kinetic theory of gas气体动力学理论

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1、Chapter16KineticTheoryofGases16-1TheIdealGasLawandtheMolecularInterpretationofTemperature16-2DistributionofMolecularSpeeds16-6MeanFreePath16-1TheIdealGasLawandtheMolecularInterpretationofTemperatureOurfirstmodelofamany-particlesystem:theIdealGasModelsofmatter:gasmodels(randommotionofpart

2、icles)Airatnormalconditions:~2.7×1019moleculesin1cm3ofairSizeofthemolecules~(2-3)×10-10m,Distancebetweenthemolecules~3×10-9mTheaveragespeed-500m/sThemeanfreepath-10-7m(0.1micron)Thenumberofcollisionsin1second-5×1091.Theidealgasmodel1)AssumptionsaboutthemoleculesinanidealgasTheidealgasmod

3、el-workswellatlowdensities(dilutedgases)•allthemoleculesareidentical,Nishuge;•themoleculesaretinycomparedtotheiraverageseparation(pointmasses);•themoleculesdonotinteractwitheachother;•themoleculesobeyNewton’slawsofmotion,theirmotionisrandom;•collisionsbetweenthemoleculesandthecontainerwa

4、llsareelastic.2)StatisticalassumptionsaboutanidealgasFInanequilibriumstate,thedistributionofmoleculesonthepositionisuniform,whichmeansthatthedensityofnumberofmoleculesisthesameeverywhere,dNNn==dVVFVelocitiesofmoleculesaredifferent.Eachmoleculehasitsvelocity,whichmaybechangedduetocollisio

5、ns.Inanequilibriumstate,velocityofeachmoleculehasthesameprobabilitytopointtoanydirections.Thatis,thedistributionofvelocityofmoleculesisuniformindirection,whichleadstothemean-squarespeedsofallcomponentsofvelocityaresame.Let22vbetheaveragevalueofvxx2theaveragevalueofv2vyyzv2theaveragevalue

6、ofv2vrzzzv2v222∑vixxvyyv+v+L+v21x2xixiv==xxNNv22∑iy∑vizv2=i2iyvz=NNSincethevelocityofthemoleculesinthegasareassumedtoberandom,thereisnopreferencetoonedirectionoranother.222vx=vy=vzForasinglemolecule2222222vx=vy=vzv=v+v+viixiyizSummingoverallmoleculesinthegas,wehave2222vvvv∑i∑ix∑iy∑iz=++N

7、NNN2222v=v+v+vxyz22212vx=vy=vz=v3222dNvxvyvzn=dVarestatisticalaveragevalues.2.CalculatingthePressureExertedbyaGasThepressurethatagasexertedonitscontainerisduetocollisionbetweengasmoleculesandthecontainerwalls.Example：consideracollisionbetweenthemoleculeofmassmandthewallof