Estimation of the virial coefficients by means of chaotic oscillations of pressure and density: Application to quantum gases with cubic equations of state

This paper analyzes how to determine the virial coefficients B and C of real gases by using a theoretical device whose pressures and densities oscillate in chaotic regime. The device is formed by a valve, a pressure controller, a pressure probe and a gas accumulator, for which the thermodynamic model has been derived from the force-mass-energy balances. This model allows keeping the gas temperature almost constant with chaotic oscillations in the inlet to the accumulator. The chaotic data are used to obtain variability in the pressures and densities, so that they can be used as experimental values from which the virial coefficients are estimated. For this purpose, several cubic and high precision equations of state for polar and non-polar gases and mixtures are used. In particular, the virial coefficient B for dry air is estimated by using high precision state equations, whereas, the virial coefficients B and C are also estimated for quantum gases (He4, He3 H2, D2, Ne) by using several modified cubic equations of state at moderate and high pressures. Furthermore, the values for the virial coefficient B obtained from numerical simulations are used to estimate the intermolecular potential and the radial distribution function. The results are in good agreement with the currently known experimental data for virial coefficients published in the literature.