In an adiabatic expansion, the temperature of one mole of an ideal monatomic gas $(\gamma = 5/3)$ decreases from $60 \text{ K}$ to $50 \text{ K}$. The work done by the gas in the process is : (Take the universal gas constant as $R = 8.3 \text{ J mol}^{-1} \text{ K}^{-1}$) (in $\text{ J}$)

The work of $146 \ kJ$ is performed in order to compress one kilo mole of gas adiabatically,and in this process,the temperature of the gas increases by $7 ^\circ C$. The gas is $(R = 8.3 \ J \ mol^{-1} K^{-1})$.

The pressure and density of a diatomic gas $\left(\gamma=\frac{7}{5}\right)$ change adiabatically from $(P, \rho)$ to $(P^{\prime}, \rho^{\prime})$. If $\frac{\rho^{\prime}}{\rho}=32$,then $\frac{P^{\prime}}{P}$ is:

$A$ gas at $N.T.P.$ is suddenly compressed to $\left(\frac{1}{4}\right)$ of its original volume. What will be the final pressure? (Given: $\gamma = \text{ratio of specific heats} = \frac{3}{2}$,$P = \text{original pressure}$)

$A$ monoatomic ideal gas,initially at temperature $T_1$,is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. $L_1$ and $L_2$ are the lengths of the gas columns before and after the expansion,respectively. The ratio $T_2 / T_1$ is

In an adiabatic change,the pressure and temperature of a monoatomic gas are related by the relation $p \propto T^{C}$,where $C$ is equal to