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 $\gamma = 1.4$).

$A$ diatomic gas of volume $2 \ m^3$ at pressure $2 \times 10^5 \ N \ m^{-2}$ is compressed adiabatically to a volume $0.5 \ m^3$. The work done in this process is,$[$Use $4^{1.4} = 6.96]$

One mole of an ideal gas $(C_p/C_v = \gamma)$ at absolute temperature $T_1$ is adiabatically compressed from an initial pressure $P_1$ to a final pressure $P_2$. The resulting temperature $T_2$ of the gas is given by

In summer,when the valve of a bicycle tube is removed,the escaping air appears cold. Why?

Assertion $(A)$: When an ideal gas is compressed adiabatically,its temperature and the average kinetic energy of the gas molecules increase.
Reason $(R)$: The kinetic energy increases because of collisions of molecules with the moving parts of the wall.

$A$ gas is compressed adiabatically until its temperature is doubled. The ratio of its final volume to initial volume will be