The value of critical temperature in terms of van der Waals' constants $a$ and $b$ is given by

We have $0.5 \, g$ of hydrogen gas in a cubic chamber of size $3 \, cm$ kept at $NTP$. The gas in the chamber is compressed keeping the temperature constant until a final pressure of $100 \, atm$ is reached. Is one justified in assuming the ideal gas law in the final state? (Hydrogen molecules can be considered as spheres of radius $1 \, \mathring{A}$).

At a temperature of $314 \,K$ and a pressure of $100 \,kPa$, the speed of sound in a gas is $1380 \,ms^{-1}$. The radius of each gas molecule is $0.5 \,Å$. The frequency of sound at which the wavelength of the sound wave in the gas becomes equal to the mean free path of the gas molecules is (Boltzmann constant $k = 1.38 \times 10^{-23} \,JK^{-1}$):

In a dilute gas at pressure $P$ and temperature $T$,the mean time between successive collisions of a molecule varies with $T$ as

What is mean free path? Derive the equation for the mean free path.

Under what conditions does a real gas obey the relation $PV = RT$?