If the volume of the gas containing $n$ number of molecules is $V,$ then the pressure will decrease due to the force of intermolecular attraction in the proportion:

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.

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:

How does the mean free path vary with the number density of a gas?

The mean free path of a molecule of diameter $5\times10^{-10} \ m$ at the temperature $41^{\circ}C$ and pressure $1.38\times10^{5} \ Pa$ is given as . . . . . . $m$. (Given $k_{B}=1.38\times10^{-23} \ J/K$).

Calculate the value of mean free path $(\lambda)$ for oxygen molecules at temperature $27^{\circ} C$ and pressure $1.01 \times 10^{5} Pa$. Assume the molecular diameter $d = 0.3 nm$ and the gas is ideal. Given Boltzmann constant $k = 1.38 \times 10^{-23} J K^{-1}$. (Result in $nm$)