During an adiabatic process,the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\frac{C_P}{C_V}$ for the gas is

An engine takes in $5$ moles of air at $20\,^{\circ}C$ and $1\,atm$,and compresses it adiabatically to $1/10^{\text{th}}$ of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules,the change in its internal energy during this process is $X\,kJ$. The value of $X$ to the nearest integer 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.

$5.6 \ L$ of Helium gas at $STP$ is compressed adiabatically to $0.7 \ L$. If the initial temperature is $T_1$,then the work done during the process is...?

One mole of an ideal gas at an initial temperature of $T \, K$ does $6 \, R \, \text{joules}$ of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is $\frac{5}{3}$, the final temperature of the gas will be

$A$ gas $(\gamma = 1.5)$ is suddenly compressed to $(1/4)^{th}$ of its initial volume. Find the ratio of its final pressure to its initial pressure.