4.2 Two vessels A and B each contain N molecules of the same perfect monatomic gas. Initially the two vessels are thermally isolated from each other, the two gases being at the same pressure P, and at temperatures TA and TB respectively. The two vessels are now brought into thermal contact, the pressure of the gases being kept constant at the value P. Find the change in entropy of the system after equilibrium is established, and show that this change is non-negative.