For the given concentration,if the ratio of the diameters of the molecules of two gases is $1: 2$,then the ratio of their mean free paths is

$A$ molecule is travelling in air at $300 \, K$ and $1 \, atm$, and the radius of the molecule is $0.6 \times 10^{-10} \, m$. Calculate the approximate mean free path of the molecule. (The number density is $2.44 \times 10^{25} \, \text{molecules}/m^3$)

The change in volume $V$ with respect to an increase in pressure $P$ has been shown in the figure for a non-ideal gas at four different temperatures ${T_1}, {T_2}, {T_3}$ and ${T_4}$. The critical temperature of the gas is

For a van der Waals gas,if $P_c, V_c$,and $T_c$ are the critical pressure,volume,and temperature respectively,then the value of $P_cV_c/T_c$ is:

The mean free path $\ell$ for a gas molecule depends upon the diameter $d$ of the molecule as:

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 $10 \ m$.