Application of the Gert Model to the Derivation of Continuum Barometric Equations and Their Experimental Verification
Year: 2026
Type: article
Abstract: This paper focuses on the practical application of the theoretical principles of extended thermodynamics and the Gert model, previously formulated in the authors' monograph, to resolve a fundamental problem in continuum mechanics: describing the macroscopic structure of a gas column within an external potential field. The paper presents an original analytical derivation of the barometric equation, completely bypassing the classical isotropic assumption of altitude-independent temperature. Based on the modified thermodynamic equilibrium principle (the Third Law in the Gert model), a mathematical simulation of the medium's polytropic distribution is executed. The calculations are carried out using the equivalent number of degrees of freedom as a variable function of state that accounts for non-thermal intermolecular interaction mechanisms during the pre-relaxation stage. The resulting differential equations for density and pressure rigorously substantiate the existence of a distinct and finite spatial boundary of the continuous medium, eliminating the mathematical paradox of the infinite exponential tail inherent in classical Laplace equations. To validate the derived patterns, they were verified against the empirical dataset of GOST 4401-81 (Standard Atmosphere). The comparison demonstrated unprecedentedly high accuracy (the deviation of the calculated profile from the experimental data across the entire troposphere remains below 1%), fully confirming the validity of the Gert model's applied framework and opening new avenues for simulating non-equilibrium gas-dynamic systems. This is the English version of the article previously published in Russian
Author: Gert, Edgar
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225319973