$A$ diatomic ideal gas is compressed adiabatically to $\frac{1}{32}$ of its initial volume. If the initial temperature of the gas is $T_1$ (in Kelvin) and the final temperature is $a T_1$,the value of $a$ is

One mole of an ideal gas at an initial temperature of $T \, K$ does $6 \, R \, \text{joules}$ of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is $\frac{5}{3}$, the final temperature of the gas will be

$Assertion :$ Air quickly leaking out of a balloon becomes cooler.
$Reason :$ The leaking air undergoes adiabatic expansion.

The internal energy of a gas will increase when it

$V$ cc volume of a gas having $\gamma = \frac{5}{2}$ is suddenly compressed to $\frac{V}{4}$ cc. The initial pressure of the gas is $P$. The final pressure of the gas will be

An ideal gas undergoes an adiabatic process from state $(P_1, V_1, T_1)$ to $(P_2, V_2, T_2)$. The work done during the process is ..... (where $\mu$ = number of moles,$C_P$ and $C_V$ = molar specific heats).