1、Chapter 1 The properties of gases1.1 The perfect gas1.1.1 The equation of state for perfect gasp R=8.3145Jmol1K-1Perfectgasequationisactuallyacombinationofthreelaws,Boyleslaw,CharleslawandAvogadrosLaw.(1)Boyles LawRobertBoyle(1627-1691),English(2)Charles LawVT(n,pconstant)JacquesCharles(1746-1823),F
2、rench(3)Avogadros LaworVn(T,patconstant)CombinationofthreelawsAvogadroslaw:Vn(T,patconstant)Boyleslaw:V1/pCharleslaw:VTCombiningthethreegaslaws,wegetVnT/p or pV=nRTTheotherformofthestate equation of perfect gas1.1.2ThemodelofperfectgasThetotalinteractionenergyEbetweentwomoleculescanbeexpressedasthes
3、umoftheattractiveenergyandtherepulsiveenergyFig1.1.3InteractionpotentialasafunctionofintermoleculardistanceIdealGasModelMoleculesmaybetreatedaspointmassesrelativetothevolumeofthesystem.(分子无体积)Intermolecularforcesofattractionandrepulsionarenegligible.(分子间无作用力)1.1.3MolargasconstantRHowtogetthevalueofR
4、?RisobtainedfromanextrapolationmethodByextrapolatingptozero,Rcanbeobtained.1.2Mixturesofidealgases1.2.1 Composition of a mixtureThemolemassofamixturecanbedefinedas:1.2.2DaltonslawThetotalpressurepofagasmixtureisequaltothesumofallthepressurespBoftheconstituentgasesalone.Thelawappliestoidealgases.John
5、Dalton(1766-1844)Partial pressureisthepressurethateachgaswouldexertifitaloneoccupiedthevolumeofthemixtureatthesametemperature.Airat0Cand50%relativehumidityPressuresareinkilopascals(kPa)ExampleAsampleofhydrogengasiscollectedoverwaterat14.0.Thepressureoftheresultantmixtureis113.0kPa.Whatisthepressuret
6、hatisexertedbythedryhydrogenalone?Thevaporpressureofwaterat14.0is1.6kPa.Solving1.2.3AmagatslawthevolumeVofagasmixtureisequaltothesumofthevolumeseachgaswouldoccupyifitexistedaloneatthemixturetemperatureandpressure.1.3 Critical constants and liquefaction of gases1.3.1 Saturated vapor pressures of liqu
7、idsSaturation vapor pressure:thepressureofavaporwhenthevaporphaseisinequilibriumwiththeliquidphaseofthatsamematerial.Liquidandvaporinequilibriumarecalledsaturated liquidandsaturated vaporrespectively.boiling point:The temperature at which the vapor pressure is equal to the atmospheric pressure.norma
8、l boiling point:Theboilingpointatapressureof101.325kPa.relative humidity:1.3.2 Critical constants of gasescritical temperatureTcCriticalpressurepcCriticalvolumeVm,c1.3.3 Liquefaction of real gases(a)TwophaseofCO2(b)increaseintemperature(c)Increasingtemperaturefurther(d)criticalpointreached1.4 Equati
9、ons of state for real gases1.4.1 Boyles temperatureTBisdefinedasBoyle temperature.1.4.2 The van der Waals equationForonemoleofgasaandbareconstant.Theconstantaisacorrectiontermforintermolecularforceandbisacorrectionfortherealvolumeofthegasmolecules.Whenp0andVmforarealgas,theequationchangesintoanideal
10、gasequation.van der Waals(1837-1923),DutchExampleThecriticaltemperature,Tc,andcriticalpressure,pc,formethaneare191Kand46.4105Parespectively.CalculatethevanderWaalsconstantsandestimatetheradiusofamethanemolecule.SolutionThevanderWaalsequationtakestheformThisrearrangestoDifferentiatingequation(1.4),we
11、getThecombinationofequations(1.4),(1.5),and(1.6)givesb,representsfourtimestheactualvolumeofthemethanemolecules1.5 The principle of corresponding states and the compression factorsTheequationsofstateforrealgaseshavedifferentspecificconstantsfordifferentgases.wewilltrytoderiveageneralizedequationofsta
12、te,whichisadequateforanycommonrealgases.1.5.1 Compression factorWehavecritical compression factorZc:Formostgases,thevaluesofZcareapproximatelyconstant,at0.260.31.1.5.2 The principle of corresponding statesDefine:pr,VrandTrarecalledreduced pressure,reduced volumeandreduced temperaturerespectively.the
13、 principle of corresponding states:realgasesatthesamereducedvolumeandreducedtemperatureexertthesamereducedpressure.1.5.3 Generalized compression factor graphsWecanseethatThus,ageneralizedcompressionfactorchartcanbeusedtogetZoncewehavethereducedtemperatureandpressure.压缩因子图由图可见：pr0，Z1；pr相同步，Tr，Z1；Tr1时
14、，曲线中断阐明气体液化；Tr不很高时，Z先降后升阐明作用力随压力旳变化。压缩因子图旳使用措施ZprTr=1.020.3由Tr=1.0,pr=2,查出Z=0.3压缩因子图旳应用（1）已知某真实气体T、p,求Z 和VmT,p求VmTr,prZ123查图计算(pVm=ZRT)（2）已知T、Vm，求Z 和pr需在压缩因子图上作辅助线式中pcVm/RT为常数，Z pr为直线关系，该直线与所求Tr 线交点相应旳Z 和pr，为所求值例1.5.1应用压缩因子图求80oC，1kg体积为10dm3旳乙烷气体旳压力解：乙烷旳 tc=32.18oC,pc=4.872MPa摩尔质量M30.0710-3kgmol-1在压
15、缩因子图上作Zpr 辅助线0.30.40.50.60.81234pr120.60.40.20.50.30.8Z1.21.151.1Tr估计Tr=1.157与Zpr线交点处：Z=0.64pr=1.28(3)已知p、Vm求 Z 和Tr需另外作图p、Vm已知式中pVm/RTc 为常数画出Z=(pVm/RTc)/TrZ=f(Tr)(pr固定,根据Zpr图绘制)两条曲线由两线交点可求出Z、Tr例1.5.2已知甲烷在p14.186MPa下旳浓度C6.02moldm-3，用普遍化压缩因子图其求温度。解：甲烷tc=82.62，pc=4.596MPaVm=1/Cpr=p/pc=14.186/4.596=3.08
16、7从压缩因子图上查得pr=3.087时(为一直线)：Z=1.487/TrZ=f(Tr)(pr=3.087)作Z Tr图pr=3.087时，Z=f(Tr)Z=1.487/Tr两线交点处Z0.89Tr=1.67SummaryFunctionofstateforidealgases：pV=nRTThelawofpartialpressure：ppB=pyBThevanderWaalsequationCriticalconstantsandreducedconstants pr=p/pc；Tr=T/Tc；Vr=V/Vctheprincipleofcorrespondingstates：gaseshavingtwoidenticalreducedconstantswouldhavethesamethirdreduceconstant.GeneralizedcompressionfactorchartHomework1.1(idealgas)1.2(idealgas)1.5(partialpressurelaw)1.10(thevanderWaalsequation)1.11(thevanderWaalsequationandcompressionfactor)
