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

EntropyandtheSecondLawofThermodynamics

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Chapter20

20-1Entropy

•  20.01IdenBfythesecondlawofthermodynamics:Ifaprocessoccursinaclosedsystem,theentropyofthesystemincreasesforirreversibleprocessesandremainsconstantforreversibleprocesses;itneverdecreases.

•  20.02IdenBfythatentropyisastatefuncBon(thevalueforaparBcularstateofthesystemdoesnotdependonhowthatstateisreached).

•  20.03CalculatethechangeinentropyforaprocessbyintegraBngtheinverseofthetemperature(inkelvins)withrespecttotheheatQtransferredduringtheprocess.

•  20.04Foraphasechangewithaconstanttemperatureprocess,applytherelaBonshipbetweentheentropychangeΔS,thetotaltransferredheatQ,andthetemperatureT(inkelvins).©2014JohnWiley&Sons,Inc.Allrights

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LearningObjec'ves

20-1Entropy

•  20.05ForatemperaturechangeΔTthatissmallrelaBvetothetemperatureT,applytherelaBonshipbetweentheentropychangeΔS,thetransferredheatQ,andtheaveragetemperatureTavg(inkelvins).

•  20.06Foranidealgas,applytherelaBonshipbetweentheentropychangeΔSandtheiniBalandfinalvaluesofthepressureandvolume.

•  20.07IdenBfythatifaprocessisanirreversibleone,theintegraBonfortheentropychangemustbedoneforareversibleprocessthattakesthesystembetweenthesameiniBalandfinalstatesastheirreversibleprocess.

•  20.08Forstretchedrubber,relatetheelasBcforcetotherateatwhichtherubber’sentropychangeswiththechangeinthestretchingdistance.©2014JohnWiley&Sons,Inc.Allrights

reserved.

LearningObjec'ves(Con'nued)

20-1Entropy

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Ifaprocessoccursinaclosedsystem,theentropyofthesystemincreasesforirreversibleprocessesandremainsconstantforreversibleprocesses.

Theisothermalexpansionofanidealgas,doneinareversibleway.

Thisprocessisirreversible;thatis,itdoesnotoccurinreverse,withthegasspontaneouslycollecBngitselfintheleShalfofthecontainer.

20-1Entropy

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ChangeinEntropy

Tofindtheentropychangeforanirreversibleprocess,replacethatprocesswithanyreversibleprocessthatconnectsthesameiniBalandfinalstates.CalculatetheentropychangeforthisreversibleprocesswiththeaboveequaBon.

HereQistheenergytransferredasheattoorfromthesystemduringtheprocess,andTisthetemperatureofthesysteminkelvinsduringtheprocess.

20-1Entropy

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TheSecondLawofThermodynamics

wherethegreater-thansignappliestoirreversibleprocessesandtheequalssigntoreversibleprocesses.EquaBonappliesonlytoclosedsystems.

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