$V$ cc volume of a gas having $\gamma = \frac{5}{2}$ is suddenly compressed to $\frac{V}{4}$ cc. The initial pressure of the gas is $P$. The final pressure of the gas will be

$A$ 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 expansion respectively,then $T_1/T_2$ is given by

$A$ monoatomic gas at pressure $P$ and volume $V$ is suddenly compressed to one-eighth of its original volume. The final pressure at constant entropy will be $.....P$.

An ideal rigid diatomic gas $(\gamma = 7/5)$ undergoes an adiabatic change. If the relation between temperature and volume is $TV^x = \text{constant}$, then the value of $x$ is:

$A$ monoatomic gas $(\gamma = 5/3)$ initially at $27^{\circ} C$ having volume $V$ is suddenly compressed to one-eighth of its original volume $(V/8)$. What is the final temperature after the compression (in $K$)?

$A$ van der Waals gas obeys the equation of state $\left(p+\frac{n^2 a}{V^2}\right)(V-n b)=n R T$. Its internal energy is given by $U=C T-\frac{n^2 a}{V}$. The equation of a quasistatic adiabat for this gas is given by