A cylindrical adiabatic container of total volume $2V_0$ is divided into two equal parts by a conducting piston which is free to move as shown in the figure. Each part contains identical gas at pressure $P_0$. Initially the temperatures of the left and right parts are $4T_0$ and $T_0$ respectively. An external force is applied on the piston of area $A$ to keep the piston at rest. The value of external force required when thermal equilibrium is reached is