An ideal gas is expanded adiabatically at an initial temperature of $300 \ K$ so that its volume is doubled. The final temperature of the hydrogen gas is $(\gamma = 1.40)$.

$A$ 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 $(\gamma = 5/3)$.

Which of the following is true in the case of an adiabatic process, where $\gamma = C_p / C_V$?

$A$ 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. If $L_1$ and $L_2$ are the lengths of the gas column before and after expansion respectively,then $T_1/T_2$ is given by

The volume of air increases by $5\%$ in its adiabatic expansion. The percentage decrease in its pressure will be ...... $\%$

For $1 \text{ mole}$ of an ideal gas,during an adiabatic process,the square of the pressure of a gas is found to be proportional to the cube of its absolute temperature. The specific heat of the gas at constant volume is ($R$ is universal gas constant)