热力学统计物理试题(d卷)new

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1、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=0.Show=02.(10points)Considerand.Show3.(20points)ConsiderachemicalreactionfollowsthatShowisopiesticequilibriumconstantIfthereactionfollowsthatcalculateisopiesticequilibriumconstantagain.4.(20points)

2、UseMaxwellvelocitydistributionlawtoshowthefluctuationofvelocityandmeantranslationalenergyrespectivelyfollowsthat,5.(20points)Theelectronicdensityofametalis.CalculatetheFermienergy,FermivelocityanddegeneratepressureofthisfreeelectronicgasattemperatureT=0K.6.(20point

3、s)UsecanonicalensembledistributiontocalculatetheinternalenergyE,freeenergyF,chemicalpotentialμ,andpressurepoftheidealgas.附简答：1.(10points)Solution=-p;=0;(4points)===0=(4points)∵≠0;=0(2points)2(10points)Solution(4points)=-1(3points)Because,thusand,(4points)3.(20point

4、s)SolutionAssumeNH3withn0mol,decomposedn0εmol，thesparepart(1-ε)n0mol,makingN2withmolandH2withmol.Totalnumberis(1+ε)n0mol.Isopiesticequilibriumconstant(5points)(5points)IfthereactionfollowsthatassumeNH3with2n0mol,decomposed2n0εmol，thesparepart2(1-ε)n0mol,makingN2wit

5、hmolandH2withmol.Totalnumberis2(1+ε)n0mol.(5points)Isopiesticequilibriumconstant(5points)4.(20points)Solution(5points)InthescopeofVanddpxdpydpz,themoleculenumberfollowsthat(5points)(5points)(5points)5.(20points)SolutionThemeannumberofelectronatonelevelεiswhentemper

6、atureT=0K:f=1ε<μ(0)f=0ε>μ(0)(5points)(5points)(5points)(5points)6.(20points)Solution(4points)ThefreeenergyF=--kTlnZ(T,V,N)=-(4points)(4points)(4points)(4points)