Statistical Physics

Statistical Physics Statistical Physics Second Revised and Enlarged Edition by Tony Guénault Emeritus Professor of Low Temperature Physics Lancaster University, UK A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-1-4020-5974-2 (PB) ISBN 978-1-4020-5975-9 (e-book) Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. www.springer.com Printed on acid-free paper First edition 1988 Second edition 1995 Reprinted 1996, 2000, 2001, 2003 Reprinted revised and enlarged second edition 2007 All Rights Reserved © 1988, 1995 A.M. Guénault © 2007 Springer No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Table of contents Preface ix 1 Basic ideas 1.1 The macrostate 1.2 Microstates 1.3 The averaging postulate 1.4 Distributions 1.5 The statistical method in outline 1.6 A model example 1.7 Statistical entropy and microstates 1.8 Summary 1 1 2 3 4 6 7 10 11 2 Distinguishable particles 2.1 The Thermal Equilibrium Distribution 2.2 What are α and β? 2.3 A statistical definition of temperature 2.4 The boltzmann distribution and the partition function 2.5 Calculation of thermodynamic functions 2.6 Summary 13 14 17 18 21 22 23 3 Two examples 3.1 A Spin- 12 solid 3.2 Localized harmonic oscillators 3.3 Summary 25 25 36 40 4 Gases: the density of states 4.1 Fitting waves into boxes 4.2 Other information for statistical physics 4.3 An example – helium gas 4.4 Summary 43 43 47 48 49 5 Gases: the distributions 5.1 Distribution in groups 5.2 Identical particles – fermions and bosons 5.3 Counting microstates for gases 5.4 The three distributions 5.5 Summary 51 51 53 55 58 61 v vi Table of contents 6 Maxwell–Boltzmann gases 6.1 The validity of the Maxwell–Boltzmann limit 6.2 The Maxwell–Boltzmann distribution of speeds 6.3 The connection to thermodynamics 6.4 Summary 63 63 65 68 71 7 Diatomic gases 7.1 Energy contributions in diatomic gases 7.2 Heat capacity of a diatomic gas 7.3 The heat capacity of hydrogen 7.4 Summary 73 73 75 78 81 8 Fermi–Dirac gases 8.1 Properties of an ideal Fermi–Dirac gas 8.2 Application to metals 8.3 Application to helium-3 8.4 Summary 83 84 91 92 95 9 Bose–Einstein gases 9.1 Properties of an ideal Bose–Einstein gas 9.2 Application to helium-4 9.3 Phoney bosons 9.4 A note about cold atoms 9.5 Summary 97 97 101 104 109 109 10 Entropy in other situations 10.1 Entropy and disorder 10.2 An assembly at fixed temperature 10.3 Vacancies in solids 111 111 114 116 11 Phase transitions 11.1