4.3. Two vessels contain the same number N of molecules of the same perfect gas. Initially the two vessels are isolated from each other, the gases being at the same temperature T but at different pressures P1 and P2. The partition separating the two gases is removed. Find the change in entropy of the system when equilibrium has been re-established, in terms of the initial pressures P1 and P2. Show that this entropy change is non-negative.