How does the mean free path of a gas depend on temperature?

$A$ container is divided into two equal parts $I$ and $II$ by a partition with a small hole of diameter $d$. The two parts are filled with the same ideal gas,but held at temperatures $T_{I} = 150 \, K$ and $T_{II} = 300 \, K$ by connecting them to heat reservoirs. Let $\lambda_{I}$ and $\lambda_{II}$ be the mean free paths of the gas particles in the two parts,such that $d \gg \lambda_{I}$ and $d \gg \lambda_{II}$. Then,the ratio $\lambda_{I} / \lambda_{II}$ is close to:

If the radius of an $O_{2}$ molecule is $40 \; \mathring{A}$,$T = 27^{\circ}C$,and $P = 1 \; \text{atm}$,find the relaxation time.

The diameter of an oxygen molecule is $2.94 \times 10^{-10} \ m$. The van der Waals gas constant '$b$' in $m^3/mol$ is:

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.

The mean free path of a molecule of $He$ gas is $\alpha$. Its mean free path along any arbitrary coordinate axis will be ...........