Calculate the entropy of mixing for a system of two monatomic ideal gases, A and B ,whose relative proportion is arbitrary. Let N be the total number of molecules and let x be the fraction of these that are of species B. You should find
delta(S) mixing=-Nk[x ln x +(1-x) ln (1-x)
delta (S(total))=delta(S(A)) + delta(S(B))=2Nk ln 2
The Attempt at a Solution
according to my thermal physics text, delta(S(A))=Nk ln 2 . The problem says that in species B , x is just a fraction of N. Then , I think I would have to conclude that delta(S(B))=x/N*(k)*ln(2).
so would my expressison be :delta(S(mixing))=delta(S(A))+delta(S(B))=Nk ln 2+ xk/N*(ln(2))