A gas is suddenly compressed to $1/4$ th of its original volume at normal temperature. The increase in its temperature is ....... $K$ $(\gamma = 1.5)$

An ideal monoatomic gas with pressure $P$, volume $V$ and temperature $T$ is expanded isothermally to a volume $2\, V$ and a final pressure $P_i$. If the same gas is expanded adiabatically to a volume $2\,V$, the final pressure is $P_a$ . The ratio $\frac{{{P_a}}}{{{P_i}}}$ is

When a gas expands adiabatically

One mole of an ideal gas at an initial temperature of $T\, K$ does $6 R$ joules of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is $5/3$, the final temperature of gas will be

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 $(\gamma = 1.4)$

A gas ($\gamma = 1.3)$ is enclosed in an insulated vessel fitted with insulating piston at a pressure of ${10^5}\,N/{m^2}$. On suddenly pressing the piston the volume is reduced to half the initial volume. The final pressure of the gas is