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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 gas mixture consists of $8$ moles of argon and $6$ moles of oxygen at temperature $T$. Neglecting all vibrational modes, the total internal energy of the system is
A gas for which $\gamma = 1.5$ is suddenly compressed to $\frac{1}{4}$ th of the initial volume. Then the ratio of the final to the initial pressure is
The specific heat of hydrogen gas at constant pressure is ${C_P} = 3.4 \times {10^3}cal/kg{\,^o}C$ and at constant volume is ${C_V} = 2.4 \times {10^3}cal/kg{\,^o}C.$If one kilogram hydrogen gas is heated from ${10^o}C$ to ${20^o}C$ at constant pressure, the external work done on the gas to maintain it at constant pressure is