Past exam of the physics B course of the University of Cambridge / 2017 / Paper 2 / Section C / C11 / Isotherms and excluded volume / Solution

For the given one-mole model,At fixed positive temperature its isotherm is an ideal-gas hyperbola shifted right by $b$: pressure diverges as $V\to b^{+}$ and tends to zero as $V\to \infty$. Higher temperatures give higher pressure at any fixed allowed volume.

For positive $b$, the volume $V-b$ is the effective volume available to molecular motion. Thus $b$ describes excluded-volume repulsion or an effective incompressible molecular core. It is a molar volume in this one-mole equation, not necessarily the literal sum of molecular geometric volume. Setting $b=0$ recovers the ideal gas law. No attractive-energy term is included.