热力学统计物理试题(D卷).docx

热力学统计物理试题(D卷)

第一篇：热力学统计物理试题(D卷)热力学·统计物理试题（D卷）适用于2002级本科物理学专业(2004-2005学年度第一学期)1.(10points)Consider(U)=0.Show(U)=0VT2.(10points)ConsiderC0and(vpVpT)T0.ShowCp03.(20points)Considerachemicalreactionfollowsthat2N232H2NH30ShowisopiesticequilibriumconstantKp274221pIfthereactionfollowsthatN23H22NH30calculateisopiesticequilibriumconstantagain.4.(20points)UseMaxwellvelocitydistributionlawtoshowthefluctuationofvelocityandmeantranslationalenergyrespectivelyfollowsthat(v)()2kTm(38)232(kT)2e0x2xdx2432,e0x2xdx438525.(20points)Theelectronicdensityofametalis5.91028/m.CalculatetheFermienergy,3FermivelocityanddegeneratepressureofthisfreeelectronicgasattemperatureT=0K.6.(20points)UsecanonicalensembledistributiontocalculatetheinternalenergyE,freeenergyF,chemicalpotentialμ,andpressurepoftheidealgas.附简答：1.(10points)Solution(UV（）T=T()T=pT)V-p;（UV)T=0;pT（pT)V(4points)UV(U,T)(V,T))T（pV=(U,T)(p,T)(p,T)(V,T)=0=（Up)T(4points)∵V（p)T≠0;（Up)T=0(2points)(10points)SolutionCpCVpVTTVTp(4points)pVTVpT=-1(3points)VpTpVCpCVTVTTppVC0)T0,thusCpV0andCv,Cp0(4points)Because（3.(20points)SolutionAssumeNH3withn0mol,decomposedn0εmol，thesparepart(1-ε)n0mol,makingN2with1n0n0molandH2withn0mol.Totalnumberis(1+ε)n0mol.xNn0(1)n022;xH2;xNH3;(1)n0(1)n0(1)n0Isopiesticequilibriumconstant(5points)Kp1(xN2)2(xH2)2(xNH3)274p211p(5points)IfthereactionfollowsthatN23H22NH0assumeNH3with2n0mol,decomposed2n0εmol，thesparepart2(1-ε)n0mol,makingN2withn0molandH2with3n0mol.Totalnumberis2(1+ε)n0mol.xNn02(1)n0;xH23n02(1)n0;xNH32(1)n02(1)n0;(5points)IsopiesticequilibriumconstantKp(xN2)(xH2)(xNH3)132p1322(1)32(1)(1)(1)22p2716(1)p(5points)4.(20points)Solution(v)2v22(5points)InthescopeofVanddpxdpydpz,themoleculenumberfollowsthatVh--12mkT(pxpypz)edpxdpydpzf(vx,vy,vz)dvxdvydvzmn2kTem2kT(vxvyvz)222dvxdvydvzm4n2kT3em2kTvvdv