$A$ real gas behaves as an ideal gas at

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.

Calculate the mean free path and relaxation time for a gas with a mean speed $\langle v \rangle = 485 \ m/s$. Assume standard conditions $(STP)$ where the number density $n \approx 2.7 \times 10^{25} \ m^{-3}$ and molecular diameter $d = 2 \ \mathring{A}$.

The mean free path for a gas,with molecular diameter $d$ and number density $n$,can be expressed as:

$A$ 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:

Write the condition for a real gas to behave as an ideal gas.