Van der Waals equation of state

The van der Waals (VDW) equation is

$p=\frac{nRT}{V-nb}-a{(\frac{n}{V})}^2$.

where:

• $p$ is the pressure

• $V$ is the volume

• $n$ is the number of moles

• $T$ is the absolute temperature

• $R$ is the Gas constant; $R=N_A{k}_B$, with $N_A$ being Avogadro constant

The VDW equation of state (EoS) takes into account two features that are absent in the Ideal Gas (EoS):

The parameter $b$ introduces somehow the repulsive behavior between pairs of molecules at short distances, it represents the minimum molar volume of the system.

whereas $a$ measures the attractive interactions between the molecules

The VDW EoS leads to a liquid-vapor equilibrium at low temperatures, with the corresponding critical point