Equation of state based on the first principles

TL;DR

This paper introduces a new first-principles-based equation of state for arbitrary media, utilizing a generalized virial theorem and a nonlinear equation for potential energy, offering an alternative to traditional models.

Contribution

It presents a novel analytical EOS derived solely from the first law of thermodynamics and a generalized virial theorem, applicable to any medium.

Findings

Provides a closed-form analytical EOS for arbitrary media.

Introduces a nonlinear Riemann-Hopf type equation for potential energy.

Offers an alternative to the classical Mie-Grüneisen EOS.

Abstract

An alternative to the well-known complete form of the Mie-Gr\"uneisen equation of state (EOS) for water is suggested. A closed analytical description of the self-consistent EOS for an arbitrary medium based only on the first law of thermodynamics and on a new form of virial theorem is obtained. This form of the virial theorem (allowing a variable power-law exponent of the particles interaction potential) is a result of the generalization of the known method of similarity (Feynman et al., 1949). In the new EOS, the description of the internal potential energy as a solution of a nonlinear Riemann-Hopf type equation is proposed.