The mean free path of molecules of a certain gas at $STP$ is $1500\,d$,where $d$ is the diameter of the gas molecules. While maintaining the standard pressure,the mean free path of the molecules at $373\,K$ is approximately $..........\,d$

Calculate the value of mean free path $(\lambda)$ for oxygen molecules at temperature $27^{\circ} C$ and pressure $1.01 \times 10^{5} Pa$. Assume the molecular diameter $d = 0.3 nm$ and the gas is ideal. Given Boltzmann constant $k = 1.38 \times 10^{-23} J K^{-1}$. (Result in $nm$)

In the adjoining figure,various isothermals are shown for a real gas. Then

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

If $n$ is the number density and $d$ is the diameter of the molecule,then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

The internal energy of real gases is determined by which of the following?