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 $\gamma = 1.4$).

$A$ sample of $1$ mole of gas at temperature $T$ is adiabatically expanded to double its volume. If the adiabatic constant for the gas is $\gamma = \frac{3}{2}$,then the work done by the gas in the process is:

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.

$A$ rigid diatomic gas $(\gamma = 7/5)$ is compressed adiabatically to volume $(V_i/32)$, where $V_i$ is the initial volume. The initial temperature of the gas is $T_i \text{ K}$ and the final temperature is $x T_i \text{ K}$. The value of $x$ is

In a thermodynamic process,there is no exchange of heat between the system and surroundings. Then the thermodynamic process is

$A$ polyatomic gas follows a law $T^2 V^\alpha = \text{constant}$. Find $\alpha$ for which the heat exchange of gas in the process becomes zero.