Adiabatic lapse rate of real gases

TL;DR

This paper derives a formula for the dry adiabatic lapse rate of atmospheres composed of real gases using two-parameter cubic and non-cubic equations of state, improving atmospheric modeling accuracy.

Contribution

It introduces a new formula for the adiabatic lapse rate of real gases based on adiabatic curves computed for molecules with various degrees of freedom, applicable to complex equations of state.

Findings

Better approximation of Titan's troposphere lapse rate compared to virial expansion.

Applicable to gases described by cubic and non-cubic equations of state.

Provides a unified method to compute adiabatic curves for real gases.

Abstract

We derive a formula for the dry adiabatic lapse rate of atmospheres composed of real gases. We restrict our study to those described by a family of two-parameter cubic equations of state and the recent Guevara non-cubic equation. Since our formula depends on the adiabatic curves, we compute them all at once, considering molecules that can move, rotate, and vibrate, for any equation of state. To illustrate our results, we estimate the lapse rate of the troposphere of Titan, obtaining a better approximation to the observed data in some instances, when compared to the estimation provided by the virial expansion up to third order.