Adiabatic lapse rate estimation using a van der Waals-type equation of state

TL;DR

This paper improves the estimation of planetary atmospheric lapse rates by revisiting van der Waals-type equations of state, incorporating molecular degrees of freedom, and demonstrating enhanced accuracy over classical models.

Contribution

It introduces a generalized van der Waals-type EOS with a temperature-dependent parameter, improving adiabatic lapse rate predictions for planetary atmospheres.

Findings

Enhanced lapse rate estimates for Titan and Venus

Better agreement with observed atmospheric data

Generalized EOS captures critical thermodynamic behavior

Abstract

We revisit a family of temperature-dependent van der Waals-type equations of state (EOS) to improve the estimation of the adiabatic lapse rate in planetary atmospheres. These EOS generalize the classical van der Waals and Berthelot models by introducing a single parameter that modulates the temperature dependence of intermolecular interactions. We analyze their thermodynamic properties, including critical behavior, spinodal and coexistence curves, and entropy. The adiabatic curves are computed by incorporating explicitly the contribution of molecular vibrational and rotational degrees of freedom. Using a generalized expression for the adiabatic lapse rate, we estimate the adiabatic lapse rate in the troposphere of Titan and Venus. Our results show that the van der Waals-type EOS reproduce observed lapse rates more accurately than the van der Waals EOS.