Thermodynamics for Chemists, Physicists and Engineers

344 Pages·2012·3.54 MB·English

by  Robert Hołyst

Thermodynamics for Chemists, Physicists and
Engineers
Robert Hołyst (cid:2) Andrzej Poniewierski
Thermodynamics
for Chemists,
Physicists and
Engineers
RobertHołyst AndrzejPoniewierski
InstituteofPhysicalChemistry InstituteofPhysicalChemistry
PolishAcademyofSciences PolishAcademyofSciences
Warsaw,Poland Warsaw,Poland
ISBN978-94-007-2998-8 ISBN978-94-007-2999-5(eBook)
DOI10.1007/978-94-007-2999-5
SpringerDordrechtHeidelbergNewYorkLondon
LibraryofCongressControlNumber:2012943136
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Preface
ThepresentworkisbasedonourtwopreviousbookspublishedinPolishandenti-
tled(inEnglishtranslation):Thermodynamicsforchemists,physicistsandengineers
[6]andThermodynamicsbyexercises[7].Thefirstone,besidesthepartdevotedto
thefundamentalsofphenomenologicalthermodynamicsanditsapplicationtophase
transitionsandchemicalreactions,containsalsoanintroductiontostatisticalther-
modynamics written by Alina Ciach. The second book is a collection of exercises
on thermodynamics together with their solutions, which correspond to the mate-
rial presented in [6]. The motivation for writing of these books was the lecture on
thermodynamicswiththeelementsofstatisticalmechanics,givenbyusattheCol-
legeofScience,whichwasapartofthephysicalchemistrycourseforthe2ndyear
undergraduate students. Presently the College of Science forms the department of
mathematics and science at the University of Cardinal Stefan Wyszyn´ski in War-
saw,butoriginallyitwasestablishedduetotheinitiativeofafewresearchinstitutes
of the Polish Academy of Sciences, including the Institute of Physical Chemistry
whereweareemployed,andstillbenefitsfromtheirscientificandresearchpoten-
tial.BecauseoflargediversityofresearchcarriedoutintheinstitutesofthePolish
AcademyofSciences,thestudiesintheCollegeofScienceareofinterdisciplinary
character.Thereforethecourseofthermodynamicsdiffersfromtraditionalcourses
of this subject at the physics or chemistry departments. In spite of many excellent
textbooksinthisfielditwasdifficulttofindone,atratheranelementarylevel,whose
scopewouldcorrespondtothemateriallecturedbyus.Thisfactinclinedustowrite
atextbookadaptedtoourneeds.However,inthecourseofwriting,wedecidedthat
ifweextendedsomewhatthescopeofthebook,itcouldalsobeusefulforthePh.D.
students in our institute, who after the second year of studies are obliged to pass
anexaminationonphysicalchemistry,whichisroughlyatthelevelofP.W.Atkins’
book[1].
Thepresentbookisnotsimplyacompilationof[6]and[7],sincewehaveintro-
ducedmanysignificantchangesandimprovements.Moreover,aswedidnotwant
the book to grow in size too much, we decided to limit its scope to phenomeno-
logical thermodynamics. To facilitate its use, we have highlighted in the text the
postulates and laws of thermodynamics, as well as the most important definitions
vii
viii Preface
and conclusions. Mathematical digressions are included in the main text, instead
of appendices, as we think that the formalism used in thermodynamics should be
treated as its integral part. We pay special attention to the compatibility of defini-
tions,terms,unitsandnotationusedinourbookwiththerecommendationsofthe
InternationalUnionofPureandAppliedChemistry(IUPAC)[4].
The book is divided into three parts. At the end of each chapter, there are ex-
ercises whose solutions are given at the end of the book. The first part, consisting
of five chapters, contains the postulates and laws of phenomenological thermody-
namicstogetherwithexamplesoftheirapplication.InChaps.2and3,weintroduce
anddiscussthebasicconceptsandquantities,suchastheequilibriumstate,param-
etersandfunctionsofstate,thermodynamicprocess,pressure,temperature,internal
energy, heat and chemical potential, relying mainly on the reader intuition. Writ-
ing Chaps. 4 and 5, we were inspired with Callen’s book [3]. Chapter 4 is mainly
devoted to entropy and the second law of thermodynamics and to the conclusions
followingfromthatlaw.InChap.5,wediscussthethermodynamicpotentialsand
naturalvariables,andalsotheconditionsofintrinsicstabilityforapuresubstance.
Lessadvancedreaderscanskipthelastpoint.
Thesecondpartisdevotedtoapplicationofthermodynamicstophasetransitions
inpuresubstances(Chap.6)andinmixtures(Chaps.8and9);Chap.7isanintro-
ductiontothermodynamicsofmulticomponentsystems.InChap.6,wegivegeneral
classificationofphasetransitionsandafewexamplesoffirstorderandcontinuous
transitions.Intherestofthebook,however,werestrictourselvestofirstordertransi-
tions.TheconceptofidealmixtureisintroducedinSect.7.5.Lessadvancedreaders
canskipSects.7.2and7.6.Thediscussionofphasetransitionsinmixturesislimited
tothecaseoftwo-componentsystems.InChap.8,wediscussthephenomenathat
canbeexplainedbythemodelofidealmixture.Nonidealmixturesareconsidered
inChap.9.Inthiscase,westudythesimplestextensionoftheidealmixturemodel
calledthesimplesolution.Tounderstandthewholematerialpresentedinthischap-
terthereaderwhoskippedSects.7.2and7.6shouldreturntothem.However,less
advancedstudentscanskiptheformalpartofChap.9andconcentrateonthephase
diagramspresented.
In partthree, weconsiderthermodynamicsystemsin whichchemicalreactions
occur.Chapter10concernsreactionsbetweenelectricallyneutralcompounds.The
law of mass action, which follows from the condition of chemical equilibrium, is
derivedforamixtureofidealgases.Thereforethematerialpresentedinthischapter
shouldbeunderstoodalsobylessadvancedstudents.Chapter11concernselectro-
chemicalsystems,inwhichchemicalreactionsoccurbetweenions.Ourmainaim
wastoshowthatduetoachemicalreactionasystemcanperformworkotherthan
themechanicalone,whichin theframework of thermodynamicscanbeexplained
by means of a reversible cell. This chapter is mainly for more advanced graduate
students.
Weknowfromourownexperiencethatforthesecondyearstudentstheconcepts
ofthedifferentialanddifferentialformareratherdifficult.Sincetheseconceptsare
crucial for the whole course of thermodynamics, we have tried to explain them in
a simple way without going into mathematical details. The second crucial mathe-
matical concept, which is used to introduce the thermodynamic potentials, is the
Preface ix
Legendre transformation. Obviously one can define enthalpy or the Helmholtz or
Gibbs free energy without any reference to that concept. On the other hand, we
think that it is easier to understand properly the meaning of natural variables of a
thermodynamicpotentialintermsoftheLegendretransformation,whichwasshown
inanelegantwaybyCallen[3].
The exercises together with solutions are to help the readers to evaluate their
understandingofthemateriallearned.Webelievethatourbookcanbeusefulboth
forthestudentsofphysics,especiallyforthosewhowanttoextendtheirknowledge
in the direction of physical chemistry, and for the students of chemistry who can
treatitasapartofthephysicalchemistrycourse.Alsostudentsofsomeengineering
departmentsorbiologymayuseit.
Althoughthesubjectofourbookisphenomenologicalthermodynamics,inafew
placeswerefertostatisticalmechanics.Tothereaderswhowishtolearnmoreabout
this important branch of science we recommend the classical books [8] and [14].
From among other books on thermodynamics, physical chemistry and chemistry
usedbyus,werecommendreferences[9],[15],[13],[1]and[11],andforadvanced
readersalso[5],[10]and[12].References[16]and[2]canserveasanintroduction
tothefieldofphasetransitionsandcriticalphenomena.
Warsaw,Poland RobertHołyst
AndrzejPoniewierski
Contents
PartI FoundationsofThermodynamics
1 HistoricalIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 BasicConceptsandDefinitions . . . . . . . . . . . . . . . . . . . . . 7
2.1 ConceptofThermodynamicEquilibrium . . . . . . . . . . . . . . 7
2.1.1 SystemandSurroundings . . . . . . . . . . . . . . . . . . 9
2.1.2 StateParametersandStateFunctions . . . . . . . . . . . . 10
2.1.3 ThermodynamicProcesses . . . . . . . . . . . . . . . . . 11
2.1.4 CalculationofPhysicalQuantitiesinQuasi-staticProcesses 14
2.2 ExtensiveParametersofState . . . . . . . . . . . . . . . . . . . . 17
2.2.1 Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.2 AmountofSubstance . . . . . . . . . . . . . . . . . . . . 18
2.2.3 InternalEnergy . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 IntensiveParametersofState . . . . . . . . . . . . . . . . . . . . 20
2.3.1 Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.2 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.3 ChemicalPotential . . . . . . . . . . . . . . . . . . . . . . 27
2.4 EquationsofState . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4.1 IdealGas . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4.2 VanderWaalsGas . . . . . . . . . . . . . . . . . . . . . . 31
2.4.3 PhotonGas . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.4.4 EquationsofStateinTermsofIntensiveParameters . . . . 32
2.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3 InternalEnergy,WorkandHeat . . . . . . . . . . . . . . . . . . . . 39
3.1 FirstLawofThermodynamics . . . . . . . . . . . . . . . . . . . . 39
3.2 IsochoricProcess . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.1 HeatCapacityatConstantVolume . . . . . . . . . . . . . 42
3.3 IsobaricProcess . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.1 HeatCapacityatConstantPressure . . . . . . . . . . . . . 43
3.4 AdiabaticProcess . . . . . . . . . . . . . . . . . . . . . . . . . . 44
xi
xii Contents
3.4.1 ReversibleAdiabaticProcess . . . . . . . . . . . . . . . . 44
3.4.2 IrreversibleAdiabaticProcessatConstantPressure. . . . . 45
3.5 IsothermalProcess . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.5.1 ReversibleIsothermalProcess . . . . . . . . . . . . . . . . 47
3.5.2 IrreversibleIsothermalProcessatConstantPressure . . . . 47
3.6 EvaporationofLiquids . . . . . . . . . . . . . . . . . . . . . . . 48
3.7 ChemicalReaction . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4 EntropyandIrreversibilityofThermodynamicProcesses . . . . . . 57
4.1 SecondLawofThermodynamics . . . . . . . . . . . . . . . . . . 57
4.1.1 EntropyMaximumPrincipleforIsolatedSystems . . . . . 60
4.2 ConditionsofThermodynamicEquilibrium . . . . . . . . . . . . . 61
4.2.1 ThermalEquilibrium . . . . . . . . . . . . . . . . . . . . 61
4.2.2 MechanicalEquilibrium . . . . . . . . . . . . . . . . . . . 65
4.2.3 EquilibriumwithRespecttotheMatterFlow . . . . . . . . 65
4.3 EntropyasaFunctionofStateParameters . . . . . . . . . . . . . 67
4.3.1 FundamentalRelationofThermodynamics . . . . . . . . . 67
4.3.2 EulerRelation . . . . . . . . . . . . . . . . . . . . . . . . 68
4.3.3 EntropyoftheIdealGas . . . . . . . . . . . . . . . . . . . 70
4.3.4 RelationBetweenEntropyandHeatCapacity . . . . . . . 71
4.4 ChangesinEntropyinReversibleProcesses . . . . . . . . . . . . 72
4.4.1 IsothermalProcess . . . . . . . . . . . . . . . . . . . . . . 72
4.4.2 IsochoricandIsobaricProcesses . . . . . . . . . . . . . . 73
4.4.3 EvaporationofLiquids . . . . . . . . . . . . . . . . . . . 74
4.5 HeatDevices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.5.1 HeatEngineandtheCarnotCycle. . . . . . . . . . . . . . 75
4.5.2 Efficiency of the Carnot Cycle and Thermodynamic
Temperature . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.5.3 RefrigeratorandtheHeatPump . . . . . . . . . . . . . . . 79
4.5.4 OtherThermodynamicCycles . . . . . . . . . . . . . . . . 81
4.6 ChangesinEntropyinIrreversibleProcesses . . . . . . . . . . . . 82
4.6.1 IrreversibleFlowofHeat . . . . . . . . . . . . . . . . . . 82
4.6.2 FreeGasExpansion . . . . . . . . . . . . . . . . . . . . . 84
4.6.3 IrreversibleChemicalReaction . . . . . . . . . . . . . . . 85
4.7 ThirdLawofThermodynamics . . . . . . . . . . . . . . . . . . . 85
4.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5 ThermodynamicPotentials . . . . . . . . . . . . . . . . . . . . . . . 89
5.1 LegendreTransformationoftheInternalEnergyandEntropy . . . 89
5.1.1 DefinitionoftheLegendreTransformation . . . . . . . . . 90
5.1.2 HelmholtzFreeEnergy . . . . . . . . . . . . . . . . . . . 92
5.1.3 Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.1.4 GibbsFreeEnergy . . . . . . . . . . . . . . . . . . . . . . 93
5.1.5 GrandThermodynamicPotential . . . . . . . . . . . . . . 95
5.1.6 MassieuFunctions . . . . . . . . . . . . . . . . . . . . . . 96
Contents xiii
5.2 NaturalVariables. . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.2.1 EquivalentRepresentationsoftheFundamentalRelation . . 97
5.2.2 ThermodynamicPotentialsfortheIdealGas . . . . . . . . 98
5.3 Free-EnergyMinimumPrinciple . . . . . . . . . . . . . . . . . . 100
5.3.1 SystemsatConstantTemperature . . . . . . . . . . . . . . 100
5.3.2 SystemsatConstantTemperatureandPressure . . . . . . . 102
5.4 ExamplesofApplicationofThermodynamicPotentials . . . . . . 105
5.4.1 RulesofCalculationofSomePartialDerivatives . . . . . . 105
5.4.2 MaxwellRelations . . . . . . . . . . . . . . . . . . . . . . 106
5.4.3 SecondPartialDerivativesoftheInternalEnergyand
ThermodynamicPotentials . . . . . . . . . . . . . . . . . 107
5.4.4 ReversibleAdiabaticProcess . . . . . . . . . . . . . . . . 111
5.4.5 FreeGasExpansion . . . . . . . . . . . . . . . . . . . . . 112
5.4.6 Joule–ThomsonProcess . . . . . . . . . . . . . . . . . . . 113
5.5 IntrinsicStabilityofaSystem . . . . . . . . . . . . . . . . . . . . 115
5.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
PartII PhaseTransitions
6 PhaseTransitionsinPureSubstances . . . . . . . . . . . . . . . . . . 123
6.1 ConceptofPhase. . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.2 ClassificationofPhaseTransitions . . . . . . . . . . . . . . . . . 124
6.2.1 First-OrderPhaseTransitions . . . . . . . . . . . . . . . . 124
6.2.2 ContinuousPhaseTransitions . . . . . . . . . . . . . . . . 125
6.2.3 EhrenfestClassification . . . . . . . . . . . . . . . . . . . 127
6.3 ConditionsofPhaseCoexistence . . . . . . . . . . . . . . . . . . 127
6.3.1 Two-PhaseCoexistence . . . . . . . . . . . . . . . . . . . 127
6.3.2 Three-PhaseCoexistence . . . . . . . . . . . . . . . . . . 131
6.4 PhaseDiagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.4.1 PhaseDiagramofaTypicalSubstance . . . . . . . . . . . 132
6.4.2 PhaseDiagramofWater . . . . . . . . . . . . . . . . . . . 134
6.4.3 PhaseDiagramof4He . . . . . . . . . . . . . . . . . . . . 135
6.5 Two-PhaseCoexistenceLines . . . . . . . . . . . . . . . . . . . . 138
6.5.1 ClapeyronEquation . . . . . . . . . . . . . . . . . . . . . 138
6.5.2 Solid–LiquidCoexistence . . . . . . . . . . . . . . . . . . 139
6.5.3 Liquid–GasCoexistence . . . . . . . . . . . . . . . . . . . 140
6.5.4 Solid–GasCoexistence . . . . . . . . . . . . . . . . . . . 140
6.6 Liquid–VapourTwo-PhaseRegion . . . . . . . . . . . . . . . . . 140
6.7 VanderWaalsEquationofState . . . . . . . . . . . . . . . . . . . 143
6.7.1 MaxwellConstruction . . . . . . . . . . . . . . . . . . . . 145
6.7.2 PrincipleofCorrespondingStates . . . . . . . . . . . . . . 146
6.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
7 Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
7.1 BasicConceptsandRelations . . . . . . . . . . . . . . . . . . . . 151
7.1.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . 151