We have formulated a grand partition function of electrons for a stellar gas and applied it to generating an equation of state. Atomic configurations are included in the grand partition function in terms of the number of the electrons bound in the configuration and their total energy. Free electrons are included in terms of their energy levels in free phase space. The perturbation of the atomic configuration by the environments is also included in terms of an occupation probability which represents the interaction of surrounding particles on the atom. Also included is the perturbation of the energy levels of the free electrons by the environment in terms of an average energy shift. According to the theory of the grand canonical ensemble, the grand partition function of electrons is used to derive a conservation equation for the electron number, which is solved for the probability of the atomic configuration. Thermodynamic functions resulting from the atomic configurations and the free electrons can thus be expressed by means of the grand partition function in analytical forms. The resulting formulae show nonideal terms in gas pressure and internal energy, as well as in the atomic configuration probabilities, which are the result of nonideal effects due to the perturbations of the atomic configurations and the free electrons by their environments.
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