Adiabatic lapse rate of non-ideal gases: The role of molecular interactions and vibrations

Abstract

We report a formula for the dry adiabatic lapse rate that depends on the compressibility factor and the adiabatic curves. Then, to take into account the non-ideal behavior of the gases, we consider molecules that can move, rotate, and vibrate and the information of molecular interactions through the virial coefficients. We deduce the compressibility factor in its virial expansion form and the adiabatic curves within the virial expansion up to any order. With this information and to illustrate the mentioned formula, we write the lapse rate for the ideal gas, and the virial expansion up to the second and third coefficient cases. To figure out the role of the virial coefficients and vibrations, under different atmospheric conditions, we calculate the lapse rate for Earth, Mars, Venus, Titan, and the exoplanet Gl 581d. Furthermore, for each one we consider three models in the virial expansion: van der Waals, square-well, and hard-sphere. Also, when possible, we compare our results to the experimental data. Finally, we remark that for Venus and Titan, which are under extreme conditions of pressure or temperature, our calculations are in good agreement with the observed values, in some instances.

arXiv comment11 pages, 9 figures

References in corpus (6)

• The HARPS search for southern extra-solar planets XI. Super-Earths (5 & 8 M_Earth) in a 3-planet system
• Is Gliese 581d habitable? Some constraints from radiative-convective climate modeling
• The extrasolar planet GL 581 d: A potentially habitable planet?
• Equation of state for all regimes of a fluid: from gas to liquid
• Evidence for the first-order phase transition at the divergence region of activity expansions
• Effects of the second virial coefficient on the adiabatic lapse rate of dry atmospheres

Cited by in corpus (1)

• Adiabatic lapse rate of real gases