E气体动理论.ppt

IntroductionInourstudyofdynamics wedevelopedmethodstocalculateenergy Anobjecthavekineticenergy gravitationalpotentialenergy orelasticpotentialenergy Tocalculatethetotalenergyofacollectionofobjects wewouldsimplyaddupthecontributionsmadebyeachobject However manyphysicalsystemcontainanimpossiblylargenumberofseparateobject Forinstance ajugofwatercontainsanenormousnumberofwatermolecules andwecanhardlycalculatetheenergyofthewaterbyaddingupthecontributionsfromeachmolecule Whatcanwesayabouttheenergyofsuchasystemandenergyexchangesthatoccurwhenitinteractswithothersystems Infollowingchapters weconsiderthesequestions Inchapter7 first weseektodosousingonlymacroscopicphysicalproperties bythiswemeanmeasurablepropertiesofbulksystemthattakenoheedofitsmicroscopicconstituents Then wewanttofindtherelationshipbetweenmacroscopicandmicroscopicphysicalquantities Inchapter8 weshallconcentrateonthefirstandsecondlawsofthermodynamics Thefirstlawofthermo dynamicsexpressestherelationshipmoreformallybyexplicitlyintroducingaheatflowtermintotheenergyconservation Thisclarificationofenergyconservation whichwasoneofthegreattriumphsofnineteenth centuryphysics arosealmostbyconsensusfromtheworkandthoughtsofmanyleadingscientistsofthetime 气体动理论和热力学基础ThefoundationsofGaskineticsandthermodynamics 1研究对象 物质的热运动和热运动与其它形式的运动之间相互转化所遵循的规律 热现象及其规律 组成宏观物体的大量微观粒子 分子 原子 的一种永不停息的无规则的运动 热运动 热现象 组成宏观物体的大量微观粒子热运动的集体表现 凡是与温度有关的物理现象都是热现象 热运动是热现象的微观实质热现象是热运动的宏观表现 实例 物体受热温度升高 体积膨胀 冰受热融化为水等 2研究方法 以物质的分子 原子结构概念和分子热运动概念为基础 将微观运动和宏观运动相联系 应用统计的方法 解释并揭示物质宏观热现象及其有关规律的本质 确立宏观量和微观量之间的关系系 1 热运动 2 微观量 宏观量 3 统计规律 Gaskinetics气体动理论 1 就整体而言 在一定状态下 物质具有一定的能量 2 从一个状态过度到另一个状态 遵从一定规律 Thermodynamics热力学 不涉及物质的微观结构 根据由观察和实验总结得出的热力学定律 从能量观点出发 分析研究在物质状态变化过程中有关热功转化的关系和条件 Chapter18Gaskinetics 1EquilibriumstateEquationofstate 2Pressureformulaforidealgas 3TemperatureandEnergy 4TheoremofequipartitionofenergyTheinternalenergyofideagas 5Maxwellspeeddistributionlaw 6MolecularmeancollisionfrequencyMeanfreepath 7Transportphenomenaingas 8Application 1EquilibriumstateEquationofstate 1Equilibriumstate平衡状态 Notes Withoutexternalaction influence Neitherdoingworknorheattransfer Macroscopiccharacteristicsdonotchangewithtime Thestatethatmacroscopiccharacteristicsdonotchangewithtimewithoutexternalaction influence thermodynamicalequilibrium 热动平衡 无外界影响时宏观性质不随时间变化的状态 1 Equilibriumstate平衡状态 2 Stateparameters状态参量VPT Volume体积V Temperature温度T Pressure压强P 2Equationofstateofidealgas理想气体状态方程 Boyle slaw Foragivensampleofgasatafixedtemperature theproductofthepressurePandthevolumeVisconstant PV constant Gay Lussac slaw Thevolumeofagivenamountofanygasisproportionaltotheabsolutetemperaturewhenthepressureisheldconstant V T constant Charles slaw Thepressureisproportionaltotheabsolutetemperaturewhenthevolumeisheldconstant P T constant Equilibriumstate平衡状态 F VPT 0 AnyobjectinthermaldynamicaalequilibriumareatthesametemperatureThermodynamicscale KelvinscaleT 273 15 t Thezerothlawofthermodynamics IfobjectsAandBareeachinthermalequilibriumwithanobjectC thentheyarealsointhermalequilibriumwitheachother Molargasconstant constant Appendix Example CalculatethedensityofoxygenatSTP standardtemperatureandpressure Themolecularmassofoxygenis32g anditcloselyobeystheidealgasequationofstateunderthiscondition Solution Consideraquantityof1molofoxygenthathasamassof32gandcontains6 022 1023molecules Tocalculatethedensity Themolecularmodelofidealgas microscopicdefinition理想气体的分子模型 微观定义 2Pressureformulaforidealgas Theselfsizeofmoleculesisfarsmallerthantheaveragedistancebetweenmolecules beingneglect分子本身的线度远小于分子平均间距 可忽略不计 2 Theinteractionsbetweenmoleculesandthewallofcontainerareneglectedexcepttheinstantofcollisions除碰撞瞬间 忽略分子之间 分子与器壁之间的相互作用 3 Thecollisionsbetweenmoleculesandthewallofcontainerareperfectelasticcollisions分子之间 分子与器壁之间的碰撞是完全弹性 2Thedominantidea主导思想 1 Idea 观点 Macroscopically宏观Forceperunitarea Microscopically微观Theconstant rapiddrumbeatofmoleculesbouncingoffthewallofthecontainerexertsasteadyaverageforceonthewall 2 Method方法 3 Result结果 Theaveragekineticenergyofasinglemolecule一个分子的平均平动动能 n Numberdensityofmolecules分子数密度 Statisticalmethod统计方法 3Thederivationofpressureformula压强公式的推导 M m Gasisextremelyrarefied Aftercollision Thechangeinmomentumofthemolecule Thetimebetweencollisionisgivenby Therateofmomentumtransferfromthemoleculetothewallis Thisistheforceonthewallfromtheith smolecule Themomentumofthemoleculebeforecollision EachoftheNmoleculesintheboxhasitsownvelocity andthereforeitsowntraveltimeandmomentumtransfer Forasinglemolecule theforceisintermittent 单个分子 作用不连续 FortheNmolecules theforceperareaispressure大量分子 作用连续Summingoverallthemoleculesinthebox thetotalrateofmomentumtransfertothewall andthustheforceonthewallcanbegot Althoughthemomentumtransferfromasinglemoleculeareintermittent thetotalmomentumtransferisadrumbeatofimpulsesthatprovidesasteadypushonthewall Ifthegasisnotextremelyrarefied themoleculemaycollidewithoneanotherbeforecompletingtheroundtrip Thesecollisionturnouttoconservebothmomentumandkineticenergy sothenetimpactonthewallisthesameasiftheparticleshadnotcollidedwithoneanother Sincethemotionofthemoleculesisrandom thecontributionsfromtheyandzcomponentshavethesamevalue itcanbegot Thetotalforceonthewallfromallthemoleculesinthebox Review 1 Idea观点 2 Method方法 Thepressureonthewallistheaverageforcedividedbythearea ConclusionAstherandommotionofthegasmoleculesbecomesmorevigorous theaveragekineticenergyincreases resultingincorrespondinglygreatpressureonthecontainingwalls Furthermore arelationshipbetweenthemacroscopicpressureandthemicroscopicaveragekineticenergyoftheindividualmoleculesofthegascanbefound 3Temperatureandenergy 1Therelationshipbetweenaveragekineticenergyandtemperature Ontheotherhand studiesofdependenceofvolumeandpressureofanidealgasontemperaturesuggesttheideal gaslaw Themeantranslationalkineticenergyofanatomormoleculeforidealgasisdirectlyproportionaltotheabsolutetemperature理想气体的分子平均平动动能与绝对温度成正比相同温度下 理想气体的分子平均平动动能均相等 Thisresultmeansthatwarmthisevidenceofdisorganizedmotionofatomandmolecules 温度是气体热运动剧烈程度的标志Temperatureisthemeasureofhotness Question 分子平均平动动能相同的不同气体 温度是否相同 Answer同 2Pressureformulas 3Root mean squarespeed方均根速率 ProportionaltotemperatureInverselyproportionaltomolecularmass 大量分子的速率平方的平均值的平方根 1Thedegreeoffreedom自由度 确定一个物体的空间位置所必需的独立坐标数目 AFreedommass自由质点 xyz Bfreedomrigidbody xyz 4EquipartitiontheoremofenergyTheinternalenergyofideagas能量均分定理理想气体内能 x y z i 3 i 6 2Thedegreeoffreedomofmolecules分子的自由度 Monoatomicmolecule单原子分子 氦 氖 氩 i 3 Diatomicmolecule双原子分子 氢 氧 氮 哑铃 连线 2个 质心 3个 i 5 Polyatomicmolecule多原子分子 co2等 Translationaldegreesoffreedom 平动自由度 i平 3Rotationaldegreesoffreedom 转动自由度 i转 3 i i平 3 i转 3 6 3Equipartitiontheoremofenergy能量均分定理 在温度为T的平衡态下 气体分子的每一自由度均有相同的平均动能kT 2 Monoatomicmoleculei 3 3kT 2 Polyatomicmoleculei 66kT 2 3kT Diatomicmoleculei 55kT 2 Notes 能量按自由度均分原理是统计性规律 能量均分原理反映分子向各个方向运动的机会均等 4Internalenergyofidealgas理想气体的内能 Commongas Idealgas Onemole Molarinternalenergy Monoatomicmolecule Diatomicmolecule Polyatomicmolecule Theinternalenergyofidealgasisproportionaltothetemperature 理想气体的内能与温度成正比 理想气体的内能是温度的单值函数 1 机械能与内能有无区别 2 机械能与内能有无联系 5Maxwellspeeddistributionlaw麦克斯韦分子速率分布定律 1Maxwellspeeddistributionfunction 表示在某一速率区间v v v内分子数占总分子数的百分比 表示分子速率在v附近单位速率间隔内的分子数占总分子数的百分率 distributionfunction 2Physicalmeaningrelatedphysicalquantities 1 分子速率在v附近单位速率间隔内分子数占总分子数的百分率 2 分子速率在v v dv内的分子数占总分子数的百分比 3 vp v 所有速率区间的分子数占总分子数的百分比为1 Mostprobablespeed最可几速率vp 曲线峰值对应的速率 vp附近单位速率间隔内的分子数占总分子数的百分比最多 4 5 Mostprobablespeed最可几速率 Root mean squarespeed方均根速率 Meanspeed平均速率 Allofthemareproportionaltoand Ex CalculatethermsspeedofoxygenmolecularatSTP Solution 6MeancollisionfrequencyMeanfreepath 1Thephysicalmeaningof Meancollisionfrequency平均碰撞次数 在平衡态下 单位时间内每个分子与其它分子相碰的平均次数 Meanfreepath平均自由程 在平衡态下 分子连续两次碰撞之间所经过的自由路程的平均值 2Theexpressionof Effectivediameter Numberdensity meanspeed 大量气体分子作无规则的热运动 分子运动过程中将不断与其它分子碰撞 使分子沿折线前进 3Thecalculationof 分子A以平均速率运动 其余均静止