Van der Waals-like State Equation for Atmosphere

Authors

  • Deusdedit Monteiro Medeiros Universidade Federal do Rio Grande do Norte, Laboratório de Pesquisas Atmosféricas, Escola de Ciências e Tecnologia, Campus Universitário de Lagoa Nova, P.O. Box 152, 59072-970, Natal, RN, Brasil
  • Isamara de Mendonça Silva Universidade Federal do Rio Grande do Norte, Laboratório de Pesquisas Atmosféricas, Escola de Ciências e Tecnologia, Campus Universitário de Lagoa Nova, P.O. Box 152, 59072-970, Natal, RN, Brasil
  • Douglas do Nascimento Silva Universidade Federal do Rio Grande do Norte, Laboratório de Pesquisas Atmosféricas, Escola de Ciências e Tecnologia, Campus Universitário de Lagoa Nova, P.O. Box 152, 59072-970, Natal, RN, Brasil
  • David Mendes Universidade Federal do Rio Grande do Norte, Departamento de Ciências Atmosféricas e Climáticas, Campus Universitário de Lagoa Nova, P.O. Box 152, 59072-970, Natal, RN, Brasil

DOI:

https://doi.org/10.11137/2020_2_55_63

Keywords:

Components of the Air, Temperature, Thermodynamics

Abstract

In this paper, we first analyze the atmosphere as a gas mixture per unit mass, which is governed by Van der Waals equation, considering the main components of the air and their respective critical properties (critical temperature TC and critical pressure pC ). After adjusting the corresponding constants and calling them I and D, we find Van der Waals state equation for the atmosphere in this context. Next, we analyze the order of magnitude of the terms in that equation and propose a Van der Waals-like form state equation depending only on D, which we call WD state equation. Additionally, we consider a physical approach for Van der Waals equation for the atmosphere, studying the pressure terms concerning intermolecular forces of repulsion and attraction in the air, and once again we find the previous WD state equation. With this new proposal, we verify that the potential temperature and the equivalent potential temperature hold for the same expressions as those set forth in atmospheric thermodynamics under the analysis of the ideal gas law. However, we discover corrections that depend on D in both the alternative form of the first law of thermodynamics and the virtual temperature.

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Published

2020-08-21

Issue

Vol. 43 No. 2 (2020)

Section

Article

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