A real gas at a very high pressure occupies

When the pressure is high, volume would be small. So, excluded volume ‘b’ cannot be ignored. But as the pressure is high, the quantity $\frac{\mathrm{a}}{{\mathrm{V}}^2}$ may be neglected in comparison with P. So the van der Waals equation reduces to

$$\begin{gathered} \mathrm{P}\left(\mathrm{V}-\mathrm{b}\right)=\mathrm{RT} \\ \mathrm{P}\left(\mathrm{V}-\mathrm{Pb}\right)=\mathrm{RT} \\ \mathrm{V}=\left(\frac{\mathrm{RT}}{\mathrm{P}}+\mathrm{b}\right) \\ \mathrm{i}.\mathrm{e}., {\mathrm{V}}_{\mathrm{real}} = {\mathrm{V}}_{\mathrm{ideal}} + \mathrm{b} \\ \therefore {\mathrm{V}}_{\mathrm{real}} > {\mathrm{V}}_{\mathrm{ideal}} \end{gathered}$$