The pressure of a motorcar tire at $27^{\circ}C$ is $2$ atmospheres. If the tire suddenly bursts,the final temperature will be ....... $K$ (Take $\gamma = 1.4$).

In an adiabatic expansion, the temperature of one mole of an ideal monatomic gas $(\gamma = 5/3)$ decreases from $60 \text{ K}$ to $50 \text{ K}$. The work done by the gas in the process is : (Take the universal gas constant as $R = 8.3 \text{ J mol}^{-1} \text{ K}^{-1}$) (in $\text{ J}$)

$A$ gas at initial temperature $T$ undergoes sudden expansion from volume $V$ to $2 \, V$. Then,

$5.6 \ L$ of helium gas at $STP$ is adiabatically compressed to $0.7 \ L$. If the initial temperature of the gas is $T \ K$,the work done in the process is ($R$ is the universal gas constant in $SI$ units).

Under an adiabatic process,the volume of an ideal gas gets doubled. Consequently,the mean collision time between the gas molecules changes from $\tau_{1}$ to $\tau_{2}$. If $\frac{C_{p}}{C_{v}}=\gamma$ for this gas,then a good estimate for $\frac{\tau_{2}}{\tau_{1}}$ is given by:

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 ........