Van der Waals equation of state

The van der Waals equation of state 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 van der Waals equation of state takes into account two features that are absent in the ideal Gas equation of state:

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 van der Waals equation of state leads to a liquid-vapor equilibrium at low temperatures, with the corresponding critical point.

Critical point

The critical point for the van der Waals equation of state can be found at

$T_c=\frac{8a}{27bR}$,

$p_c=\frac{a}{27b^2}$

and at

$v_c=3b$.

References

1. J. D. van der Waals "On the Continuity of the Gaseous and Liquid States", Dover Publications ISBN: 0486495930
2. Luis Gonzalez MacDowell and Peter Virnau "El integrante lazo de Van der Waals", Anales de la Real Sociedad Española de Química 101 #1 pp. 19-30 (2005)