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We reach a thermodynamic interpretation of CODET model and its prediction to electrons density and temperature grounded on the physics of hydro magnetism in global equilibrium. The thermodynamic interpretation finds consistency with the model with a magneto-matter medium that is diamagnetic, in the context of ideal magnetohydrodynamics (MHD). It is further noticed that the CODET predicts a polytropic anomalous index for the electron gas of the Sun's corona. It is shown that this unusual characteristic is consistent with assuming that the low quiescent solar corona is a magneto-matter state which possesses an underlying structure that was earlier described to explain the 2-D adsorption process by a surface of a solid of molecules of a gas at a given temperature and pressure by Langmuir. In our case, it is assumed that we are in the presence of a 3-D similar coalescence process, i.e. a Langmuir amorphous lattice in thermodynamic equilibrium. In this way, constitutive properties of the medium magnetic permeability, the non-dispersive acoustic speed, the expected equilibration time for the 1.1 to 1.3$R_{\odot}$, and energy density are determined quantitatively for most of the quiescent corona in a near solar minimum that extends for several months from 2008 to 2009.

The plasma $\beta$ is important to investigate the interchanging roles of plasma and magnetic pressure in the solar atmosphere. It can help to describe features over the photosphere and their changes at different heights. The goal is to obtain the plasma $\beta$ variations through the solar corona during the solar cycles 23 and 24. The plasma $\beta$ is reconstructed in different layers of the solar atmosphere. For this purpose, we use an updated version of COronal DEnsity and Temperature (CODET) model. In this version, we selected different features in the solar atmosphere such as Quiet Sun (QS), faculae and Active Regions (ARs). We calculate the $\beta$ variations at different layers in the solar corona (R= 1.14, 1.19, 1.23, 1.28, 1.34, 1.40, 1.46, 1.53, 1.61, 1.74, 1.79, 1.84 and 1.90 $R_{\odot}$). In the photosphere, we use temperature values from FALC model to obtain plasma $\beta$ in QS and faculae. Additionally, variations of the magnetic and kinetic pressure were modelled during the last solar cycles at coronal heights. Accepted for publication in ApJ.