中国石油大学历年物理化学考研公式推导题(真题)

1推导题（06）统计热力学导出独立离域子体系：N！qT－kANln，VhmkTqt2332。试求：(1)对理想气体：0qqqt，其中0q为体系零点能(2)从经典力学理论导出：pVAT(3)证明理想气体符合pV=nRT的状态方程。（12分）解：(1)原题存疑。0qqqqqqqqtneVrt，其中0q=neVrqqqq仅为T的函数，与V无关。(2)pdVSdTdA故pVAT(3)N！kTqT－NkAlnln=N！kTqNkTqT－Nktlnlnln0CVqtlnlnln其中C仅为T的函数，与V无关p=TVATtVqNkTlndVVdNkTlnVNkT1VnRT1故nRTpV（05）已知TVU=VTpT－p证明pC－VC=－T2pTVTVp证明：pC－VC=pTH－VTU=pTU+ppTV－VTU①dU=dTTUV+dVVUTpTU=VTU+TVUpTV②2②代入①得：pC－VC=TVUpTV+ppTV=(TVU+p)pTV③将已知式TVU=VTpT－p代入③得：pC－VC=VTpTpTV④又：VTppVTTpV=－1VTp=－pVTTVp⑤⑤代入④得：pC－VC=－T2pTVTVp证毕（03）1、研究发现C2Cl4+Cl2→C2Cl6的反应具有很高的量子效率，因此推断该反应可能为自由基历程，实验提出的反应历程为：Cl2+h2Cl·Cl·+C2Cl4·C2Cl5·C2Cl5+Cl2Cl·+C2Cl6·C2Cl5+·C2Cl5C2Cl6+C2Cl4试求反应的速率方程微分式：dtClCd62=？(10分)解:dtClCd62=2522·ClClCk+2523·ClCk①对自由基[Cl·]、52·ClC可用定态法dtCld·==aIk0－421·ClCClk+2522·ClClCk=0②dtClCd52·==421·ClCClk－2522·ClClCk－22523·ClCk=0③式②+③得：aIk0=22523·ClCk3252·ClC=302kIk④52·ClC=302kIk⑤式④、⑤代入①得：dtClCd62=23022ClkIkk+20Ik推毕（03）请证明：当一个纯物质的膨胀系数α=V1pTV=T1时，它的摩尔恒压热容Cp与压力无关（T为绝对温度）证明：TppC=TpTHp=pTpHT①dH=TdS+VdpTpH=TTpS+V=－TpTV+V②其中引用了麦克斯韦关系TpS=－pTV因α=V1pTV=T1pTV=TV③式③代入式②得：TpH=0④式④代入式①得：TppC=0证毕（02）请证明TVU=TVTp－p证明：dU=TdS－pdVTVU=TTVS－p①引用麦克斯韦关系TVS=VTp②式②代入式①得：TVU=TVTp－p证毕4（99）试根据i,g特性及热力学基本关系式证明：对i,g.：HTJpT,=02、证明：H=f(T,p)pTHTHHppT=－1HpT=pTHTpH①dH=TdS+Vdp，i,g即理想气体TpH=TTpS+V=－TpTV+V=－TTV+V=0②式②代入式①得：HTJpT,=0得证我的网络硬盘地址：里面有很多考研资料，欢迎来下载