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.

Consider an ideal gas at pressure $p$, volume $V$ and temperature $T$. The mean free path for molecules of the gas is $L$. If the radius of gas molecules, as well as pressure, volume and temperature of the gas are doubled, then the mean free path will be

Ten small planes are flying at a speed of $150 \ km/h$ in total darkness in an air space that is $20 \times 20 \times 1.5 \ km^3$ in volume. You are in one of the planes, flying at random within this space with no way of knowing where the other planes are. On the average, about how long a time will elapse between near collisions with your plane? Assume for this rough computation that a safety region around the plane can be approximated by a sphere of radius $10 \ m$.

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.

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.

State the differences between an ideal gas and a real gas.