Van der waals equation of state

Van der Waals (vdW) invented his equation of state about 150 year ago. This equation described the liquidgas phase transition and predicted an existence of the critical point. The vdW equation of state remains today the most familiar and one of the most successful model in molecular physics. It is presented in all text books on statistical physics. However, several important questions concerning the vdW model had no answers. Only very recently these questions were discussed in the literature, and several important extensions of the vdW equation of state were developed. These new results presented in this article correspond to the grand canonical ensemble formulation, the effects of quantum statistics, and applications of the vdW model to nuclear matter taking into account Fermi statistics for interacting protons and neutrons. A special attention is also paid to the particle number fluctuations in a vicinity of the vdW critical point. Published under an exclusive license by AIP Publishing.