  {\bf Context.} Numerical models of the evolution of interstellar and
integalactic plasmas often assume that the adiabatic parameter $\gamma$ (the
ratio of the specific heats) is constant (5/3 in monoatomic plasmas). However,
$\gamma$ is determined by the total internal energy of the plasma, which
depends on the ionic and excitation state of the plasma. Hence, the adiabatic
parameter may not be constant across the range of temperatures available in the
interstellar medium. {\bf Aims.} We aim to carry out detailed simulations of
the thermal evolution of plasmas with Maxwell-Boltzmann and non-thermal
($\kappa$ and $n$) electron distributions in order to determine the temperature
variability of the total internal energy and of the adiabatic parameter. {\bf
Methods.} The plasma, composed of H, He, C, N, O, Ne, Mg, Si, S, and Fe atoms
and ions, evolves under collisional ionization equilibrium conditions, from an
initial temperature of $10^9$ K. The calculations include electron impact
ionization, radiative and dielectronic recombinations and line excitation. The
ionization structure was calculated (...) using the Gauss elimination method
with scaled partial pivoting. Numerical integrations (...) were carried out
using the double-exponential over a semi-finite interval method. In both
methods a precision of $10^{-15}$ is adopted. {\bf Results.} The total internal
energy of the plasma is mainly dominated by the ionization energy for
temperatures lower than $8\times 10^4$ K with the excitation energy having a
contribution of less than one percent. In thermal and non-thermal plasmas
composed of H, He, and metals, the adiabatic parameter evolution is determined
by the H and He ionizations leading to a profile in general having three
transitions. However, for $\kappa$ distributed plasmas these three transitions
are not observed for $\kappa<15$ (...). In general, $\gamma$ varies from 1.01
to 5/3.
