On the Influence of the Ionization-Recombination Processes on the Hydrogen Plasma Polytropic Index

An analytical approximation for the polytropic index of a hydrogen gas has been derived. The derived expressions can be useful for theoretical work and numerical calculations. These results open the possibility of direct computation of these thermodynamic quantities, rather than interpolating from tables. Additionally, the polytropic index is graphically represented as a function of temperature and density. It is concluded that the partially ionized hydrogen plasma cannot be exactly polytropic. The calculated deviations from the monoatomic value 5/3 are significant and measurable. The present theory supposes that hydrogen molecules are completely dissociated, and this analytical result for pure hydrogen plasma can be applied for the solar chromosphere, where He ionization is negligible and H-2 dissociation is almost complete. These two conditions define the ranges of applicability of temperatures and densities. The analytical result for pure hydrogen plasma is a test example of how this approach can be extended for an arbitrary gas cocktail.