Ex. 5

An insulated container is originally divided in half by a partition, and each half is originally occupied by $n$ moles of an different ideal gas at temperature $T_0$. The partition is removed without doing any work. What is the change in entropy?

Since these are ideal gases, they do not interact. Each species is oblivious of the existence of the other and the entropy change for each is just the same as in the free expansion of Ex. 4. Thus the total entropy change is given by $\Delta S=2nR \ln 2$. Note that the total mixing - which we know will happen eventually - is exactly the change which maximises the entropy.