Theoretical Physics 5: Thermodynamics

292 Pages·2017·2.062 MB·English

by  Wolfgang Nolting

Wolfgang Nolting
Theoretical
Physics 5
Thermodynamics
Theoretical Physics 5
Wolfgang Nolting
Theoretical Physics 5
Thermodynamics
123
WolfgangNolting
Inst.Physik
Humboldt-UniversitätzuBerlin
Berlin,Germany
ISBN978-3-319-47909-5 ISBN978-3-319-47910-1 (eBook)
DOI10.1007/978-3-319-47910-1
LibraryofCongressControlNumber:2016943655
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General Preface
TheninevolumesoftheseriesBasicCourse:TheoreticalPhysicsarethoughttobe
textbookmaterialforthestudyofuniversitylevelphysics.Theyareaimedtoimpart,
in a compact form, the most important skills of theoretical physics which can be
usedasbasisforhandlingmoresophisticatedtopicsandproblemsintheadvanced
study of physics as well as in the subsequent physics research. The conceptual
designofthepresentationisorganizedinsuchawaythat
ClassicalMechanics(volume1)
AnalyticalMechanics(volume2)
Electrodynamics(volume3)
SpecialTheoryofRelativity(volume4)
Thermodynamics(volume5)
are considered as the theory part of an integrated course of experimental and
theoretical physics as is being offered at many universities starting from the first
semester.Therefore,thepresentationisconsciouslychosentobeveryelaborateand
self-contained,sometimessurelyatthe costofcertainelegance,sothatthecourse
is suitableevenforself-study,at firstwithoutanyneedof secondaryliterature.At
anystage,nomaterialisusedwhichhasnotbeendealtwithearlierinthetext.This
holds in particular for the mathematical tools, which have been comprehensively
developed starting from the school level, of course more or less in the form of
recipes,suchthatrightfromthebeginningofthestudy,onecansolveproblemsin
theoreticalphysics. The mathematicalinsertionsare always then pluggedin when
theybecomeindispensabletoproceedfurtherintheprogramoftheoreticalphysics.
It goes without saying that in such a context, not all the mathematical statements
canbeprovedandderivedwithabsoluterigor.Instead,sometimesareferencemust
be made to an appropriate course in mathematics or to an advanced textbook in
mathematics. Nevertheless, I have tried for a reasonably balanced representation
so that the mathematical tools are not only applicable but also appear at least
“plausible”.
v
vi GeneralPreface
Themathematicalinterludesareofcoursenecessaryonlyinthefirstvolumesof
thisseries,whichincorporatemoreorlessthematerialofabachelorprogram.Inthe
secondpartoftheserieswhichcomprisesthemodernaspectsoftheoreticalphysics,
QuantumMechanics:Basics(volume6)
QuantumMechanics:MethodsandApplications(volume7)
StatisticalPhysics(volume8)
Many-BodyTheory(volume9),
mathematical insertions are no longer necessary. This is partly because, by the
time one comes to this stage, the obligatory mathematics courses one has to take
in order to study physics would have provided the required tools. The fact that
training in theory has already started in the first semester itself permits inclusion
of parts of quantum mechanics and statistical physics in the bachelor program
itself. It is clear that the content of the last three volumes cannot be part of an
integrated course but rather the subject matter of pure theory lectures. This holds
in particular for Many-Body Theory which is offered, sometimes under different
names,e.g.,AdvancedQuantumMechanics,in the eighthorso semester ofstudy.
In this part, new methods and concepts beyond basic studies are introduced and
discussed which are developed in particular for correlated many particle systems
whichinthemeantimehavebecomeindispensableforastudentpursuingamaster’s
orahigherdegreeandforbeingabletoreadcurrentresearchliterature.
In all the volumes of the series Theoretical Physics, numerous exercises are
included to deepen the understanding and to help correctly apply the abstractly
acquired knowledge. It is obligatory for a student to attempt on his own to adapt
and apply the abstract concepts of theoretical physics to solve realistic problems.
Detailedsolutionstotheexercisesaregivenattheendofeachvolume.Theideais
tohelpastudenttoovercomeanydifficultyataparticularstepofthesolutionorto
checkone’sowneffort.Importantlythesesolutionsshouldnotseducethestudentto
followtheeasywayoutasasubstituteforhisowneffort.Attheendofeachbigger
chapter,Ihaveaddedself-examinationquestionswhichshallserveasaself-testand
maybeusefulwhilepreparingforexaminations.
I should not forget to thank all the people who have contributed one way or
another to the success of the book series. The single volumes arose mainly from
lectures which I gave at the universities of Muenster, Wuerzburg, Osnabrueck,
and Berlin (Germany),Valladolid (Spain), and Warangal(India). The interest and
constructive criticism of the students provided me the decisive motivation for
preparing the rather extensive manuscripts. After the publication of the German
version,Ireceivedalotofsuggestionsfromnumerouscolleaguesforimprovement,
and this helped to further develop and enhance the concept and the performance
of the series. In particular, I appreciate very much the support by Prof. Dr. A.
Ramakanth,a long-standingscientific partnerand friend,who helpedme in many
respects,e.g.,whatconcernsthecheckingofthetranslationoftheGermantextinto
thepresentEnglishversion.
GeneralPreface vii
SpecialthanksareduetotheSpringercompany,inparticulartoDr.Th.Schneider
and his team. I remember many useful motivations and stimulations. I have the
feelingthatmybooksarewelltakencareof.
Berlin,Germany WolfgangNolting
August2016
Preface to Volume 5
The main goal of the present volume 5 (Thermodynamics) is exactly the same as
that of the total course on Theoretical Physics. It is thought to be accompanying
textbook material for the study of university-level physics. It is aimed to impart,
in a compact form, the most important skills of theoretical physics which can be
usedasbasisforhandlingmoresophisticatedtopicsandproblemsintheadvanced
study of physics as well as in the subsequent physics research. It is presented
in such a way that it enables self-study without the need for a demanding and
laboriousreferenceto secondaryliterature. For the understandingof the text, it is
onlypresumedthatthereaderhasagoodgraspofwhathasbeenelaboratedinthe
precedingvolumes1,2,3,and4.Mathematicalinterludesarealwayspresentedin
a compact and functional form and practiced when they appear indispensable for
the further development of the theory. Such mathematical insertions, though, are
becoming of course decreasingly necessary with the increasing volume number.
For the whole text, it holds that I had to focus on the essentials, presenting
them in a detailed and elaborate form, sometimes consciously sacrificing certain
elegance.Itgoeswithoutsayingthat,afterthebasiccourse,secondaryliteratureis
neededtodeepentheunderstandingofphysicsandmathematics.Thermodynamics
belongstotheclassicaltheoriesbutwouldthematicallybebetteroffasapreludeto
StatisticalMechanics.Thelattercanbeoffered,however,asmodern,nonclassical
theory (Quantum Statistics) only at a later stage of the study, namely, after
we have dealt with the Quantum Mechanics (volumes 6 and 7). The classical
phenomenologicalThermodynamics takes its concept formation directly from the
experimentanddoesthereforenotneed,incontrasttotheQuantumStatistics,any
quantum-mechanical element. As a rule, it is a module of the bachelor program
in physics and has therefore to be integrated into the first (classical) part of this
course on theoretical physics. The exact position of Thermodynamics in such a
course is, however,notunique.It can also be offeredbefore the Electrodynamics.
Thermodynamicsis, asascience ofheat,aclassicalphenomenologicaltheoryand
fortheunderstandingofwhich,physicaltermsliketemperatureandheathavetobe
introduced.Thesequantitiesare reasonablydefinableonlyformacroscopicmany-
particlesystemsbeingcompletelymeaninglessforasingleparticle.Thefulltheory
ix
x PrefacetoVolume5
of Thermodynamicsis based on a few fundamentaltheorems or laws, which have
to be considered here as theoretically non-provable but experimentally unrefuted
empiricalfacts.Astothesetheorems,aswellastothetermstemperatureandheat,
we have to content ourselves, in the framework of thermodynamics, to a certain
degree, with an intuitive self-understanding. A systematic reasoning is possible
only with Statistical Mechanics (volume 8) which is thus to be considered as
complementaryto thermodynamics.It is consistent with, at least in its version as
QuantumStatistics, theprinciplesofquantummechanicswhichwillbedeveloped
in the volumes 6 and 7. This volume on Thermodynamics arose from lectures I
gaveattheGermanuniversitiesinMuenster,Wuerzburg,andBerlin.Theanimating
interestofthestudentsinmylecturenoteshasinducedmetopreparethetextwith
special care. The present one as well as the other volumes are thought to be the
textbookmaterialforthestudyofbasicphysics,primarilyintendedforthestudents
rather than for the teachers. I am thankful to the Springer company,especially to
Dr. Th. Schneider, for accepting and supporting the concept of my proposal. The
collaborationwasalwaysdelightfulandveryprofessional.Adecisivecontribution
tothebookwasprovidedbyProf.Dr.A.RamakanthfromtheKakatiyaUniversity
ofWarangal(India).Hedeservesalotofthanks!
Berlin,Germany WolfgangNolting
September2016
Contents
1 BasicConcepts ............................................................... 1
1.1 ThermodynamicSystems.............................................. 2
1.2 State,Equilibrium ..................................................... 4
1.3 TheConceptofTemperature.......................................... 6
1.4 EquationsofState ..................................................... 7
1.4.1 IdealGas....................................................... 8
1.4.2 VanderWaalsGas ............................................ 10
1.4.3 IdealParamagnet.............................................. 14
1.4.4 WeissFerromagnet............................................ 15
1.5 Work.................................................................... 18
1.6 Exercises............................................................... 22
1.7 Self-ExaminationQuestions .......................................... 26
2 LawsofThermodynamics................................................... 29
2.1 FirstLawofThermodynamics,InternalEnergy ..................... 29
2.2 HeatCapacities ........................................................ 33
2.3 Adiabatics,Isotherms.................................................. 35
2.4 SecondLawofThermodynamics..................................... 38
2.5 CarnotCycle........................................................... 41
2.6 Absolute,ThermodynamicTemperatureScale....................... 45
2.7 EntropyasStateQuantity ............................................. 48
2.8 SimpleConclusionsfromtheThermodynamicLaws................ 55
2.9 Exercises............................................................... 61
2.10 Self-ExaminationQuestions .......................................... 71
3 ThermodynamicPotentials ................................................. 75
3.1 ‘Natural’StateVariables .............................................. 75
3.2 LegendreTransformation ............................................. 77
3.3 HomogeneityRelations................................................ 81
3.4 TheThermodynamicPotentialsoftheIdealGas..................... 83
3.5 EntropyofMixing..................................................... 87
3.6 Joule-ThomsonEffect................................................. 91
xi