An iron rod of heat capacity $C$ is heated to temperature $8T_0$. It is then put in a cylindrical vessel of adiabatic walls having two moles of air which can be treated as a diatomic ideal gas at temperature $T_0$ and closed by a movable piston which is also adiabatic. The atmospheric pressure is $P_0$. The cylinder with the piston combined have a heat capacity $2C$. Find the equilibrium temperature. (Assume the temperature of air to be uniform and equal to the vessel at all times).

• A
  $\left( \frac{8C + 7R}{3C + 7R} \right) T_0$
• B
  $\left( \frac{10C + 7R}{C + 7R} \right) T_0$
• C
  $\left( \frac{8C + 7R}{C + 7R} \right) T_0$
• D
  $\left( \frac{10C + 7R}{3C + 7R} \right) T_0$