$A$ 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.

$5$ moles of Hydrogen $\left(\gamma=\frac{7}{5}\right)$ initially at $S.T.P.$ are compressed adiabatically so that its temperature becomes $400^{\circ} C$. The increase in the internal energy of the gas in kilo-joules is $\left(R=8.30 \ J \ mol^{-1} \ K^{-1}\right)$.

The $P-V$ diagram for two adiabatic processes is given. Curves $1$ and $2$ correspond to:

$A$ tyre pumped to a pressure of $2 \text{ atm}$ suddenly bursts. If the temperature of air before expansion is $T$, then the air temperature after the tyre bursts is (Assume the expansion is adiabatic and adiabatic constant $\gamma = \frac{3}{2}$).

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

$A$ gas at initial temperature $T$ undergoes sudden expansion from volume $V$ to $2 \, V$. Then,