$A$ mixture of gases at $STP$ for which $\gamma = 1.5$ is suddenly compressed to $\frac{1}{9}$th of its original volume. The final temperature of the mixture is .......... $^{\circ}C$.

$A$ cylinder with a movable piston contains $3 \ moles$ of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator,and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?

$A$ 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.

When a gas expands adiabatically,its volume is doubled while its absolute temperature is decreased by a factor of $2$. The value of the adiabatic constant $\gamma$ is

When an ideal diatomic gas undergoes adiabatic expansion,if the increase in its volume is $0.5 \%$,then the change in the pressure of the gas is

In the $P-V$ diagram shown,there are two adiabatic parts of the same gas intersecting two isothermals at $T_1$ and $T_2$. The ratio $\left(\frac{V_b}{V_a}\right)$ is equal to