  The pressure and internal energy of an ultracold plasma in a state of
quasi-equilibrium are evaluated using classical molecular dynamics simulations.
Coulomb collapse is avoided by modeling electron-ion interactions using an
attractive Coulomb potential with a repulsive core. We present a method to
separate the contribution of classical bound states, which form due to
recombination, from the contribution of free charges when evaluating these
thermodynamic state variables. It is found that the contribution from free
charges is independent of the choice of repulsive core length-scale when it is
sufficiently short-ranged. The partial pressure associated with the free
charges is found to closely follow that of the one-component plasma model,
reaching negative values at strong coupling, while the total system pressure
remains positive. This pseudo-potential model is also applied to
Debye-H\"{u}ckel theory to describe the weakly coupled regime.
