  An initial theoretical attempt to explain the observed decrease of the
polytropic/adiabatic index $\gamma$ in the solar corona has been accomplished.
The chemical reactions of the ionization-recombination processes in local
thermodynamic equilibrium (LTE) of a solar plasma cocktail containing heavy
elements are found to cause $1.1 < \gamma \leq 5/3$ in the quiet solar
atmosphere. It is also shown that the quiet solar atmosphere is in LTE
justifying this theoretical study. This result is obtained by numerically
solving the Saha equation and subsequently using a newly derived equation for
calculation of the polytropic index from thermodynamic partial derivatives of
the enthalpy and pressure with respect to density and temperature. In addition,
a comparison between calculated in this way polytropic index and measured from
spectroscopic observations of propagating slow magneto-hydrodynamics (MHD)
waves in coronal loops shows that LTE ionization accounts for very small part
of the observed decrease of $\gamma$ meaning that the solar plasma in the
active region is not in LTE as expected. However, the observed dependency of
higher polytropic index at higher temperatures is confirmed by the current
theoretical approach. It is concluded that to account for the polytropic index
decrease in the active regions of the solar corona, it is necessary kinetic
non-LTE ionization calculations to be performed.
