The $P-V$ graph of an ideal gas cycle is shown. The adiabatic process is described by the region

$A$ gas at $N.T.P.$ is suddenly compressed to one-fourth of its original volume. If $\gamma = 1.5$,then the final pressure is

In an adiabatic process,the density of a diatomic gas becomes $32$ times its initial value. The final pressure of the gas is found to be $n$ times the initial pressure. The value of $n$ is

$A$ diatomic gas $\left(\gamma = \frac{7}{5}\right)$ is compressed adiabatically to volume $\frac{V_0}{32}$,where $V_0$ is its initial volume. The initial temperature of the gas is $T_i$ in Kelvin and the final temperature is $xT_i$ in Kelvin. The value of $x$ 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.

The mean kinetic energy of monoatomic gas molecules under standard conditions is $\langle E_1 \rangle$. If the gas is compressed adiabatically $8$ times to its initial volume,the mean kinetic energy of gas molecules changes to $\langle E_2 \rangle$. The ratio $\frac{\langle E_2 \rangle}{\langle E_1 \rangle}$ is