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.
Highlights
One of the main goals of thermodynamics is the search for the state equation of the system being studied (Luiz, 2007)
A state of thermodynamic equilibrium in a homogeneous fluid is characterized by a state equation which depends on thermodynamic variables pressure P, volume V and temperature T, through a function f (P,V,T)=0 (Young et al, 1989)
Assuming that Lv ⁄cp is independent from temperature TL, we verified that and, when we integrated the above expression, with the condition that the potential temperature tends to the equivalent potential temperature θe when ws/TL →0, we found the equivalent potential temperature which is the same expression in the context of an ideal gas for the atmosphere
Summary
One of the main goals of thermodynamics is the search for the state equation of the system being studied (Luiz, 2007). This paper first considers Van der Waals equation for the atmosphere, from the gases that compose air, using the critical temperature and the critical pressure of each constituent gas. In this sense, Van der Waals specific constants for the atmosphere are determined and denominated I and D. When we consider D = 0 in the expressions determined in this new proposal, the alternative form of the first law of thermodynamics and the virtual temperature, corresponding to the ideal gas law for the atmosphere, are retrieved
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