物理化学知识点归纳

···············································································1···············································································3·······························································································7·························································································10·························································································12·············································································14·····························································································16·····································································20·····································································24·············································································2711.UQW∆=+dUQWδδ=+eddUQpVδ=−2.dVWpVδ=−21dVVVWpV=−∫00VW=0VW=21()VWpVV=−−21()VWpVV=−−21dVVVWpV=−∫3.HUpV=+dVVVQUCTTδ∂⎛⎞==⎜⎟∂⎝⎠dpppQHCTTδ∂⎛⎞==⎜⎟∂⎝⎠pVCCnR−=24.WQU∆H∆WQU∆H∆000021lnVnRTV−21lnVnRTV00021dTVTCT∫21dTVTCT∫21dTpTCT∫epV−∆QUW=∆−21dTVTCT∫21dTpTCT∫21dTVTCT∫22111pVpVγ−−021dTVTCT∫21dTpTCT∫21()1nRTTδ−−QUW=∆−21dTVTCT∫21dTpTCT∫5.-1pHTTHpCpµ⎛⎞⎛⎞∂∂==−⎜⎟⎜⎟∂∂⎝⎠⎝⎠6.pQH=∆VQU=∆()gpVQQnRT−=∆rmfm()BBHHBυ∆=∆∑\\rmcm()BBHHBυ∆=−∆∑\\7.21rm2rm1r()()dTpTHTHTCT∆=∆+∆∫31.hWQη=ch1TTη=−CarnotchcTTTβ=−Carnotirrηη≤2.Clausius3.ClausiusBAB=A0iiiQSTδ→∆−≥∑4.HelmholtzGibbsAUTS=−GHTSUpVTSApV=−=+−=+5.d0S≥Helmholtzd0A≤Gibbsd0G≤6.MaxwelldddUTSpV=−VUTS∂⎛⎞=⎜⎟∂⎝⎠TUpV∂⎛⎞=−⎜⎟∂⎝⎠SVTpVS∂∂⎛⎞⎛⎞=−⎜⎟⎜⎟∂∂⎝⎠⎝⎠dddHTSVp=+pHTS∂⎛⎞=⎜⎟∂⎝⎠SHVp⎛⎞∂=⎜⎟∂⎝⎠pSTVpS⎛⎞∂∂⎛⎞=⎜⎟⎜⎟∂∂⎝⎠⎝⎠dddASTpV=−−VAST∂⎛⎞=−⎜⎟∂⎝⎠TApV∂⎛⎞=−⎜⎟∂⎝⎠TVSpVT∂∂⎛⎞⎛⎞=⎜⎟⎜⎟∂∂⎝⎠⎝⎠4dddGSTVp=−+pGST∂⎛⎞=−⎜⎟∂⎝⎠TGVp⎛⎞∂=⎜⎟∂⎝⎠pTSVpT⎛⎞∂∂⎛⎞=−⎜⎟⎜⎟∂∂⎝⎠⎝⎠7.Gibbs-Helmholtz2pGHTTT⎡∆⎤⎛⎞∂⎜⎟⎢⎥∆⎝⎠⎢⎥=−∂⎢⎥⎢⎥⎣⎦2pAUTTT⎡∆⎤⎛⎞∂⎜⎟⎢⎥∆⎝⎠⎢⎥=−∂⎢⎥⎢⎥⎣⎦8.,,SAG∆∆∆∆S1pVTVmr,rnCddddTpVUWTQTTSδδ−==−=22,m1121,m12lnlnlnlnVpTVSnCnRTVTpnCnRTp∆=+=+2112lnlnVpSnRnRVp∆==2,m1lnVTSnCT∆=2,m1lnpTSnCT∆=2,mdVnCSTT∆=∫3,mdpnCSTT∆=∫4/SHT∆=∆5//SQTQT∆==−61267rmmBBSSν∆=∑\\G∆510G∆=2GHTS∆=∆−∆3()()2211GHTSHTSTS∆=∆−∆=∆−−G∆A∆10A∆=2()AUTSGpV∆=∆−∆=∆−∆3()()2211AUTSUTSTS∆=∆−∆=∆−−A∆9.1()()()m11/B,B,0HnHSHTTpTpUHpVGApVββααββααββααβαβααβ∆=∆∆=∆⎯⎯⎯⎯⎯⎯⎯⎯⎯→∆=∆−∆∆=∆=−∆\\\\\()()B,B,Tppαβ⎯⎯→\\()()212121,m,,m,,m,21112111dddTpTTVTTpTHnCTUnCTnCSTTGHTSSTSAUTSSTSααα∆=∆=∆=∆=∆−+∆−⎡⎤⎣⎦∆=∆−+∆−⎡⎤⎣⎦∫∫∫()()212121,m,,m,,m,21112111dddTpTTVTTpTHnCTUnCTnCSTTGHTSSTSAUTSSTSβββ∆=∆=∆=∆=∆−+∆−⎡⎤⎣⎦∆=∆−+∆−⎡⎤⎣⎦∫∫∫()()()m2s2S/B,B,0HnHSHTTpTpUHpVGApVββααββααββααβαβααβ∆≈∆∆=∆⎯⎯⎯⎯⎯⎯⎯⎯⎯→∆=∆−∆∆=∆=−∆\210000ln(0ddppVVHUpSnRpGVpApV∆∆∆=∆=∆=∫∫\\210000ln(0ddppVVHUpSnRpGVpApV∆∆∆=∆=∆=∫∫\\62()()()()()()BfmBfmrmBBBmrmBrmrmgBfmrmBrmrmgBBBR25P25BHHHSSppUHnRTGGAGnRTνννν∆=∆=−∆∆=⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→∆=∆−∆∆=∆∆=∆−∆∑∑∑∑\\\\\\\\\\\\\()()()()()()()()()()()()rmrm298Krmrm298Krmrmgrmrmrmrmrmrm298Kd298KdRKPKTpTpHTHCTCSTSTTTpTpUTHTnRTGHTTSTAUTTST∆=∆+∆∆∆=∆+⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯→∆=∆−∆∆=∆−∆∆=∆−∆∫∫\\\\\\\\\\\\\\7RaoultHenry1.CBBB,,TpnZZn≠∂⎛⎞=⎜⎟∂⎝⎠1kBBBZnZ==∑Gibbs-Duhem11dd0kkBBBBBBnZxZ====∑∑BBBHUpVHUpV=+⇒=+BBBAUTSAUTS=−⇒=−BBBGHTSGHTS=−⇒=−BBTTGGVVpp∂∂⎛⎞⎛⎞=⇒=⎜⎟⎜⎟∂∂⎝⎠⎝⎠BBppGGSSTT∂∂⎛⎞⎛⎞=−⇒=−⎜⎟⎜⎟∂∂⎝⎠⎝⎠,,CCBBppnTTnSVSVpTpT⎛⎞⎛⎞∂∂∂∂⎛⎞⎛⎞=−⇒=−⎜⎟⎜⎟⎜⎟⎜⎟∂∂∂∂⎝⎠⎝⎠⎝⎠⎝⎠2.,,,,,,,,CCCCBBBBBTpnSVnSpnTVnGUHAnnnnµ∂∂∂∂⎛⎞⎛⎞⎛⎞⎛⎞====⎜⎟⎜⎟⎜⎟⎜⎟∂∂∂∂⎝⎠⎝⎠⎝⎠⎝⎠3.ddddddddddddddddBBBBBBBBBBBBUTSpVnHTSVpnASTpVnGSTVpnµµµµ=−+=++=−−+=−−+∑∑∑∑84.Raoult*AAAppx=HenryBxBmBcBpkxkmkc===5.(,)()ln(/)TpTRTppµµ=+\\(,)()ln(/)TpTRTfpµµ=+\\*(,)()ln(/)(,)lnBBBBTpTRTppTpRTxµµµ=+=+\\*(,)(,)lnBBBTpTpRTxµµ=+*,m(,)()dpBBpTpTVpµµ=+∫\\*(,)(,)lnAAATpTpRTxµµ=+**(,)(,)ln(,)()ln(/)(,)ln(,)()ln(/)(,)ln(,)()ln(/)BBBBxBBBmBBBcTpTpRTxTpTRTkpmTpRTTpTRTkmpmcTpRTTpTRTkcpcµµµµµµµµµµ=+=+=+=+=+=+\\\\\\\\\\*(,)(,)lnAAAAAATpTpRTaaxµµγ=+=*,,,,,,,,,(,)(,)ln(,)ln/(,)ln/BBBxBxBxBBmBmBmBBBcBcBcBTpTpRTaaxTpRTaammTpRTaaccµµγµγµγ=+==+==+=\\6.()2ff*ffus()BmBARTAKmnTHn==⋅∆∆()2*bbvbapb()AmBTRTKMHAKm∆=⋅∆=BVnRTΠ=97.Gibbs-Duhemd0BBBnµ=∑Duhem-Marfulelnln0ABABABTTppxxxx∂∂⎛⎞⎛⎞−=⎜⎟⎜⎟∂∂⎝⎠⎝⎠101.rmrmflnGGRTQ∆=∆+\rmflnGRTK∆=−\\2.()f/BBBKfpυ=∏\\afpKKK==\\\()ppBKKpυ∑=\\xpBpKKpυ−∑⎛⎞=⎜⎟⎝⎠\\cpBRTKKpυ−∑⎛⎞=⎜⎟⎝⎠\\ppKKKγ=\\3.Gibbsrm,BBBTpGGυµξ∂⎛⎞∆==⎜⎟∂⎝⎠∑4.rm0BBBGυµ∆=∑rm0BBBGυµ∆==∑rm0BBBGυµ∆=∑5.rm2dlndHKTRT∆=\\rm0H∆\dln0dKT\K\116.*xmlnpKVpRT∂∆⎛⎞=⎜⎟∂⎝⎠pKcKxK0BBυ∑7.0BBυ∑0BBυ∑121.'CSRR=−−SRR’R’1.2.3.2.2fCΦ=−+2fCΦn=−+*1fCΦ=−+123.1C=23fCΦΦ=−+=−0312ClapeyronddpHtTV∆=∆Clausius-Clapeyronvap/sub211211ln()HppRTT∆=−4.2C=24fCΦΦ=−+=−0413px−Tx−5.6.133C=25fCΦΦ=−+=−0514.141.2.(),,UVNΩ1pΩ=xΩxpΩΩ=3.BoltzmanlnSkΩ=4.Boltzmann/*/ijkTiikTjjgeNNgeεε−−=∑5./ikTiiqgeε−=∑trvenqqqqqq=⋅⋅⋅⋅lnNAkTq=−ln!NqAkTN=−,lnlnNVNqSkqNkTT∂⎛⎞=+⎜⎟∂⎝⎠,lnln!NVNqqSkNkTNT∂⎛⎞=+⎜⎟∂⎝⎠,lnlnNTNqGkTqNkTVV∂⎛⎞=+⎜⎟∂⎝⎠,lnln!NTNqqGkTNkTVNV∂⎛⎞=+⎜⎟∂⎝⎠2,lnVNqUNkTT∂⎛⎞=⎜⎟∂⎝⎠152,,lnlnVNTNqqHNkTNkTVTV∂∂⎛⎞⎛⎞=+⎜⎟⎜⎟∂∂⎝⎠⎝⎠,lnTNqpNkTV∂⎛⎞=⎜⎟∂⎝⎠2,lnVVNVqCNkTTT∂⎡∂⎤⎛⎞=⎜⎟⎢⎥∂∂⎝⎠⎣⎦6.Bose-Einstein1iiigNeαβε−−=−7.Femi-Dirac1iiigNeαβε−−=+161.QzEF=2.iiiiijjjjQnzrtQnzr==∑1ittt+−=+=∑∑∑3.RΩGS1−Ω1AGRlκ==4.1m1m21Sm−⋅5.1m1molmcκΛ=6.mm(1)cΛΛβ∞=−7.mm,+m,Λνλνλ∞∞∞+−−=+8.MAMAzzνννν+−+−+−→+()lnBBBTRTaµµ=+\Bµνµνµ++−−=+Bµνµνµ++−−=+\\\17()lnTRTaµµ+++=+\()lnTRTaµµ−−−=+\Baaaνν+−+−=⋅()1/aaaννν+−±+−=⋅()1/νννγγγ+−±+−=⋅()1/mmmννν+−±+−=⋅9