If the molecular radius of hydrogen gas is $0.5 \ \mathring A$,then the mean free path of hydrogen gas molecules at $0 \ ^\circ C$ temperature and $1 \ atm$ pressure is ........ $\mathring A$. (Given $k_B = 1.38 \times 10^{-23} \ J \ K^{-1}$)

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

An ideal gas in a closed container is slowly heated. As its temperature increases,which of the following statements are true?
$(A)$ The mean free path of the molecules decreases.
$(B)$ The mean collision time between the molecules decreases.
$(C)$ The mean free path remains unchanged.
$(D)$ The mean collision time remains unchanged.

What is mean free path?

Statement-$1$: Real gas approaches ideal gas behaviour for low pressures and high temperatures.
Statement-$2$: At low pressure,the density of a gas is very low.

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion,the average time of collision between molecules increases as $V^q$,where $V$ is the volume of the gas. The value of $q$ is $\left( \gamma = \frac{C_P}{C_V} \right)$.