Abstract
As experimental measurements of thermodynamic properties have improved in accuracy, to five or six figures, over the decades, cubic equations that are widely used for modern thermodynamic fluid property data banks require ever-increasing numbers of terms with more fitted parameters. Functional forms with continuity for Gibbs density surface ρ(p,T) which accommodate a critical-point singularity are fundamentally inappropriate in the vicinity of the critical temperature (Tc) and pressure (pc) and in the supercritical density mid-range between gas- and liquid-like states. A mesophase, confined within percolation transition loci that bound the gas- and liquid-state by third-order discontinuities in derivatives of the Gibbs energy, has been identified. There is no critical-point singularity at Tc on Gibbs density surface and no continuity of gas and liquid. When appropriate functional forms are used for each state separately, we find that the mesophase pressure functions are linear. The negative and positive deviations, for both gas and liquid states, on either side of the mesophase, are accurately represented by three or four-term virial expansions. All gaseous states require only known virial coefficients, and physical constants belonging to the fluid, i.e., Boyle temperature (TB), critical temperature (Tc), critical pressure (pc) and coexisting densities of gas (ρcG) and liquid (ρcL) along the critical isotherm. A notable finding for simple fluids is that for all gaseous states below TB, the contribution of the fourth virial term is negligible within experimental uncertainty. Use may be made of a symmetry between gas and liquid states in the state function rigidity (dp/dρ)T to specify lower-order liquid-state coefficients. Preliminary results for selected isotherms and isochores are presented for the exemplary fluids, CO2, argon, water and SF6, with focus on the supercritical mesophase and critical region.
Highlights
There is a long history and an extensive literature of cubic equations-of-state, going back 140 years, from van der Waals renowned two-term equation for Andrew’s original p-V-T data on carbon dioxide [1], to current research and compilations with hundreds of terms and parameters
From the foregoing analysis, we conclude that the pressure equation-of-state, and all other state functions, can be expressed inequation-of-state, terms of a few physical constants
Fromthermodynamic the foregoing analysis, we conclude that the pressure and all other belonging to the fluid, and coefficients in virial expansions
Summary
There is a long history and an extensive literature of cubic equations-of-state, going back 140 years, from van der Waals renowned two-term equation for Andrew’s original p-V-T data on carbon dioxide [1], to current research and compilations with hundreds of terms and parameters. In the case of pressure, the negative and positive adjacent deviations for liquid and gas on othereither isothermal thermodynamic state functions inrequire the mesophase are linear functions of density. The parameterizations only physical constants belonging to the In the case of pressure, the negative and positive adjacent deviations for liquid and gas on either side are specific fluid, Boyle temperature (TB), critical temperature (TC), and coexisting densities along the quadratic. We investigate equations-of-state for gas, liquid and mesophase separately, each of which, in experimental properties a pure fluid over the whole specific range oftoequilibrium existence. Here,Comparisons we investigate formade gas, via liquid and mesophase separately, of which, with equations-of-state experimental data are the NIST thermo-physical databankeach [3]. Accuracy, and provide a foremost criteria for testing the alternative description to van der Waals underlying science of critical and supercritical behavior of fluids as described in references [4,5,6,7,8,9]
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