On the ionization equilibrium of hot hydrogen plasma and thermodynamic-consistency of formulating finite internal partition functions

TL;DR

This paper investigates the thermodynamic consistency of finite internal partition functions in nonideal hydrogen plasma, identifying inaccuracies in existing formulations and proposing a new, more accurate approach that improves understanding and modeling of plasma ionization equilibrium.

Contribution

It introduces a criterion for the separability of the configurational free energy and presents a consistent formulation for finite internal partition functions in hydrogen plasma.

Findings

Identifies inaccuracies in existing formulations of IPFs

Proposes a new criterion for free energy separability

Demonstrates the effectiveness of the new formulation with an example

Abstract

The problem of formulating a thermodynamically-consistent finite internal partition function (IPF) in nonideal hydrogen plasma systems is investigated and analyzed within the chemical picture revealing inaccuracies and inconsistencies buried in widely used formulations in the literature. The analysis carried out here, though performed for the simplest case of pure nonideal hydrogen plasma, it shows all specific features of the problem and is extendable to the general case of a complex multi-component plasma mixture. A criterion for the separability of the configurational component of the free energy is presented and an accurate and consistent formulation of the problem is introduced. The presented criterion and the introduced consistent formulation of the problem clear ambiguities in other formulations in the literature and provide a better understanding of the problem. An illustrative example is worked out showing simplicity and effectiveness of the proposed consistent formulation and the importance of terms, essential for thermodynamic consistency, which are commonly neglected by other authors in the literature.