A converging equation of state of a weakly nonideal hydrogen plasma without mystery

Abstract

A detailed independent derivation of the equation of state of a weakly nonideal hydrogen plasma is presented. The impetus for this work was the demand for high accuracy of the equation of state of the solar plasma in relation to the problems of modern helioseismology, accuracy sufficient for reproducing the velocity of sound on the Sun from optical measurement results with errors not exceeding 10−4. The existing equations for the second virial coefficient in the expansion of the Helmholtz thermodynamic potential for a system of electrons and protons in powers of the activities of these particles involve certain procedures for the removal of the arising divergences that provoke questions and require independent verification. The suggested equation of state is used to qualitatively estimate the accuracy of various physical and chemical models. The speed of sound and adiabatic exponent calculated along the solar trajectory are presented for a model hydrogen plasma. The calculations were performed with the inclusion of relativistic corrections, electron degeneracy effects, radiation pressure in the plasma, Coulomb interaction in the Debye-Hückel approximation with diffraction and exchange corrections, and converging contributions of bound and scattering states.