《大學(xué)物理簡明教程》 課件 17-3 GASES

GasesTopicsinthislecture:KinetictheoryofidealgasesIdealgaslawPressureInternalenergyDegreesoffreedomMonatomicanddiatomicmoleculesTemperatureMaxwellBoltzmanndistributionofspeedsGasFillsthewholecontainerCanbecompressedKineticTheoryofGasesAssumptionsofkinetictheory

GascontainsmanymoleculesMoleculeshavenegligiblevolumeDirectionofmotionofmoleculesisrandomMoleculesexertnoforceoneachother,exceptwhencollideElasticcollisionsbetweenmoleculesandwithwallsAimingtomodelthebehaviourofaidealgaswithcomputersimulationsOurfirstunderstandingofgasmoleculeswasfromobservingdustparticlesmovingerratically.IdealGasLaw

R=molargasconstant=8.31JK-1mol-11Mole=6.02×1023particles=Avogadro’sNumber=NAP=pressure(Pa)V=volume(m3)T=temperature(K)n=numberofmoles1atm=1.013×105Pa1bar=105Pa1atm=1013millibar1Pa=1Nm-2FromexperimentsweseethatforfixedmassofgasIngeneralQuestion1Whatmassofoxygenisinthecylinderifithasavolumeof6litres,andisatapressureof10atmat20C?1atm=1.013x105PaMolarmassoxygen=32gNowPAUSEthevideoandtrytosolveQ1Question1Whatmassofoxygenisinthecylinderifithasavolumeof6litres,andisatapressureof10atmat20C?1atm=1.013x105PaMolarmassoxygen=32gHowdoeskinetictheoryexplainpressure?Pressureisduetocollisionsofmoleculeswiththewalls(andtheirchangeofmomentum).

PressureInitialmomentumofmolecule=+mvxFinalmomentumofmolecule=-mvxChangeofmomentumpermolecule=2mvx=densityInternalEnergyTheinternalenergyofagasisthesumthekineticandpotentialenergyofthemolecules.Inanidealgasthemoleculesdonotattracteachother,sotheyonlyhavekineticenergy.Whenheated,howistheenergystored?….asinternalenergyTranslationRotation3possibledegreesoffreedompermolecule3possibledegreesoffreedompermoleculeInternalEnergy–DegreesofFreedomEachwayinwhichasystemcanabsorbenergyiscalledadegreeoffreedomperdegreeoffreedomOnaverage,eachmoleculehasinternalenergyEquipartitiontheoremInternalEnergy–monatomicmoleculesU=internalenergy(J)k=Boltzmann’sconstant1.38×10-23(J/K)T=temperature(K)R=gasconstant=8.31Jmol-1K-1xyzE.g.He,Ne,Ar,Amonatomicmoleculehas3degreesoffreedomPermole,amonatomicgashas

but

Sointernalenergypermoleofmonatomicgas

InternalEnergy–diatomicmoleculesSointernalenergypermoleofdiatomicgas

Adiatomicmoleculehas5degreesoffreedom

E.g.H2,O2,N2,xyz

Generalequationforwholesampleofgas

Question2Determinetheinternalenergyof1moleofHelium(He)at20C2molesofhydrogen(H2)at27C

NowPAUSEthevideoandtrytosolveQ2

Question2

Determinetheinternalenergyof1moleofHelium(He)at20C(ii)2molesofhydrogen(H2)at27C

AveragekineticenergypermoleAveragekineticenergypermolecule

TemperatureMultiplyingbothsidesbyNARearranging:-Soweseethatrmsmeans-rootmeansquareM=molarmassTemperatureisproportionaltotheaveragemoleculartranslationalkineticenergy

Question3Theaveragespeedofairmoleculesinstillairatroomtemperatureisapproximately:-

Azero

B1mm/s(electrondriftspeedinmetal)

C2m/s(walkingspeed)

D30m/s(fastcar)

E500m/s(supersonicaeroplane)

F3×108m/s(speedoflight)NowPAUSEthevideoandtrytosolveQ3

Question3

Theaveragespeedofairmoleculesinstillairatroomtemperatureisapproximately:-

Azero

B1mm/s(electrondriftspeedinmetal)

C2m/s(walkingspeed)

D30m/s(fastcar)

E500m/s(supersonicaeroplane)

F3×108m/s(speedoflight)TheMaxwellBoltzmannDistributionJamesClerkMaxwell

1831-1879LudwigBoltzmann

1844-1906DistributionchangewithtemperatureVmax(speedofpeak)increaseswithtemperatureAreaundercurveremainsconstant,sopeaklowerFractionofMoleculesFractionofMoleculesAreaunderthecurveproportionaltototalnumberofmoleculesEvaporation-lossoffastmoleculesShapere-establishesitselfVmaxreducedwithreducedtemperatureAreaundercurvereducedassomemoleculeslostspeedFractionofMoleculesQuestion4Twodifferentsamplesofnitrogen,initiallyatdifferenttemperatures,aremixedtogether.ArethefollowingstatementsTRUEorFALSE?

(a)Themoleculeswillcollideandkineticenergywillbetransferreduntilallmoleculeshaveexactlythesameenergy.

(b)Beforemixingthespeedsofallthemoleculesofthehottergaswerehigherthanthoseofthecoolergas.

NowPAUSEthevideoandtrytosolveQ4Question4Twodifferentsamplesofnitrogen,initiallyatdifferenttemperatures,aremixedtogether.ArethefollowingstatementsTRUEorFALSE?

(a)Themoleculeswillcollideandkineticenergywillbetransferreduntilallmoleculeshaveexactlythesameenergy.

(b)Beforemixingthespeedsofallthemoleculesofthehottergaswerehigherthanthoseofthecoolergas.

SummaryIdealgasequationKinetictheoryisusedtomodelthebehaviourofanidealgas,intermofthemolecularbehaviourPressureisexplainedbythechangeinmomentumasthemolecu