$A$ monoatomic gas is suddenly compressed to $(1/8)^{\text{th}}$ of its initial volume adiabatically. The ratio of the final pressure to initial pressure of the gas is $(\gamma = 5/3)$.

In a thermodynamic process, helium gas obeys the law $TP^{-2/5} = \text{constant}$. The heat given to the gas when the temperature of $2$ moles of the gas is raised from $T$ to $4T$ ($R$ is the universal gas constant) 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

During an adiabatic process, the pressure is proportional to the cube of the temperature. Then ${C_p}/{C_v}$ is . . . . . . .

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 ....... $J$.

$A$ work of $166.28 \ J$ is done to adiabatically compress one mole of a gas. If the increase in the temperature of the gas is $8^{\circ} C$,the gas is $\left(R=8.314 \ J \ mol^{-1} \ K^{-1}\right)$