Thermodynamic Properties of Nonideal Gases. II. The Strongly Ionized Gas

The thermodynamic equilibrium properties of strongly ionized multicomponent gas mixtures are investigated by application of the free-energy minimization method. For high-temperature regions where the Coulomb interaction is the dominant perturbation, the many-body partition function is developed from quantum cluster-expansion theory. The Coulomb free energy is given as the sum of the first- and second-order direct-interaction terms, plus the first three exchange-interaction terms. All five terms are exact in the classical limit, i. e., where Maxwell-Boltzmann statistics apply. The direct terms are correct for weak electron degeneracy and include wave-mechanical effects, while the first-order exchange term is exact for all degrees of degeneracy. The theoretical model is applied to multicomponent mixtures of hydrogen and of helium in the temperature range 50-2000 eV. The combination of the ring term plus higher-order terms significantly extends the region of applicability of the model over a classical electrostatic model. Specifically, electron degeneracy, the short-range cutoff in the ring term, and the three-rung ladder (second-order direct) term all operate to produce much less divergent thermodynamic results at a given density and temperature. First-order exchange is important even at moderate values of the electron-degeneracy parameter. The thermodynamic results indicate that evaluation of the exact quantum-mechanical ring term is essential for wider application of the perturbation-expansion theory, as is the development of a second-order exchange term for arbitrary degeneracy.