流体相平衡的分子热力学课后习题答案

SolutionsManualtoAccompanyMolecularThermodynamicsofFluid-PhaseEquilibriaThirdEditionJohnM.PrausnitzRüdigerN.LichtenthalerEdmundoGomesdeAzevedoPrenticeHallPTRUpperSaddleRiver,NewJersey07458”2000PrenticeHallPTRPrenticeHall,Inc.UpperSaddleRiver,NJ07458ElectronicTypesetting:EdmundoGomesdeAzevedoAllrightsreserved.Nopartofthisbookmaybereproduced,inanyformorbyanymeans,withoutpermissioninwritingfromthepublisher.Allproductnamesmentionedhereinarethetrademarksoftheirrespectiveowners.PrintedintheUnitedStatesofAmerica1098765432ISBN0-13-018388-1Prentice-HallInternational(UK)Limited,LondonPrentice-HallofAustraliaPty.Limited,SydneyPrentice-HallCanadaInc.,TorontoPrentice-HallHispanoamericana,S.A.,MexicoPrentice-HallofIndiaPrivateLimited,NewDelhiPrentice-HallofJapan,Inc.,TokyoSimon&SchusterAsiaPte.Ltd.,SingaporeEditoraPrentice-HalldoBrasil,Ltda.,RiodeJaneiroCONTENTSPrefaceiSolutionstoProblemsChapter21SolutionstoProblemsChapter317SolutionstoProblemsChapter429SolutionstoProblemsChapter549SolutionstoProblemsChapter681SolutionstoProblemsChapter7107SolutionstoProblemsChapter8121SolutionstoProblemsChapter9133SolutionstoProblemsChapter10153SolutionstoProblemsChapter11165SolutionstoProblemsChapter12177SOLUTIONSTOPROBLEMSCHAPTER21.Fromproblemstatement,wewanttofind.wwPT/bgvUsingtheproduct-rule,wwFHGIKJwwFHGIKJwwFHGIKJPTTPPTvvvBydefinition,DPPTwwFHGIKJ1vvandNTTPwwFHGIKJ1vvThen,wwFHGIKJuuPTPTvDN18105321033856...barC-1DIntegratingtheaboveequationandassumingDPandNTconstantoverthetemperaturerange,weobtain'PPTDN'TFor'T=1qC,weget'P33.8bar12SolutionsManual2.Giventheequationofstate,PVnbRTFHGIKJwefind:wwFHGIKJwwFHGIKJSVPTnRVnbTVwwFHGIKJwwFHGIKJSPVTnRPTPwwFHGIKJwwFHGIKJUVTPTPTV0wwFHGIKJwwFHGIKJwwFHGIKJUPUVVPTTT0wwFHGIKJwwFHGIKJHPTVTVnbTForanisothermalchange,'SPTdVnRVnbVnbnRPPVVVwwFHGIKJz122112lnln'UUVVPdPTTPPwwFHGIKJwwFHGIKJLNMMOQPPz120'HTVTVdPnbPPPPPwwFHGIKJLNMMOQPPz2112bg'''GHTSnbPPnRTPPFHGIKJ2112bgln'''AUTSnRTPPFHGIKJln123SolutionsManual3.Thisentropycalculationcorrespondstoaseriesofstepsasfollows:sTP(saturatedliq.=298.15K=0.03168bar)1sTP(saturatedvapor,=298.15K=0.03168bar)2sTP(vapor,=298.15K=1bar)3sss31223s1oo''vap1112vap(2436)(18.015)147.19JKmol298.15hssTo'u'''sTdPPPP2323owwFHGIKJLNMMOQPPzvBecausevRTP(idealgas),323211ln1.0(8.31451)ln0.0316828.70JKmolPsRPo§·'¨¸©¹§u¨©¹·¸032(HO,vapor)147.1928.7069.96ss11188.45JKmol4SolutionsManual4.BecauseDRTPv,PRTRTDvvv232/orPRTvvv22323323(6)(23)TPRTw§·¨¸w©¹vvvvv2,AsT=373.15K,R=0.0831451barLK-1mol-1,andmolarmassis100gmol-1,v231.LmolwwFHGIKJuPTv3324533245108.barLmol.Pammol-13wgkPcT2233281141100102310332451024621wwFHGIKJFHGIKJuuuFHGIKJuuFHGIKJuuFHGIKJvvkgmNsmolkgmmolNmolmmms232322(.)..,w157ms15.Assumeathree-stepprocess:5SolutionsManual(1)Isothermalexpansiontov=f(idealgasstate)(2)Isochoric(visconstant)cool-ingtoT2(3)Isothermalcompressiontov2VTv=(1)(2)(3)(,)Tv(,)Tv1122Foranisentropicprocess,''''ssss1230Becauses=s(v,T),dssdsTdTTwwFHGIKJwwFHGIKJvvvordsPTdcTdTwwFHGIKJvvvbyusingtherelationswwFHGIKJwwFHGIKJSPTTvv(Maxwellrelation)wwFHGIKJwwFHGIKJsTTuTcTvvv1then,22110TTcPPsddTTTTffww§·§·'¨¸¨¸ww©¹©¹³³³vvvvvvvvvdUsingvanderWaals’equationofstate,PRTbavv2wwFHGIKJPTRbvvThus,6SolutionsManual21021lnTTbcsRdbT§·'¨¸©¹³vvvTTosimplify,assumeccRpv00v222RTPThen,202112lnlnpRTbcRPTbRT§·§·¨¸¨¸¨¸©¹©¹v22(82.0578)()45623.15ln(3.029)ln60045TTuªºu«»¬¼T2203K6.PRTbaRTbaRTLNMMMMOQPPPPvvvvv211Becauseb221v,11122FHGIKJbbbvvvThus,PRTbaRTbFHGIKJLNMMOQPPvvv1122orPRTbaRTbvvvFHGIKJ11227SolutionsManualBecausezPRTBCvvv12thesecondvirialcoefficientforvanderWaalsequationisgivenbyBbaRT7.StartingwithduTdsPdvwwFHGIKJwwFHGIKJwwFHGIKJwwFHGIKJwwFHGIKJuPTsPPPTTPPTTPTvvvTAsvRTPBRTPbaT2wwFHGIKJvTRPaTP23wwFHGIKJvTRTPT2Then,wwFHGIKJuPaTT22202audS§·'¨¸W©¹³P22auS'W8SolutionsManual8.TheequationPnTmRTFHGIKJvv212/bgcanberewrittenas()()//PTPmTnnmRT1231223/22vvvvvvv3212120FHGIKJFHGIKJmRTPnPTnmPT//(1)Atthecriticalpoint,therearethreeequalrootsforv=vc,or,equivalently,wwFHGIKJwwFHGIKJPPTTcTTcvv220(2)vvvvvvvvccccbg33223330ComparingEqs.(1)and(2)atthecriticalpoint,mRTPccc3v(3)nPTccc1223/v(4)nmPTccc123/v(5)FromEqs.(3),(4),and(5)weobtainmcv3(6)vcccccRTPmRTP388ornPTRTPccccc32764212252v//Theequationofstatemayberewritten:9SolutionsManualPRTmnRTFHGGGIKJJJvvv113/2orzPRTmnRTvvv113/2Fromcriticaldata,m004281.Lmoln6378.bar(Lmol)K121/2At100qCandatv=(6.948)u(44)/1000=0.3057Lmol-1,z=0.815ThisvalueofzgivesP=82.7bar.TablesofDinforcarbondioxideat100qCandv=6.948cm3g-1,giveP=81.1barorz=0.799.9.WewanttofindthemolarinternalenergyuTbasedonareferencestatechosensothat(,)vuT(,)00vofThen,uTuTuTuTuTuTuTuduTdTTTT(,)(,)(,)(,)(,)(,)(,)limlimvvvvvvvvvvvvvvvofofofofwwFHGIKJwwFHGIKJoffoffzz000(1)Schematicallywehave:12Ref.stateIdealgas(,)Tv30v=vIdealgasIntermediatestateIdealgas(,)TvStateofinterestRealgas(,)Tv10SolutionsManualInEq.(1)wearetaking1molofgasfromthereferencestate1tothestateofinterest3throughanintermediatestate2,characterizedbytemperatureTandvolumevof,i