EQUATIONS OF STATE 2010-12

《EQUATIONS OF STATE 2010-12 》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、EQUATIONSOFSTATEMinHuang,PhDChemicalEngineeringTongjiUniversityEquationsofState•EquationofstateorEOS•Thermodynamicrelationshipsbetweenthreepropertiesofapure(orone-component)substance.•ThetermEOSmostcommonlyreferstotherelationshipofthepropertiesp,V,andTofagas.•Solidsandliquidsa

2、realsodescribedbyp-V-Tequationsofstate,butareverydifferentinforms.EquationsofState•TheEOSrelatingV,p,andTprovidesnoinformationabouttheotherthermodynamicproperties,inparticularabouttheinternalenergyUandtheentropyS.•KnowledgeofthefunctionU(T,V)requiresinformationaboutthesubstanc

3、ebeyondthatcontainedinitsp-V-Trelationship.FunctionalrelationshipssuchasU(T,V)aresometimescalledthermalequationsofstate.TheJouleexperiment∂UπT=∂VTTheJouleexperiment•Jouledetectednotemperaturechange,–i.e.q=0.•Anyworkdone?Sincethegaswasexpandingagainstzeropressurenoworkwas

4、done,–sow=0.–∆U=q+w=0(1stlaw).•Theprocessisatconstantinternalenergy.TheJouleexperiment•Foramoleofidealgas•∆u=c∆TormoregenerallyvT2∆u=c∆T∫vT1•Bydefinition,onemoleofgas,h=u+pv•Forchangefromstate1tostate2•∆h=∆u+∆(pv)=∆u+∆(RT)=c∆T+R∆T=c∆TvpTheJouleexperiment•Foronemoleofidealgas–∆

5、u=c∆Tv–∆h=c∆Tp–c=c+Rpv•Independentofp,V•Ifcandcvarywithtemperature,vpT2T2∆u=c∆T∆h=c∆T∫Tv∫Tp11TheJouleexperiment•InJoule’sexperiment,clearly,ΔV≠0becausethegasexpandedtofillbothbulbs.Thequestionwas,didTchange?ΔTwasmeasuredtobezero,notemperaturechange.•Ineffect,Joulewastryingtome

6、asurethederivative∂T∂VU•Andfound∂T=0∂VUTheJouleexperiment•Joulefound∆T=0,eventhoughpandVdochange•ThatmeansU≠f(p,V),butthatU=f(T)•FromtheEuler'schainrelation,∂U∂U∂T∂VT∂VT=−==0∂VU∂UCV∂TV∂U•Therefore,foridealgas,=0∂VTTheJoule-Thompsonexpe

7、riment•ItsoonbecameapparentthattheresultoftheJouleexpansionexperimentwasnotvalidforrealgases.Amoreaccurateexperiment,slightlydifferent,wascarriedoutbyJouleandJ.J.Thompsontofurtherelucidatethepropertiesonrealgasesunderexpansion.TheJoule-Thompsonexperiment•Thetotalworkisw=−p(0−V

8、)−p(V−0)1122=pV−pV1122•Sinceq=0,thechangeininternalenergyofth