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.

$A$ $25 \times 10^{-3} \, m^3$ volume cylinder is filled with $1 \, mol$ of $O_2$ gas at room temperature $(300 \, K)$. The molecular diameter of $O_2$ is $0.3 \, nm$ and its root mean square speed is $200 \, m/s$. What is the average collision rate (per second) for an $O_2$ molecule?

If the mean free path is doubled,the pressure becomes:

There are two identical chambers,completely thermally insulated from surroundings. Both chambers have a partition wall dividing the chambers into two compartments. Compartment $1$ is filled with an ideal gas and Compartment $3$ is filled with a real gas. Compartments $2$ and $4$ are vacuum. $A$ small hole (orifice) is made in the partition walls and the gases are allowed to expand into the vacuum.
Statement $-1$: No change in the temperature of the gas takes place when an ideal gas expands in a vacuum. However,the temperature of a real gas goes down (cooling) when it expands in a vacuum.
Statement $-2$: The internal energy of an ideal gas is only kinetic. The internal energy of a real gas is kinetic as well as potential.

If the molecular radius of hydrogen gas is $0.5 \ \mathring A$,then the mean free path of hydrogen gas molecules at $0 \ ^\circ C$ temperature and $1 \ atm$ pressure is ........ $\mathring A$. (Given $k_B = 1.38 \times 10^{-23} \ J \ K^{-1}$)

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: