Dimensions

116

(3)

6.7 Other Uses of the Density of States; Debye's Theory of the Heat Capacity of Solids

119

(6)

6.8 Equipartition

125

(3)

6.9 Brownian Motion

128

(1)

6.10 Electrical (Johnson) Noise

128

(2)

6.11 The Classical Partition Function: Orientational Multiplicity

130

(3)

6.12 Envoi

133

(1)

6.13 Problems

134

(5)

7 Systems with a Variable Number of Particles: The Chemical Potential

139

(24)

7.1 A System in Contact with a Particle Reservoir: Diffusive Equilibrium

139

(2)

7.2 The Chemical Potential

141

(2)

7.3 Free Enthalpy of a Multicomponent System

143

(2)

7.4 Electrochemical Potential

145

(3)

7.5 Probability of Occupancy: The Grand Partition Function

148

(8)

7.6 Chemical Potential and Free Energy

156

(1)

7.7 Fluctuations in Occupancy

157

(1)

7.8 Envoi

158

(1)

7.9 Problems

158

(5)

8 Perfect Gases

163

8.1 Distribution Functions

163

(2)

8.2 Fermions; The Fermi-Dirac Distribution

165

(2)

8.3 Bosons; the Bose-Einstein Distribution

167

(1)

8.4 The Ideal Monatomic Gas and the Maxwell-Boltzmann Distribution

168

(3)

8.5 Envoi

171

(1)

8.6 Problems

171

9 Ideal Gases and Solutions

115

(86)

9.1 Ideal Monatomic Gases: Introduction

175

(1)

9.2 The Maxwell Distribution: Velocity Distribution in an Ideal Gas

176

(2)

9.3 Free Energy and Entropy of an Ideal Monatomic Gas; the Sackur-Tetrode Equation

178

(3)

9.4 Entropy of Mixing of Ideal Gases; Gibbs' Paradox

181

(1)

9.5 Particles with Internal Structure; Ideal Polyatomic Gases

182

(5)

9.6 Heat Capacity of an Ideal Gas at Constant Pressure

187

(1)

9.7 Isentropic Expansion of an Ideal Gas

188

(3)

9.8 The Ideal Gas as a Spring; the Velocity of Sound

191

(2)

9.9 Ideal Solutions and Osmotic Pressure

193

(3)

9.10 Envoi

196

(1)

9.11 Problems

196

(5)

10 Black Body Radiation and the Photon Gas

201

(20)

10.1 Field-Carrying Bosons; the Photon

201

(1)

10.2 Thermodynamics of Radiation; Cavity Radiation

201

(3)

10.3 Kirchhoff's Radiation Law and the Brightness Theorem

204

(1)

10.4 The Stefan-Boltzmann Law

205

(3)

10.5 Isentropic Expansion; the Cosmic Microwave Background

208

(1)

10.6 Radiative Transfer

209

(1)

10.7 Photon Statistics and the Planck Radiation Law

210

(5)

10.8 The Greenhouse Effect

215

(1)

10.9 Envoi

216

(1)

10.10 Problems

216

(5)

11 The Perfect Bose Gas: Bose-Einstein Condensation

221

(10)

11.1 Conserved Bosons

221

(1)

11.2 Bose-Einstein Condensation

222

(5)

11.3 Experimental Observation of Bose-Einstein Condensation in Perfect Gases

227

(1)

11.4 Envoi

228

(1)

11.5 Problems

228

(3)

12 The Perfect Fermi Gas

231

(20)

12.1 Electrons in Metals

231

(4)

12.2 Heat Capacity of a Degenerate Electron Gas

235

(5)

12.3 Internal Energy at 0 K; Fermi Pressure

240

(3)

12.4 Fermi Gases at Nonzero Temperature; the Changeover to the Ideal Gas

243

(3)

12.5 Envoi

246

(1)

12.6 Problems

247

(4)

13 Electrons and Holes in Semiconductors

251

13.1 Metals, Insulators, and Semiconductors

251

(2)

13.2 Density of States Near a Band Edge

253

(4)

13.3 Intrinsic Conduction in a Pure Semiconductor

257

(1)

13.4 Impurities in Semiconductors; Extrinsic Conduction

258

(5)

13.5 The p-n Junction

263

(6)

13.6 Envoi

269

(1)

13.7 Problems

269

14 Phase Transitions

213

(106)

14.1 First Order Transitions

273

(4)

14.2 Superheating and Supercooling

277

(3)

14.3 Properties of the Coexistence Curve; the Clausius-Clapeyron Equation

280

(6)

14.4 Second Order Transitions: The Ferromagnet; Order-Disorder Transitions

286

(8)

14.5 The van der Waals Model of an Imperfect Gas

294

(10)

14.6 Landau's Theory of Phase Transitions

304

(7)

14.7 Envoi; Critical Fluctuations and the Failure of Mean Field Theory

311

(1)

14.8 Problems

312

(7)

15 Heat Engines

319

(24)

15.1 The Carnot Engine

319

(9)

15.2 The Steam Engine

328

(3)

15.3 Internal Combustion Engines: the Otto and Diesel Cycles

331

(6)

15.4 Refrigerators and Heat Pumps: The Vapor-Compression Cycle

337

(2)

15.5 Envoi

339

(1)

15.6 Problems

339

(4)

16 Transport Processes

343

(26)

16.1 Quasi-Ideal Gases

343

(1)

16.2 Scattering Processes; Mean Free Path

343

(3)

16.3 Mobility and Diffusivity; the Einstein Relation

346

(4)

16.4 General Treatment of Transport Processes in Gases

350

(1)

16.5 Thermal Conductivity

351

(3)

16.6 Viscosity

354

(2)

16.7 Effect of Density on Transport Coefficients; the Low Density (Knudsen) Regime

356

(2)

16.8 The Diffusion Equation

358

(4)

16.9 Envoi

362

(1)

16.10 Problems

363

(6)

A Expansion in Series

369

A.1 The Use of Infinite Series in Physics

369

(1)

A.2 The Taylor-McLaurin and Binomial Series

369

(3)

A.3 Expansion Around an Extremum

372

(1)

A.4 A More Complicated Example

373

(1)

A.5 Functions of More Than One Variable

374

B Review of Quantized States

315

(66)

B.1 Introduction: Wave-Particle Duality and the Dispersion Relation for a Particle

375

(1)

B.2 Particle in a Box

376

(1)

B.3 Electron Spin in a Magnetic Field

377

(1)

B.4 The Harmonic Oscillator

377

(2)

B.5 The Quantum Rotator

379

(1)

B.6 The Hydrogen-Like Atom

379

(2)

C Proof That the Zero'th Law Implies the Existence of Temperature

381

(4)

D Some Results in Probability Theory

385

(10)

D.1 Derivation of the Binomial Coefficients c(N,r)

385

(2)

D.2 Stirling's Approximation to the Factorial

387

(1)

D.3 Mean Values (Averages) over a Distribution

388

(1)

D.4 Binomial Distribution

389

(1)

D.5 Gaussian Distribution

390

(2)

D.6 Poisson Distribution

392

(1)

D.7 Derivation of the Multiplicity Function for a System of Identical Oscillators

392

(1)

D.8 Random Walk Program

393

(2)

E Differentials, Partial Derivatives, and the Maxwell Relations

395

(6)

E.1 Differentials

395

(1)

E.2 Triple Product of Partial Derivatives

396

(1)

E.3 Relation Between Cross Derivatives

397

(1)

E.4 Exact and Inexact Differentials

398

(1)

E.5 Maxwell Relations

399

(2)

F Standing Wave Solutions of the Wave Equation

401

(4)

G The Equipartition Theorem

405

(6)

H Some Results in the Kinetic Theory of Gases

411

(4)

H.1 Introduction

411

(1)

H.2 Particle Flux in a Perfect Gas

411

(2)

H.3 Pressure Exerted by a Gas

413

(2)

Glossary

415

(16)

List of Symbols

431

(8)

Physical Constants

439

(2)

Bibliography

441

(2)

Index

443

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Statistical and Thermal Physics: Fundamentals and Applications

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Statistical and Thermal Physics: Fundamentals and Applications

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