$A$ polyatomic gas is compressed to $\left(\frac{1}{8}\right)^{\text{th}}$ of its original volume adiabatically. If its initial pressure is $P_0$,what will be its new pressure (in $P_0$)? (Given: $\gamma = \frac{C_p}{C_v} = \frac{4}{3}$)

$A$ monoatomic gas is filled in a cylindrical container with a piston at temperature $T_1$. It undergoes an adiabatic expansion such that its temperature becomes $T_2$. If $L_1$ and $L_2$ are the lengths of the gas column before and after the expansion respectively,then $T_1/T_2$ is equal to:

The $P-V$ diagram for two gases during an adiabatic process is shown in the figure. Curves $A$ and $B$ correspond to:

$A$ gas $(\gamma = 1.3)$ is enclosed in an insulated vessel fitted with an insulating piston at a pressure of $10^5 \ N/m^2$. On suddenly pressing the piston,the volume is reduced to half the initial volume. The final pressure of the gas is:

$A$ 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

Five moles of Hydrogen gas initially at $STP$ is compressed adiabatically so that its temperature becomes $673 \, K$. The increase in internal energy of the gas is $(R=8.3 \, J \, mol^{-1} \, K^{-1}, \gamma=1.4$ for diatomic gas$)$ (in $kJ$)