The

*van der Waals equation* is a cubic

equation of state, proposed by Dutch physicist

Johannes van der Waals in 1873, quantitatively describing the relationship between pressure, volume and temperature of a substance.

The *van der Waals equation* was a historic landmark since the derivation of the Ideal Gas Law, because the model included quantitative terms for the volumes of the molecules, and the attractive/repulsive forces between them. Also, the model qualitatively explains the coexistence of liquid and vapor phases, and the occurence of the critical state.

Van der Waals received the Nobel
Prize in 1910 for his research on the gaseous and liquid states of matter. The *van der Waals equation* is the basis for many equations of state that are currently in use.

The *van der Waals equation* is given as:

P = nRT / (V-nb) - an^{2}/V^{2}

where P= Pressure, V= Volume, T= Absolute Temperature, n= number of moles, a= attraction parameter, b= repulsion parameter (= *effective molecular volume*).

For a=b=0, the *van der Waals equation* reduces to the Ideal Gas Law.

Also note that the *van de Waals equation* can be written in a virial form:

Z = 1 +(b - a/RT)(1/V) + (b/V)^{2} + (b/V)^{3} + ...