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 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 heat capacity $2C$ . Find the equilibrium temperature . (Assume temperature of air to be uniform and equal to vessel at all times) .
Diffcult
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$\mathrm{C}\left(8 \mathrm{T}_{0}-\mathrm{T}\right)=2 \mathrm{C}\left(\mathrm{T}-\mathrm{T}_{0}\right)+2 \times \frac{7 \mathrm{R}}{2}\left(\mathrm{T}-\mathrm{T}_{0}\right)$
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