$A$ 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.

$A$ monoatomic ideal gas, initially at temperature $T_{1}$, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_{2}$ by releasing the piston suddenly. If $l_{1}$ and $l_{2}$ are the lengths of the gas column before and after the expansion respectively, then the value of $\frac{T_{1}}{T_{2}}$ will be

An ideal gas is found to obey $p V^{3/2} = \text{constant}$ during an adiabatic process. If such a gas initially at a temperature $T$ is adiabatically compressed to half of its initial volume, then its final temperature is

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

In an adiabatic process,which of the following statements is true?

The pressure in the tyre of a car is four times the atmospheric pressure at $300 \ K$. If this tyre suddenly bursts,its new temperature will be $(\gamma = 1.4)$.