Van der Waals equation of state

The van der Waals (VDW) equation is

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

where:

• $p$ is the pressure

• $V$ is the volume

• $n$ is the number of moles

• $T$ is the absolute temperature

• Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R } is the Gas constant; Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R = N_A k_B } , with Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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