An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes $32$ times its initial value. If the final pressure of the gas is $128$ atmospheres,the value of $\gamma$ for the gas is:

$A$ sample of gas with $\gamma=1.5$ is taken through an adiabatic process in which the volume is compressed from $1200 \, cm^3$ to $300 \, cm^3$. If the initial pressure is $200 \, kPa$,find the absolute value of the work done by the gas in the process in Joules.

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:

An ideal gas at $127^{\circ} C$ is compressed suddenly to $\frac{8}{27}$ of its initial volume. If $\gamma=\frac{5}{3}$ for the ideal gas, then the rise in its temperature is: (in $K$)

$A$ 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 ...... $\text{atm}$.

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.