Solution Manual For Thermal Physics, 2nd Edition

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CHAPTER22.1)ENTROPYANDTEMPERATURE(a)o=logg=logC+(3N/2)logU.(80/3U)y=1/1=(3N/2)(1/U),henceU=3Nt/2.(®)(2%0/00%)N=(38/2)(-1/U%)<0.2.2)PARAMAGNETISMStateswithspinexcess2shavetheenergyU=-2smB,hences=-U/2mB.Insertioninto(40)yields(41).From(41)obtain(3a/3U)yB=1/t==U/m?B2N.SolveforU:U=<U>==n2B2N/t=-MB.HenceM/Nm=mB/t.2.3)QUANTUMHARMONICOSCILLATOR(a)From(1.55):0=logg=log(N+n-1)!=logn!-log(N-1)!=log(N+n)!-logn!-logN!ReplacingN-1byNisequivalenttoneglectingaterm~log((N+n)/N},whichforlargeNissmallcomparedtothefactorialterms.WiththeStirlingapproximation:o=(N+n)log(N+n)-nlogn-NlogN=(N+n)log[(N+n)/N]-nlog(n/N)=N[(1+n/N)log(l+n/N)-(n/N)log(n/N)].(b)Setn=U/MwandNfw=Uy(N):0(UN)=N[(1+U/U))log(1+U/U)=(U/Uy)log(u/ug)].-3-[2.3]StudyXY

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