Analysis of the state equations of a real gas at high pressures with the virial coefficients obtained from controlled chaotic oscillations

Abstract

This paper investigates several cubic and non-cubic state equations of real gases at high pressures by using the virial coefficients estimated from chaotic oscillations with a mechanical-thermal device. The mechanical part is formed by a cylinder with a piston whose motion is limited by means of a nonlinear spring, a damper and a nonlinear control force to decouple the mechanical and thermal subsystems. To maintain the gas temperature approximately constant, a linear PI controller and a nonlinear control law which manipulates the flow rate of two heating coils inside the cylinder are added. The stability of the mechanical subsystem is analyzed through the first Lyapunov value, whose harmonic variation leads to chaotic behavior with great pressures and an almost constant temperature. The chaotic simulations for nonpolar gases are treated like experimental data to obtain an arbitrary number of virial coefficients which reproduce the state equation in a prescribed pressure range. The validity of the proposed device has been corroborated by using another alternative route to chaos and calculating the fugacity coefficient. The analytical calculations are in good agreement with the numerical simulations.