Problems in Thermodynamics and Statistical Physics

by Peter T. Landsberg (Editor)

Overview

Well respected and widely used, this volume presents problems and full solutions related to a wide range of topics in thermodynamics, statistical physics, and statistical mechanics. The text is intended for instructors, undergraduates, and graduate students of mathematics, physics, chemistry, and engineering. Twenty-eight chapters, each prepared by an expert, proceed from simpler to more difficult subjects. Similarly, the early chapters are easier than the later ones, making the book ideal for independent study.Subjects begin with the laws of thermodynamics and statistical theory of information and of ensembles, advancing to the ideal classical gases of polyatomic molecules, non-electrolyte liquids and solutions, and surfaces. Subsequent chapters explore imperfect classical and quantum gas, phase transitions, cooperative phenomena, Green function methods, the plasma, transport in gases and metals, Nyquist's theorem and its generalizations, stochastic methods, and many other topics.

Product Details

ISBN-13:	9780486795041
Publisher:	Dover Publications
Publication date:	05/15/2014
Series:	Dover Books on Physics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	592
File size:	55 MB
Note:	This product may take a few minutes to download.

About the Author

Peter T. Landsberg (1922–2010) taught at University College Cardiff from 1959 to 1971 and held the chair in Applied Mathematics at the University of Southampton from 1982 to 1987. He wrote, edited, and coauthored 11 books, including Dover's Thermodynamics and Statistical Mechanics, and more than 400 scientific papers.

Table of Contents

Authors v

Preface vii

1 The laws of thermodynamics P. T. Landsberg 1

Mathematical preliminaries 1

Quasistatic changes 4

The First Law 6

The Second Law 9

Simple ideal fluids 11

Joule-Thomson effect 21

Thermodynamic cycles 23

Chemical thermodynamics 28

The Third Law 33

Phase changes 34

Thermal and mechanical stability 37

2 Statistical theory of information and of ensembles P.T. Landsberg 44

Entropy maximisation: ensembles 44

Partition functions in general 48

Entropy maximisation: probability distributions 51

Most probable distribution method 53

Some general principles 60

3 Statistical mechanics of ideal systems P.T. Landsberg 63

Maxwell distribution 63

Classical statistical mechanics 67

Virial theorem 72

Oscillators and phonons 74

The ideal quantum gas 80

Constant pressure ensembles 92

Radiative emission and absorption 93

4 Ideal classical gases of polyatomic molecules C.J. Wormald 98

The translational partition function 98

Thermodynamic properties and the theory of fluctuations 100

The classical rotational partition function 103

The quantum mechanical rotational partition function 105

A convenient formula for the high temperature rotational partition function 108

Thermodynamic properties arising from simple harmonic model of vibration 110

Corrections to the rigid rotator-harmonic oscillator model 113

Contributions to the thermodynamic properties arising from low lying electronic energy levels 118

Calculation of the thermodynamic properties of HC1 from spectroscopic data 121

Thermodynamic properties of ethane 127

5 Ideal relativistic classical and quantum gases P.T. Landsberg 132

6 Non-electrolyte liquids and solutions A.J.B. Cruickshank 140

Cell theories of the liquid state 142

Equation of state treatment of liquids 154

Binary solutions 168

7 Phase stability, co-existence, and criticality A.J.B. Cruickshank 193

Singulary systems 193

Binary systems 214

8 Surfaces J.M. Haynes 230

The Gibbs model of a surface 230

9 The imperfect classical gas P.C. Hemmer 246

The equation of state 246

The virial expansion 254

Pair distribution function. Virial theorem 261

10 The imperfect quantum gas D.ter Haar 270

The equation of state 270

Second quantisation formalism 278

11 Phase transitions D.ter Haar 282

Einstein condensation of a perfect boson gas 282

Vapour condensation 289

Hard sphere gas 293

12 Cooperative phenomena D.ter Haar 303

13 Green function methods D.ter Haar 319

Mathematical preliminaries 319

General formalism 320

The Kubo formula 323

The Heisenberg ferromagnet 324

14 The plasma (D. ter Haar) 333

15 Negative temperatures and population inversion U.M. Titulaer 341

Dynamic polarization 346

A model of laser action 348

16 Recombination rate theory in semiconductors J.S. Blakemore 350

17 Transport in gases D.J. Griffiths 378

18 Transport in metals J.M. Honig 401

19 Transport in semiconductors J.M. Honig 432

20 Fluctuations of energy and number of particles C.W. McCombie 448

21 Fluctuations of general classical mechanical variables C.W. McCombie 457

22 Fluctuations of thermodynamic variables: constant pressure systems, isolated systems C.W. McCombie 465

23 Time dependence of fluctuations: correlation functions, power spectra, Wiener-Khintchine relations C.W. McCombie 472

24 Nyquist's theorem and its generalizations C.W. McCombie 489

25 Onsager relations C.W. McCombie 502

26 Stochastic methods', master equation and Fokker-Planck equation I. Oppenheim K. E. Shuler G.H. Weiss 511

27 Ergodic theory, H-theorems, recurrence problems D.ter Haar 531

28 Variational principles and minimum entropy production S. Simons 549

Macroscopic principles 549

Electron flow problems 557

Author index 563

Subject index 565