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273()Vol.27,No.320048JOURNALOFZHEJIANGNORMALUNIVERSITY(Nat.Sci.)Aug.2004:1001-5051-(2004)03-0268-04X李伟琦(金华广播电视大学理工系,浙江金华321000):,,:,.:;;;;;;:O645.15:A,,,/0,/0/0..[1][2],.,T,p(1),Ls=Ll,dLs(1)XdLl(1).(1),T+dT,p+dp(2),dLs(2)=dLl(2).(2),,,(2).[2,3].,,L*1(s)=Ll1(l)=L*1(l)+RTlnx1.(3),lnx1=L*1(s)-L*1(l)RT=$GmRT;(4)5lnx15Tp=1R55T$GmTp=-$HmRT2.(5)(3),5L*1(s)5Tp=-SsmX-Slm=5L*1(l)5Tp,dL*1(s)XdL*1(l).(6),.,[1](5),5lnx15TpdT+5lnx15pTdp=1R55T$GmTpdT+1R55p$GmTTdp.(7).(5)(1)R5lnx15TpX5S*m(s)5Tp-5S*m(l)5Tp,(8)X:2003-11-10;:2003-12-09:(1961-),,,.:.(5).$Ld$L,(5)(2).1(5)?T,p,p?dp=0?.[1](7),.1.1[2],(4)5RTlnx15Tp=5($L*)T5Tp=-$Sm=-$HmT.(9)12,,x2x1,dx0;p2*=p1*xp1*,dp*0.1,dpdT=$Sm$Vm0,Tf,2Tf,1,dT0.(3)$L=L2(Tf,2,p2,x)-L1(Tf,1,p1)=RTlnx0;d$L0.1~4,Ñ(x=1),Ò.1~3,,,..23:5L5pT=Vm0,52L5p2T=5Vm5pT=-Vp0;()2693:5L5Tp=-Sm0,52L5T2p=-5Sm5Tp=-CpT0.()(10)1~3(),4L-T-p:,,ÑÒ,Ò-Ñ,1-Ñ,Ñ-2.pÑ0ÑTÑ0Ñ2,2,4122Ò.12ÑÒ.dL(T,p)=5L5pTdp+5L5TpdT=dLT+dLp.(11),dLÒ-1L,22,2.,2,.,[1](5)(4).(5),.(7):.[1].1.2(5)$L3(5)$L3,Ñ2,,d$L.(8).图5实时态平衡两条相线1.3(6):(1)2.(6)L-T5.(10).5,T5,,(),,,,.,,.,LT5.(2)))).62L-T.图6两类相变(6),.,SA=SB,.[1].,,,,..2/0(5)1x15x15Tp,(12),/0./0.,.[4]dlnp*s1dTdT=dlnp*l1dTdT+dlnx1dx2dx2,(13)270()2004().3.(13)3,.,(5),.3[1],(6)2(Lg=Ll)1(T=f(p)).:,T,p,p,dp.,(5)dp,.4()2(),/0/0,(dp=0,1).().,Tf=f(p*),p*Tf,Tfp*(5)4(),$L{p,Tf[p*(x)]}pTf2:Tf,p,;T,p*,,;p*(x).,,/50/d0,dx1dT=x1dlnx1dT=x1d($L1)RTdT=-x1RT#$Sm=-$HmRT2#x1.(14)4[2,3],(4)$L.$Gm,$Hm.,22,,$T,.,[4,5],$Hm.,(5).:[1].[J].,2000,15(1):48-51.[2],..3[M].:,1992:137.[3].()[M].:,1979:137.[4],,.()[M].:,1979:244.[5],,.()[M].:,1979:272-273.ConclusionofthefreezingpointdepressionequationwithimagepatternLIWe-iqi(DepartmentofScienceandEngineering,JinhuaRadioandTelevisionUniversity,JinhuaZhejiang321000,China)Abstract:Onthequestioncausedbytheeasyconclusionofthefreezingpoint,theauthertriedtofindreasonsfromtheaugelofdifferentialgeometrybyparsingtheimage.Reasonsfoundbytheauthorcanbesummarizedas:theindis-tinctconceptofpartialdifferentialandcompounddifferential.Keywords:freezepointdepression;chemicalpotential;degreesoffreedom;completedifferential;partialdifferential;differentialcomponent;figureanalyses(薛荣)2713: