$A$ fixed amount of nitrogen gas ($1$ mole) is taken and subjected to pressure and temperature variations. The experiment is performed at high pressures and various temperatures. The results obtained are shown in the figure. The correct variation of $PV/RT$ with $P$ for nitrogen gas at high temperatures will be exhibited by:

Given below are two statements:
Statement $(I)$: The mean free path of gas molecules is inversely proportional to the square of the molecular diameter.
Statement $(II)$: The average kinetic energy of gas molecules is directly proportional to the absolute temperature of the gas.
In the light of the above statements,choose the correct answer from the options given below:

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

The mean free path for a gas at temperature $300 \ K$ and pressure $600 \ \text{torr}$ is $10^{-7} \ m$. The mean free path of the gas at a temperature $400 \ K$ and pressure $200 \ \text{torr}$ will be

Under which of the following conditions is the law $PV = RT$ obeyed most closely by a real gas?

$A$ $25 \times 10^{-3} \, m^3$ 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?