Problem 2.153

Two identical thermally insulated vessels interconnected by a tube with a valve contain one mole of the same ideal gas each. The gas temperature in one vessel is equal to $T_{1}$ and in the other, $T_{2}$. The molar heat capacity of the gas of constant volume equals $C_{V}$ The valve having been opened, the gas comes to a new equilibrium state. Find the entropy increment $\Delta S$ of the gas. Demonstrate that $\Delta S>0$