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) .
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) .
- 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
$\left( {\frac{{10C\ +\ 7R}}{{3C\ +\ 7R}}} \right){T_0}$
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