Gibbs Free Energy Equation of State for Solid Methane from 21 to 300 K and up to 5000 MPa

Abstract

A Gibbs free energy equation of state (EoS) for phase I of solid methane has been developed with an original functional form. The EoS has a validity range from 21 to 300 K and up to 5000 MPa. The EoS parameters have been regressed on the literature data of molar volume, isothermal compressibility, thermal expansion, and isobaric and isochoric heat capacity. To the knowledge of the authors, this EoS is the most complete published model for phase I of solid methane in terms of the number of data of different thermodynamic properties used for the regression of the parameters and extension of the temperature and pressure validity range. The EoS represents the thermodynamic data within their estimated experimental uncertainty, and it maintains a physically correct behavior when extrapolated to high temperatures and pressures. The developed EoS for solid methane has been coupled with the reference equation of state for the fluid phases developed by Setzmann and Wagner in 1991 for calculating the melting and sublimation curves, and the predictions are in good agreement with the available data.

Gibbs Free Energy Equation of State for Phase I of Solid Benzene from 15 to 488 K and up to 1165 MPa

“…The development of the Gibbs free energy equation of state for phase I of solid benzene follows the analytical procedure shown by Stringari et al 71 for phase I of solid methane. The expression for the Gibbs free energy is obtained by integration of the equations for the molar volume, v s (p, T), and isobaric heat capacity, c p s (T):…”

“…where A, B, C, D, E, F, G, H, I, J, and L are parameters. Equations 2 and 3 have been developed by Stringari et al 71 and selected among different trial functional forms, following two criteria: 1. A functional form that results in an analytical expression when integrated with respect to temperature and pressure; 2.…”

“…A simple form with a minimum number of parameters for representing the temperature and pressure dependence of the experimental data maintaining at the same time a physically correct behavior in the temperature and pressure regions where data are scarce or absent. The expression of the molar volume is the same as that adopted in the work of Stringari et al 71 Nevertheless, in this work, the parameters C and F have been set equal to zero.…”

“…With respect to the equation for the isobaric heat capacity adopted in the work of Stringari et al, 71 eq 3 presents the supplementary term LT 2 , necessary for obtaining a better representation of the heat capacity data of benzene.…”

“…The development of the Gibbs free energy equation of state for phase I of solid benzene follows the analytical procedure shown by Stringari et al for phase I of solid methane.…”