The derivation of equations of state for fluid phases of a partially ionized gas or plasma is addressed from a fundamental point of view. The results of the Thomas-Fermi model always yield pressures which are less than or equal to that of an ideal Fermi gas. On the other hand, the spherical cellular model shows significant "overpressure" relative to the ideal Fermi gas in certain regions of low density and low temperature. This effect is studied in considerable detail. A nonthermodynamic region, more or less overlapping the regions of overpressure, is found. It is characterized by a negative specific heat at constant volume. An independent electron model within a Z -electron cell is employed. The inadequacy of the wave function in the low-density, low-temperature nonthermodynamic region is shown to be the cause of this overpressure. Numerical examples of the theory for several elements (Li, N, Al, K, and Er) are reported. These results reduce in various limits of temperature and density to the expected behavior, except in the aforementioned region.
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