.S=kInW =N:k1+Hng;-ln(N/q)g.e∈iMkT)川 =>Nk 1+Ing;-In(N/q)Ing;+E/kT] =N,kIn(eqN)+∈kT] = (N:∈)/T+∑N:kn(eqN) U/T +NkIn(eq/N) =U/T一FT=S热 得证∴ S = k㏑W =ΣNik [1+lngi－ln((N/q)gi .e-∈i/kT)] =ΣNi k [1+lngi－ln(N/q)－lngi + ∈i /kT] =ΣNik [㏑(eq/N) + ∈i /kT] = (ΣNi∈i ) /T +ΣNik㏑(eq/N) = U/T +Nk㏑(eq/N) = U/T－F/T=S热 ∴ 得证