One mole of a diatomic gas undergoes a process :

\(P = \frac{P_o}{1 + (\frac{V}{V_o})^3}\)

where P_o and V_o are constants. The translational kinetic energy of the gas when V = V_o is given by : 

\(\frac{3P_o V_o}{4}\)

\(P = \frac{P_o}{1 + (\frac{V}{V_o})^3 } = \frac{P_o}{2}\)

\(T = \frac{P_o V_o}{2R}\)

Therefore translational kinetic energy is equal to :

\(\frac{3}{2}RT = \frac{3R}{2} \frac{P_o V_o}{2R}\)

\(\frac{3}{2}RT = \frac{3P_o V_o}{4}\)