Statistical Mechanics: Fundamentals and Model Solutions

348 Pages·2021·10.165 MB·English

by  Teunis C Dorlas

Statistical Mechanics

Statistical Mechanics
Fundamentals and Model Solutions
Second Edition
Teunis C. Dorlas
Second edition published [2021]
by CRC Press
6000 Broken Sound Parkway NW, Suite 300, Boca Raton, FL 33487-2742
and by CRC Press
2 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
© 2021 Taylor & Francis Group, LLC
[First edition published by CRC Press 1999]
CRC Press is an imprint of Taylor & Francis Group, LLC
Reasonable efforts have been made to publish reliable data and information, but the author and pub-
lisher cannot assume responsibility for the validity of all materials or the consequences of their use.
The authors and publishers have attempted to trace the copyright holders of all material reproduced
in this publication and apologize to copyright holders if permission to publish in this form has not
been obtained. If any copyright material has not been acknowledged please write and let us know so
we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced,
transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or
hereafter invented, including photocopying, microfilming, and recording, or in any information stor-
age or retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, access www.copyright.
com or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA
01923, 978-750-8400. For works that are not available on CCC please contact mpkbookspermissions@
tandf.co.uk
Trademark notice: Product or corporate names may be trademarks or registered trademarks and are
used only for identification and explanation without intent to infringe.
Library of Congress Cataloging-in-Publication Data
Names: Dorlas, T. C. (Teunis Christiaan), 1955- author.
Title: Statistical mechanics : fundamentals and model solutions / Teunis C.
Dorlas, School of Theoretical Physics Dublin Institute for Advanced
Studies.
Description: Second edition. | Boca Raton : CRC Press, 2021. | Includes
bibliographical references and index.
Identifiers: LCCN 2020055180 | ISBN 9780367471750 (paperback) | ISBN
9780367478810 (hardback) | ISBN 9781003037170 (ebook)
Subjects: LCSH: Statistical mechanics.
Classification: LCC QC174.8 .D68 2021 | DDC 530.13--dc23
LC record available at https://lccn.loc.gov/2020055180
ISBN: 9780367478810 (hbk)
ISBN: 9780367471750 (pbk)
ISBN: 9781003037170 (ebk)
Typeset in Computer Modern font
by KnowledgeWorks Global Ltd.
Access the support material at: www.routledgetextbooks.com/textbooks/instructor_downloads/
In memory of my parents

Contents
Preface xi
Introduction xiii
Acknowledgments xxi
Section I Thermodynamics
hapter
C 1(cid:4) The Zeroth Law 3
hapter
C 2(cid:4) The First Law 7
hapter
C 3(cid:4) Differentials 13
hapter
C 4(cid:4) The Second Law 17
hapter
C 5(cid:4) Thermal Engines and Refrigerators 23
hapter
C 6(cid:4) The Fundamental Equation 29
hapter
C 7(cid:4) Convexity 35
hapter
C 8(cid:4) Thermodynamic Potentials 43
hapter
C 9(cid:4) Phase Transitions 49
hapter
C 10(cid:4) Magnetism 57
hapter
C 11(cid:4) Refrigeration and Liquefaction 61
vii
viii (cid:4) Contents
hapter
C 12(cid:4) Examples of Phase Transitions 69
hapter
C 13(cid:4) Equations of State for Solids 75
hapter
C 14(cid:4) Applications in Chemistry 79
hapter
C 15(cid:4) Black-Body Radiation 83
hapter
C 16(cid:4) The Big Bang 87
hapter
C 17(cid:4) The Constitution of Stars 93
Section II Fundamentals of Statistical Mechanics
hapter
C 18(cid:4) Quantum Mechanics 107
hapter
C 19(cid:4) Non-Interacting Localized Spins 119
hapter
C 20(cid:4) Large Deviation Theory 125
hapter
C 21(cid:4) The Paramagnet Revisited 137
hapter
C 22(cid:4) Identical Localized Free Particles 141
hapter
C 23(cid:4) Quantum Gases 145
hapter
C 24(cid:4) Ensembles 153
hapter
C 25(cid:4) The Thermodynamic Limit 157
hapter
C 26(cid:4) LDP for the Energy Density 163
Section III Models in Statistical Mechanics
hapter
C 27(cid:4) A Simple Model for Rubber 177
hapter
C 28(cid:4) The Ising Model 181
hapter
C 29(cid:4) The Weiss-Ising Model 195
Contents (cid:4) ix
hapter
C 30(cid:4) The Mean-Field Lattice Gas 201
hapter
C 31(cid:4) Metals and the Electron Gas 207
hapter
C 32(cid:4) White-Dwarf Stars 213
hapter
C 33(cid:4) Phonons 219
hapter
C 34(cid:4) Boson Condensation and Liquid Helium 223
hapter
C 35(cid:4) Superconductivity 235
hapter
C 36(cid:4) Mayer Expansion for a Classical Gas 249
hapter
C 37(cid:4) Cluster Expansion and Polymer Models 257
ppendix
A A(cid:4) Probability Theory 279
ppendix
A B(cid:4) Quantum Mechanics 287
ppendix
A C(cid:4) Convexity 297
Index 319