Statistical and Thermal Physics: Fundamentals and Applications

by Sturge ,M.D.

• ISBN13: 9781568811963
• ISBN10: 1568811969
• Format: Hardcover
• Copyright: 2003-09-24
• Publisher: CRC PRESS

Summary

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.

Table of Contents

Preface	xiii
1 Introduction	1	(4)
2 Temperature, Work, and Heat	5	(26)
2.1 Thermal Equilibrium and the Zero'th Law of Thermodynamics	5	(1)
2.2 Empirical Temperature	6	(6)
2.3 Work and Heat; the First Law of Thermodynamics	12	(5)
2.4 Reversible and Irreversible Processes	17	(1)
2.5 Magnetic Work	18	(4)
2.6 Enthalpy	22	(1)
2.7 Heat Capacity	23	(2)
2.8 Envoi	25	(1)
2.9 Problems	26	(5)
3 Macrostates and Microstates	31	(14)
3.1 Macrosystems, Microsystems, and Multiplicity	31	(2)
3.2 The Spin 1/2 Magnet	33	(6)
3.3 Multiplicity and Disorder	39	(3)
3.4 Envoi: Multiplicity in Other Systems	42	(1)
3.5 Problems	42	(3)
4 Entropy, Free Energy, and the Second Law of Thermodynamics	45
4.1 The Condition for Thermal Equilibrium	45	(2)
4.2 Entropy and the Second Law	47	(2)
4.3 Absolute Temperature	49	(2)
4.4 Negative Temperature	51	(1)
4.5 Entropy and Heat: Isentropic and Isothermal Processes	52	(3)
4.6 Entropy of Mixing	55	(1)
4.7 Free Energy	56	(3)
4.8 The Gibbs-Helmholtz Equation	59	(1)
4.9 Free Enthalpy (Gibbs Free Energy)	60	(3)
4.10 Adiabatic Processes	63	(1)
4.11 Irreversible Adiathermal Processes	64	(3)
4.12 The Third Law of Thermodynamics	67	(1)
4.13 Envoi	68	(1)
4.14 Problems	68
5 The Canonical Distribution: The Boltzmann Factor and the Partition Function	13	(94)
5.1 A System in Contact with a Heat Bath	73	(1)
5.2 The Boltzmann Factor and the Canonical Distribution	74	(2)
5.3 The Partition Function	76	(2)
5.4 The Many-Particle Partition Function	78	(2)
5.5 Examples of the Use of the Canonical Distribution	80	(6)
5.6 Fluctuations	86	(2)
5.7 Obtaining the Entropy and Free Energy from the Partition Function	88	(2)
5.8 Scaling of Energy and Temperature	90	(1)
5.9 Free Energy and Equilibrium	90	(6)
5.10 Thermally Activated Processes: Arrhenius' Law	96	(3)
5.11 Envoi	99	(1)
5.12 Problems	99	(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