One mole of a monoatomic real gas satisfied the equation $\mathrm{p}\left(\mathrm{V}-\mathrm{b}\right)=\mathrm{R}\mathrm{T}$ where b is a constant. The relationship of interatomic potential V(r) and interatomic distance r for the gas is given by

In thermodynamics, the $\mathrm{P}-\mathrm{V}$ work done is given by $\mathrm{w}=-\int {\mathrm{dVP}}_{\mathrm{ext}}$. For a system undergoing a particular process, the work done is,

$\mathrm{w}=-\int \mathrm{dV}\left(\frac{\mathrm{RT}}{\mathrm{V}-\mathrm{b}}-\frac{\mathrm{a}}{{\mathrm{V}}^2}\right)$. This equation is applicable to a

If the distribution of molecular speeds of a gas is as per the figure shown below, then the ratio of the most probable, the average, and the root mean square speeds, respectively, is