Correlation between the Kinetic and Potential Energy of an Ionized Gas

Abstract

The thermodynamic functions of a system of free electrons and ions are calculated by the methods of classical statistical mechanics under the condition that bound-particle states with negative internal energy, e.g., atoms, are explicitly excluded from the partition function. This exclusion is found to have the following consequences: (1) The radial distribution function of electrons about ions has the form $g^{+-}\mathrm{}\left(r\right)=2\mathrm{}\pi {\left(\pi kT\right)}^{-\frac{3}{2}}\times \int 0^{\infty }\exp (-\frac{\epsilon }{\mathrm{kT}}){[\epsilon +w(r\left)\right]}^{\frac{1}{2}}d\epsilon$, where $\epsilon$ is the internal energy of an ion-electron pair and $w\left(r\right)\mathrm{}$ is a potential of average force. (2) $w\left(r\right)\mathrm{}$ is obtained as an iterative solution of the nonlinearized Poisson equation and used for calculating the system's potential energy $U$. No divergence arises and $U$ is found different from the Debye-Hückel energy $U_D$ by amounts between 5 and 10% of $U_D$. (3) The average kinetic energy at position r is found to depend on $w\left(\mathrm{r}\right)$. The total kinetic system energy per particle is found to differ from $\frac{3kT}{2}$ by about 50% of $U_D$.