Thermodynamics & Statistical Mechanics by Stowe

572 Pages·2007·4.42 MB·English

by  Keith Stowe

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An Introduction to Thermodynamics and Statistical
Mechanics, Second Edition
Thisintroductorytextbookforstandardundergraduatecoursesin
thermodynamicshasbeencompletelyrewrittentoexploreagreaternumberof
topicsmoreclearlyandconcisely.Startingwithanoverviewofimportant
quantumbehaviors,thebookteachesstudentshowtocalculateprobabilitiesin
ordertoprovideafirmfoundationforlaterchapters.Itthenintroducestheideas
of“classicalthermodynamics”--internalenergy,interactions,entropy,andthe
fundamentalsecondlaw.Theseideasareexploredbothingeneralandasthey
areappliedtomorespecificprocessesandinteractions.Theremainderofthe
bookdealswith“statisticalmechanics”--thestudyofsmallsystemsinteracting
withhugereservoirs.
ThechangesinthisSecondEditionhavebeenmadeasaresultofmorethan10
yearsofclassroomtestingandfeedbackfromstudents.Tohelpstudentsreview
theimportantconceptsandtesttheirnewlygainedknowledge,eachtopicends
withaboxedsummaryofideasandresults.Everychapterhasnumerous
homeworkproblems,coveringabroadrangeofdifficulties.Answersaregiven
toodd-numberedproblems,andsolutionstoeven-numberedproblemsare
availabletoinstructorsatwww.cambridge.org/9780521865579.
K S isaprofessorofphysicsatCaliforniaPolytechnicState
Universityandhasworkedtherefor32years.Hehasspenttimeatthe
UniversityofWashington,Harvard,theUniversityofNorthCarolina,andthe
UniversityofMichigan.AswellashavingwrittentheFirstEditionof
IntroductiontoThermodynamicsandStatisticalMechanics,hehasalsowritten
booksonoceanscience.

An Introduction to
Thermodynamics and
Statistical Mechanics
Second Edition
Keith Stowe
California Polytechnic State University
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521865579
© K. Stowe 2007
This publication is in copyright. Subject to statutory exception and to the provision of
relevant collective licensing agreements, no reproduction of any part may take place
without the written permission of Cambridge University Press.
First published in print format 2007
ISBN-13 978-0-511-27406-0 eBook (EBL)
ISBN-10 0-511-27406-8 eBook (EBL)
ISBN-13 978-0-521-86557-9 hardback
ISBN-10 0-521-86557-3 hardback
Cambridge University Press has no responsibility for the persistence or accuracy of urls
for external or third-party internet websites referred to in this publication, and does not
guarantee that any content on such websites is, or will remain, accurate or appropriate.
Contents
Preface page vii
Listofconstants,conversions,andprefixes xii
PartI Settingthescene 1
1 Introduction 3
PartII Smallsystems 23
2 Statisticsforsmallsystems 25
3 Systemswithmanyelements 40
PartIII Energyandthefirstlaw 63
4 Internalenergy 65
5 Interactionsbetweensystems 79
PartIV Statesandthesecondlaw 99
6 Internalenergyandthenumberofaccessiblestates 101
7 Entropyandthesecondlaw 117
8 Entropyandthermalinteractions 135
PartV Constraints 153
9 Naturalconstraints 155
10 Models 186
11 Choiceofvariables 210
12 Specialprocesses 226
13 Engines 252
14 Diffusiveinteractions 287
PartVI Classicalstatistics 327
15 Probabilitiesandmicroscopicbehaviors 329
16 Kinetictheoryandtransportprocessesingases 352
17 Magneticpropertiesofmaterials 369
18 Thepartitionfunction 382
v
vi Contents
PartVII Quantumstatistics 399
19 Introductiontoquantumstatistics 401
20 Quantumgases 422
21 Blackbodyradiation 438
22 Thethermalpropertiesofsolids 457
23 Theelectricalpropertiesofmaterials 477
24 Lowtemperaturesanddegeneratesystems 504
Appendices 531
Furtherreading 537
Problemsolutions 538
Index 551
Preface
Goals
Thesubjectofthermodynamicswasbeingdevelopedonapostulatorybasislong
before we understood the nature or behavior of the elementary constituents of
matter.Aswebecamemorefamiliarwiththeseconstituents,wewerestillslowto
placeourtrustinthe“new”fieldofquantummechanics,whichwastellingusthat
their behaviors could be described correctly and accurately using probabilities
andstatistics.
Theinfluenceofthishistoricalsequencehaslingeredinourtraditionalther-
modynamics curriculum. Until recently, we continued to teach an introductory
courseusingthemoreformalandabstractpostulatoryapproach.Now,however,
thereisagrowingfeelingthatthestatisticalapproachismoreeffective.Itdemon-
stratesthefirmphysicalandstatisticalbasisofthermodynamicsbyshowinghow
thepropertiesofmacroscopicsystemsaredirectconsequencesofthebehaviors
oftheirelementaryconstituents.Anaddedadvantageofthisapproachisthatitis
easilyextendedtoincludesomestatisticalmechanicsinanintroductorycourse.
Itgivesthestudentabroaderspectrumofskillsaswellasabetterunderstanding
ofthephysicalbases.
Thisbookisintendedforuseinthestandardjuniororseniorundergraduate
courseinthermodynamics,anditassumesnopreviousknowledgeofthesubject.
Itrytointroducethesubjectassimplyandsuccinctlyaspossible,withenough
applicationstoindicatetherelevanceoftheresultsbutnotsomanyasmightrisk
losingthestudentindetails.Therearemanyadvancedbooksofhighqualitythat
canhelptheinterestedstudentprobemoredeeplyintothesubjectanditsmore
specializedapplications.
I try to tie everything straight to fundamental concepts, and I avoid “slick
tricks”andthe“pyramiding”ofresults.Iremainfocusedonthebasicideasand
physicalcauses,becauseIbelievethiswillhelpstudentsbetterunderstand,retain,
andapplythetoolsandresultsthatwedevelop.
Active learning
Ithinkthatreallearningmustbeanactiveprocess.Itisimportantforthestudent
toapplynewknowledgetospecificproblemsassoonaspossible.Thisshouldbea
vii
viii Preface
dailyactivity,andproblemsshouldbeattemptedwhiletheknowledgeisstillfresh.
Aroutineoffrequent,timely,andshortproblem-solvingsessionsisfarsuperior
toafewinfrequentproblem-solvingmarathons.Forthisreason,attheendofeach
chapterthetextincludesaverylargenumberofsuggestedhomeworkproblems,
whichareorganizedbysection.Solutionstotheodd-numberedproblemsareat
theendofthebookforinstantfeedback.
Active learning can also be encouraged by streamlining the more passive
components.Thesoonerthestudentunderstandsthetextmaterial,thesoonerhe
orshecanapplyit.Forthisreason,IhaveputthetopicsinwhatIbelievetobethe
mostlearning-efficientorder,andIexplaintheconceptsassimplyandclearlyas
possible.Summariesarefrequentandareincludedwithinthechapterswherever
Ithinkwouldbehelpfultoafirst-timestudentwrestlingwiththeconcepts.They
arealsoshadedforeasyidentification.Hopefully,thisstreamliningofthepassive
aspectsmightallowmoretimeforactiveproblemsolving.
Changes in the second edition
Theentirebookhasbeenrewritten.Myprimaryobjectiveforthesecondedition
hasbeentoexploremoretopics,morethoroughly,moreclearly,andwithfewer
words.ToaccomplishthisIhavewrittenmoreconcisely,combinedrelatedtopics,
and reduced repetition. The result is a modest reduction in text, in spite of the
broadenedcoverageoftopics.
InadditionIwantedtocorrectwhatIconsideredtobethetwobiggestproblems
withthefirstedition:thelargenumberofuncorrectedtyposandanincomplete
description of the chemical potential. A further objective was to increase the
number and quality of homework problems that are available for the instructor
orstudenttoselectfrom.Theserangeindifficultyfromwarm-upstochallenges.
Inthiseditionthenumberofhomeworkproblemshasnearlydoubled,averaging
around40perchapter.Inaddition,solutions(andoccasionalhints)totheodd-
numberedproblemsaregivenatthebackofthebook.Myexperiencewithstudents
atthislevelhasbeenthatsolutionsgivequickandefficientfeedback,encouraging
thosewhoaredoingthingscorrectlyandhelpingtoguidethosewhostumble.
Thefollowinglistexpandsuponthemoreimportantnewinitiativesandfea-
turesinthiseditioninorderoftheirappearance,withthechaptersandsections
indicatedinparentheses.
(cid:1)
Fluctuationsinobservables,suchasenergy,temperature,volume,numberofparticles,
etc.(Sections3A,3C,7C,9B,19A)
(cid:1)
Improveddiscussionandillustrationsofthechemicalpotential(Sections5C,8A,9E,
14A)
(cid:1)
The explicit dependence of the number of accessible states on the system’s internal
energy,volume,andnumberofparticles(Chapter6)
(cid:1)
Behaviorsnearabsolutezero(Sections9H,24A,24B)