The adiabatic elasticity of a diatomic gas at $NTP$ is ........ $N/m^2$.

$A$ mass of diatomic gas $(\gamma = 1.4)$ at a pressure of $2 \text{ atm}$ is compressed adiabatically so that its temperature rises from $27^{\circ}C$ to $927^{\circ}C$. The pressure of the gas in the final state is ...... $\text{atm}$.

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

$Assertion :$ Adiabatic expansion is always accompanied by fall in temperature.
$Reason :$ In adiabatic process, volume is inversely proportional to temperature.

$A$ gas is kept in a container having walls which are thermally non-conducting. Initially,the gas has a volume of $800 \ cm^3$ and a temperature of $27^{\circ} C$. The change in temperature when the gas is adiabatically compressed to $200 \ cm^3$ is ......... $K$. (Take $\gamma=1.5$,where $\gamma$ is the ratio of specific heats at constant pressure and at constant volume.)

Two moles of an ideal monoatomic gas occupy a volume $V$ at $27^{\circ}C$. The gas expands adiabatically to a volume $2V$. Calculate $(a)$ the final temperature of the gas and $(b)$ the change in its internal energy.