AS = k[(NA + NB) in Ya + YER - Na In A - Np in...
AS = k[(NA + NB) in Ya + YER - Na In A - Np in Val (identical gases). VA +VB NB) In NA + NB VA NAIN NA (identical gases). (6.37) (6.37) Problem 6.8. Entropy of mixing of identical particles (a) Use (6.37) to show that AS = 0 if the two gases have equal densities before separation. Write NA = PVA and NB=pVB. (b) Why is the entropy of mixing nonzero if the two gases initially have different densities even though the particles are identical? (6.38) If the two gases are not identical, the total entropy after mixing is S =k[NA in VAHVB + Ng In V4+, VB + Naf(T,ma) + Npf(T, mb)]. ΝΑ Then the entropy of mixing becomes VA +VB VA+VB ΝΑ NB For the special case of NA = NB = N and VA =VB =V, we find AS = 2Nk In 2. +VB NA NA Ng In (6.39) (6.40)