$A$ gas expands adiabatically at constant pressure such that its temperature $T \propto \frac{1}{\sqrt{V}}$. The value of $C_P/C_V$ for the gas is:

$A$ motor-car tyre has a pressure of $2\,atm$ at $27\,^{\circ}C$. It suddenly bursts. If $\gamma = (C_p/C_v) = 1.4$ for air,find the resulting temperature.

If $\gamma$ denotes the ratio of two specific heats of a gas, the ratio of the slopes of adiabatic and isothermal $PV$ curves at their point of intersection is:

The internal energy of a gas will increase when it

$P-V$ plots for two gases during adiabatic processes are shown in the figure. Plots $1$ and $2$ should correspond respectively to

$A$ gas at $N.T.P.$ is suddenly compressed to $\left(\frac{1}{4}\right)$ of its original volume. What will be the final pressure? (Given: $\gamma = \text{ratio of specific heats} = \frac{3}{2}$,$P = \text{original pressure}$)