$A$ sample of gas at temperature $T$ is adiabatically expanded to double its volume. The work done by the gas in the process is (given $\frac{C_{P}}{C_{V}}=\gamma=\frac{3}{2}$,$R=$ gas constant).

During the adiabatic expansion of $2$ moles of a gas,the internal energy of the gas is found to decrease by $2 \ J$. The work done during the process on the gas will be equal to ....... $J$.

One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is $100 K$ and the universal gas constant $R = 8.0 J mol^{-1} K^{-1}$,the decrease in its internal energy,in Joule,is. . . . .

During an adiabatic process,the pressure of a gas is found to be proportional to the cube of its temperature. The ratio $C_P / C_V$ for this gas is ........

$A$ gas $(\gamma = 1.5)$ is suddenly compressed to $(1/4)^{th}$ of its initial volume. Find the ratio of its final pressure to its initial pressure.

$P-V$ plots for two gases during an adiabatic process are shown. Plots $(1)$ and $(2)$ correspond to