Two gases-argon (atomic radius $0.07 \; nm$,atomic weight $40$) and xenon (atomic radius $0.1 \; nm$,atomic weight $140$) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to:

$Assertion:$ Mean free path of a gas molecule varies inversely as the density of the gas.
$Reason:$ Mean free path varies inversely as the pressure of the gas.

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion,the average time of collision between molecules increases as $V^q$,where $V$ is the volume of the gas. The value of $q$ is $\left( \gamma = \frac{C_P}{C_V} \right)$.

If the pressure of a gas in a closed container is reduced,the mean free path of the molecules will ......

$A$ fixed amount of nitrogen gas ($1$ mole) is taken and subjected to pressure and temperature variations. The experiment is performed at high pressures and various temperatures. The results obtained are shown in the figure. The correct variation of $PV/RT$ with $P$ for nitrogen gas at high temperatures will be exhibited by:

Statement-$1$: Real gas approaches ideal gas behaviour for low pressures and high temperatures.
Statement-$2$: At low pressure,the density of a gas is very low.