Equation of state for a partially ionized gas

The derivation of equations of state for fluid phases of a partially ionized gas or plasma is addressed from a fundamental point of view. First, a cubic cellular model and then a spherical cellular model is deduced far the hot curve limit (or ideal Fermi gas). Next the Coulomb interactions are added to the spherical model for general ionic charge Z. A numerical example of the theory for the case of hydrogen is reported, and it reduces in various limits of temperature and density to the expected behavior. It displays an electron, localization-delocalization phase transition of the normal liquid-gas character.