Mean free path of molecules in a polyatomic gas is independent of

The mean free path of molecules of a certain gas at $STP$ is $1500\,d$,where $d$ is the diameter of the gas molecules. While maintaining the standard pressure,the mean free path of the molecules at $373\,K$ is approximately $..........\,d$

Calculate the ratio of the mean free paths of the molecules of two gases having molecular diameters $1\,\mathring{A}$ and $2\,\mathring{A}$. The gases may be considered under identical conditions of temperature,pressure,and volume.

$A$ system consists of two types of gas molecules $A$ and $B$ having the same number density $2 \times 10^{25} \, /m^3$. The diameters of $A$ and $B$ are $10 \, \mathring{A}$ and $5 \, \mathring{A}$ respectively. They undergo collisions at room temperature. The ratio of the average distance covered by molecule $A$ to that of $B$ between two successive collisions is $..... \times 10^{-2}$.

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.

An ideal gas is enclosed in a cylinder at a pressure of $2 \, atm$ and a temperature of $300 \, K$. The mean time between two successive collisions is $6 \times 10^{-8} \, s$. If the pressure is doubled and the temperature is increased to $500 \, K$,the mean time between two successive collisions will be close to: