Gaussian integrals - courses.physics.ucsd.edu · 19 Summary © 2014 John Wiley & Sons, Inc. All...
Transcript of Gaussian integrals - courses.physics.ucsd.edu · 19 Summary © 2014 John Wiley & Sons, Inc. All...
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Gaussianintegrals
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19Summary
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Kine'cTheoryofGases• relatesthemacroscopicproperBesofgasestothemicroscopicproperBesofgasmolecules.
Avogadro’sNumber
• Molerelatedtomassofamolecule
IdealGasAnidealgasisoneforwhichthepressurep,volumeV,andtemperatureTarerelatedby
Eq.19-5
TemperatureandKine'cEnergy• TheaveragetranslaBonalkineBcenergypermoleculeofanidealgasis
Eq.19-24
Eq.19-1
Eq.19-4
MaxwellSpeedDistribu'on• ThethreemeasuresofdistribuBonofspeed
Eq.19-31
Eq.19-35
Eq.19-22
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EntropyandtheSecondLawofThermodynamics
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Chapter20
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20-1Entropy
• 20.01IdenBfythesecondlawofthermodynamics:Ifaprocessoccursinaclosedsystem,theentropyofthesystemincreasesforirreversibleprocessesandremainsconstantforreversibleprocesses;itneverdecreases.
• 20.02IdenBfythatentropyisastatefuncBon(thevalueforaparBcularstateofthesystemdoesnotdependonhowthatstateisreached).
• 20.03CalculatethechangeinentropyforaprocessbyintegraBngtheinverseofthetemperature(inkelvins)withrespecttotheheatQtransferredduringtheprocess.
• 20.04Foraphasechangewithaconstanttemperatureprocess,applytherelaBonshipbetweentheentropychangeΔS,thetotaltransferredheatQ,andthetemperatureT(inkelvins).©2014JohnWiley&Sons,Inc.Allrights
reserved.
LearningObjec'ves
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20-1Entropy
• 20.05ForatemperaturechangeΔTthatissmallrelaBvetothetemperatureT,applytherelaBonshipbetweentheentropychangeΔS,thetransferredheatQ,andtheaveragetemperatureTavg(inkelvins).
• 20.06Foranidealgas,applytherelaBonshipbetweentheentropychangeΔSandtheiniBalandfinalvaluesofthepressureandvolume.
• 20.07IdenBfythatifaprocessisanirreversibleone,theintegraBonfortheentropychangemustbedoneforareversibleprocessthattakesthesystembetweenthesameiniBalandfinalstatesastheirreversibleprocess.
• 20.08Forstretchedrubber,relatetheelasBcforcetotherateatwhichtherubber’sentropychangeswiththechangeinthestretchingdistance.©2014JohnWiley&Sons,Inc.Allrights
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LearningObjec'ves(Con'nued)
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20-1Entropy
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Ifaprocessoccursinaclosedsystem,theentropyofthesystemincreasesforirreversibleprocessesandremainsconstantforreversibleprocesses.
Theisothermalexpansionofanidealgas,doneinareversibleway.
Thisprocessisirreversible;thatis,itdoesnotoccurinreverse,withthegasspontaneouslycollecBngitselfintheleShalfofthecontainer.
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20-1Entropy
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ChangeinEntropy
Tofindtheentropychangeforanirreversibleprocess,replacethatprocesswithanyreversibleprocessthatconnectsthesameiniBalandfinalstates.CalculatetheentropychangeforthisreversibleprocesswiththeaboveequaBon.
HereQistheenergytransferredasheattoorfromthesystemduringtheprocess,andTisthetemperatureofthesysteminkelvinsduringtheprocess.
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20-1Entropy
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TheSecondLawofThermodynamics
wherethegreater-thansignappliestoirreversibleprocessesandtheequalssigntoreversibleprocesses.EquaBonappliesonlytoclosedsystems.
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