Approximate Thermodynamics State Relations in Partially Ionized Gas Mixtures

[摘要] In practical applications, the thermodynamic state relations of partially ionized gas mixtures are usually approximated in terms of the state relations of the pure partially ionized constituent gases or materials in isolation. Such approximations are ordinarily based on an artificial partitioning or separation of the mixture into its constituent materials, with material k regarded as being confined by itself within a compartment or subvolume with volume fraction {alpha}k and possessing a fraction {beta}k of the total internal energy of the mixture. In a mixture of N materials, the quantities {alpha}k and {beta}k constitute an additional 2N--2 independent variables. The most common procedure for determining these variables, and hence the state relations for the mixture, is to require that the subvolumes all have the same temperature and pressure. This intuitively reasonable procedure is easily shown to reproduce the correct thermal and caloric state equations for a mixture of neutral (non-ionized) ideal gases. Here we wish to point out that (a) this procedure leads to incorrect state equations for a mixture of partially ionized ideal gases, whereas (b) the alternative procedure of requiring that the subvolumes all have the same temperature and free electron density reproduces the correct thermal and caloric state equations for such a mixture. These results readily generalize to the case of partially degenerate and/or relativistic electrons, to a common approximation used to represent pressure ionization effects, and to two-temperature plasmas. This suggests that equating the subvolume electron number densities or chemical potentials instead of pressures is likely to provide a more accurate approximation even in nonideal plasma mixtures.

[发布日期] 2003-12-30 [发布机构] Lawrence Livermore National Laboratory

[关键词] Approximations;Electron Density;Gases;Compartments;Thermodynamics