Statistical thermodynamics: fundamentals and applications

466 Pages·2005·2.143 MB·English

by  Professor Normand Laurendeau

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STATISTICAL THERMODYNAMICS: FUNDAMENTALS
AND APPLICATIONS
Statistical Thermodynamics: Fundamentals and Applications discusses the
fundamentals and applications of statistical thermodynamics for beginning
graduate students in the engineering sciences. Building on the prototypical
Maxwell–Boltzmann method and maintaining a step-by-step development of
thesubject,thisbookmakesfewpresumptionsconcerningstudents’previous
exposure to statistics, quantum mechanics, or spectroscopy. The book begins
with the essentials of statistical thermodynamics, pauses to recover needed
knowledgefromquantummechanicsandspectroscopy,andthenmovesonto
applications involving ideal gases, the solid state, and radiation. A full intro-
duction to kinetic theory is provided, including its applications to transport
phenomenaandchemicalkinetics.Ahighlightofthetextbookisitsdiscussion
of modern applications, such as laser-based diagnostics. The book concludes
withathoroughpresentationoftheensemblemethod,featuringitsuseforreal
gases.Eachchapteriscarefullywrittentoaddressstudentdifficultiesinlearn-
ingthischallengingsubject,whichisfundamentaltocombustion,propulsion,
transportphenomena,spectroscopicmeasurements,andnanotechnology.Stu-
dentsaremadecomfortablewiththeirnewknowledgebytheinclusionofboth
exampleandpromptedhomeworkproblems.
NormandM.LaurendeauistheRalphandBettyeBaileyProfessorofCombus-
tionatPurdueUniversity.Heteachesatboththeundergraduateandgraduate
levelsintheareasofthermodynamics,combustion,andengineeringethics.He
conductsresearchinthecombustionsciences,withparticularemphasisonlaser
diagnostics, pollutant formation, and flame structure. Dr. Laurendeau is well
knownforhispioneeringresearchonthedevelopmentandapplicationofboth
nanosecondandpicosecondlaser-inducedfluorescencestrategiestoquantita-
tivespeciesconcentrationmeasurementsinlaminarandturbulentflames.He
hasauthoredorcoauthoredover150publicationsinthearchivalscientificand
engineeringliterature.ProfessorLaurendeauisaFellowoftheAmericanSoci-
ety of Mechanical Engineers and a member of the Editorial Advisory Board
forthepeer-reviewedjournalCombustionScienceandTechnology.
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Statistical Thermodynamics
Fundamentals and Applications
NORMAND M. LAURENDEAU
PurdueUniversity
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camʙʀɪdɢe uɴɪveʀsɪtʏ pʀess
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Cambridge University Press
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© Cambridge University Press 2005
This publication is in copyright. Subject to statutory exception and to the provision of
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without the written permission of Cambridge University Press.
First published in print format 2005
ɪsʙɴ-13 978-0-511-14062-4 eBook (NetLibrary)
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ɪsʙɴ-10 0-521-84635-8 hardback
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Idedicatethisbooktomyparents,
MauriceandLydiaRoyLaurendeau.
Theirgiftofbountifulloveandsupport...
Continuestofillmewiththejoyofdiscovery.
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Contents
Preface page xv
1 Introduction 1
1.1 TheStatisticalFoundationofClassicalThermodynamics 1
1.2 AClassificationSchemeforStatisticalThermodynamics 3
1.3 WhyStatisticalThermodynamics? 3
PARTONE. FUNDAMENTALSOFSTATISTICAL
THERMODYNAMICS
2 ProbabilityandStatistics 7
2.1 Probability:DefinitionsandBasicConcepts 7
2.2 PermutationsandCombinations 10
2.3 Probability Distributions: Discrete and Continuous 11
2.4 TheBinomialDistribution 13
2.5 ThePoissonDistribution 15
2.6 TheGaussianDistribution 16
2.7 CombinatorialAnalysisforStatisticalThermodynamics 18
2.7.1 DistinguishableObjects 19
2.7.2 IndistinguishableObjects 20
ProblemSetI. ProbabilityTheoryandStatisticalMathematics
(Chapter2) 23
3 TheStatisticsofIndependentParticles 29
3.1 EssentialConceptsfromQuantumMechanics 30
3.2 TheEnsembleMethodofStatisticalThermodynamics 31
3.3 TheTwoBasicPostulatesofStatisticalThermodynamics 32
3.3.1 TheM–BMethod:SystemConstraintsandParticle
Distribution 33
3.3.2 TheM–BMethod:MicrostatesandMacrostates 33
3.4 TheMostProbableMacrostate 35
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viii Contents
3.5 Bose–EinsteinandFermi–DiracStatistics 37
3.5.1 Bose–EinsteinStatistics 37
3.5.2 Fermi–DiracStatistics 38
3.5.3 TheMostProbableParticleDistribution 39
3.6 EntropyandtheEquilibriumParticleDistribution 40
3.6.1 TheBoltzmannRelationforEntropy 40
3.6.2 IdentificationofLagrangeMultipliers 41
3.6.3 TheEquilibriumParticleDistribution 42
4 ThermodynamicPropertiesintheDiluteLimit 45
4.1 TheDiluteLimit 45
4.2 CorrectedMaxwell–BoltzmannStatistics 46
4.3 TheMolecularPartitionFunction 47
4.3.1 TheInfluenceofTemperature 49
4.3.2 CriterionforDiluteLimit 50
4.4 InternalEnergyandEntropyintheDiluteLimit 51
4.5 AdditionalThermodynamicPropertiesintheDilute
Limit 53
4.6 TheZeroofEnergyandThermodynamicProperties 55
4.7 IntensiveThermodynamicPropertiesfortheIdealGas 56
Problem Set II. Statistical Modeling for Thermodynamics
(Chapters 3–4) 59
PARTTWO. QUANTUMMECHANICSANDSPECTROSCOPY
5 BasicsofQuantumMechanics 69
5.1 HistoricalSurveyofQuantumMechanics 69
5.2 TheBohrModelfortheSpectrumofAtomicHydrogen 72
5.3 ThedeBroglieHypothesis 76
5.4 AHeuristicIntroductiontotheSchro¨dingerEquation 78
5.5 ThePostulatesofQuantumMechanics 80
5.6 TheSteady-StateSchro¨dingerEquation 83
5.6.1 Single-ParticleAnalysis 84
5.6.2 MultiparticleAnalysis 85
5.7 TheParticleinaBox 86
5.8 TheUncertaintyPrinciple 90
5.9 IndistinguishabilityandSymmetry 92
5.10 ThePauliExclusionPrinciple 94
5.11 TheCorrespondencePrinciple 95
6 QuantumAnalysisofInternalEnergyModes 97
6.1 Schro¨dingerWaveEquationforTwo-ParticleSystem 97
6.1.1 ConversiontoCenter-of-MassCoordinates 98
6.1.2 SeparationofExternalfromInternalModes 99
6.2 TheInternalMotionforaTwo-ParticleSystem 99
6.3 TheRotationalEnergyModeforaDiatomicMolecule 100
6.4 TheVibrationalEnergyModeforaDiatomicMolecule 104