Prediction of the liquid–vapor equilibrium pressure using the quasi-Gaussian entropy theory

Abstract

We derived a method to evaluate the liquid-vapor equilibrium pressure, with high accuracy over a large range of temperature, using the quasi-Gaussian entropy theory. The final expression that we obtain for the equilibrium pressure as a function of the temperature can be considered as a very accurate approximate solution of the Clausius-Clapeyron equation. The method was applied to water, methanol and mercury, and was compared to two usual approximations of the Clausius-Clapeyron equation.

Role of attractive methane-water interactions in the potential of mean force between methane molecules in water

“…53,54 A gamma distribution is qualitatively satisfactory here but not as accurate as the Gumbel distribution. As does the present work, those previous studies emphasized realizability in free energy models: free energy evaluations can benefit from restriction to legitimate probability distributions.…”

“…A gamma distribution of interaction energies has been proposed in a different statistical thermodynamic setting for closing and integrating a differential equation for an entropic equation of state. 53,54 A gamma distribution is qualitatively satisfactory here but not as accurate as the Gumbel distribution. As does the present work, those previous studies emphasized realizability in free energy models: free energy evaluations can benefit from restriction to legitimate probability distributions.…”

“…A distinction from that preceding work 53,54 is that we study here the distribution of an intensive characteristic, a possibility noted before. 53 Then the central limit theorem is not available to force the unconditioned distribution toward a normal (gaussian) form.…”

Clausius–Clapeyron equation and saturation vapour pressure: simple theory reconciled with practice

“…none of the above referenced books contains it). Even when it is mentioned, it is still presented along with (1), which may again be characterized as the best known approximation to calculate the liquid-vapour equilibrium pressure [9].…”

On the use of the quasi-Gaussian entropy theory in noncanonical ensembles. I. Prediction of temperature dependence of thermodynamic properties

“…Hence up to now this theory has been used only in an approximate way to describe temperature dependence in noncanonical ensemble conditions. 5,6 In this paper we will describe how to extend the quasi-Gaussian entropy theory to obtain the temperature dependence of the thermodynamic functions in the isothermalisobaric and grand canonical ensemble in an exact way. This is accomplished by using a different reference state and distributions of full thermodynamic properties ͑internal energy, enthalpy͒ instead of excess ones.…”