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Van der Waals – Maxwell Equation

As particles in the van der Waals model are considered as hard spheres. Their configurational phase space can be acknowledged and is regarded to be less than the size of the volume of the system. The volume occupied by particles, N, is denoted by its population and size of each sphere. The residual potential energy, U, in the system can be equated to (V-Nb)N to reflect attraction in the configurational phase space. A mean of this value approximates the behaviour. This expression is consistent for high density interactions. At high density, hard spheres are in closer proximity and hence attractions to each other are stronger.

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This is expressed as: . Hence the mean-field approximation can be expressed by the following: . It is found that the van der Waals equation is corresponds to the number of particles, N, temperature, T, and the Boltzmann’s constant, kB. Although this equation can approximate behaviour of gases and liquids independently. At the point of coexistence between the two phases, it finds difficulty in expressing its true physical nature. In closer analysis, graphically it shows characteristics opposing laws of thermodynamics. The greatest sign of this characteristic is the existence of three different volumes at a same amount of pressure. As seen in Figure. 

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