# The Virial Effect--Applications for SF\({}_{6}\) and CH\({}_{4}\) Thermal Plasmas
## 2 Equations and Methods
### Results and Discussion  
In order to validate our tool, we compared our results with two examples found in the literature at atmospheric pressure:  
- Case 1: pure argon;
- Case 2: air with 78.084% N\({}_{2}\), 20.946% O\({}_{2}\), 0.036% CO\({}_{2}\), and 0.934% Ar.  
In order to properly compare the results with the literature, we considered the same species (Table 2) reported by authors of past studies.  
The composition obtained from our tool in Case 1 is shown with those of three other studies [2; 11; 16] in Figure 1. For the air plasma, our results were compared with the calculation of [PERSON] [5], and are plotted in Figures 2 and 3 (Figure 2 shows the atomic and ionic species, and Figure 3 shows the molecular species).  
In the two cases (Ar and Air), a good agreement could be observed. At low temperatures, the neutral species were dominant. When the temperature increased, we observed different types of processes. In the case of argon, the ionization of the atoms and the simultaneous apparition of electrons occurred. In the case of air, we noted the dissociation of the molecules, the recombination processes, the apparition of electrons, and the ionization of atoms, but also the electronic attachments. Nevertheless, for some species, some of the results displayed differences between the literature and our calculations. These were generally due to the sources used for the internal partition function of each species. In Figure 1, the results from Godin [2] are based on the data available from Drawin & Felenbok [39]. In this database, the internal partition functions are given versus temperature, with values of the lowering of ionization potential. For the results of Rat [16], the source was not given, but the shift in argon atom density observed at high temperature could be due to the fact that the Ar\({}^{+3}\) ion  
\begin{table}
\begin{tabular}{c c} \hline
**Gas** & **Chemical Species** \\ \hline Argon & Ar, Ar +, Ar +2, Ar +3, e\({}^{-}\). \\ \hline Air & N, N\({}^{+}\), N\({}^{+2}\), O, O\({}^{+}\), O\({}^{+2}\), O\({}^{-}\), C, C\({}^{+}\), C\({}^{+2}\), C\({}^{-}\), Ar, Ar\({}^{+}\), Ar\({}^{+2}\), N\({}_{2}\), N\({}_{2}\), N\({}_{2}\)\({}^{+}\), NO, NO\({}^{+}\), O\({}_{2}\), O\({}_{2}\)\({}^{+}\), C\({}_{2}\), CO, \\ N\({}_{2}\)O, NO\({}_{2}\), CO\({}_{2}\), e\({}^{-}\). \\ \hline \end{tabular}
\end{table}
Table 2: Chemical species considered for argon and air plasma compositions.  
was not taken into account by this author. For the air composition, the partition functions calculated by [PERSON] [5] were determined from data in the literature [37; 38; 39]. Furthermore, his calculation method was different from ours, as he used the minimization of Gibbs free energy.  
Although most papers from the literature used tabulated values for the partition functions, we chose to calculate them from the available data of the NIST database [38] for monoatomic species, and from the JANAF database [37] for molecules.  
Figure 1: Evolution of species: argon; P = 1 bar \(-\) local thermal equilibrium (LTE). Comparison of ours results with [PERSON] et al [11], [PERSON] [2] and [PERSON] et al [16].  
Figure 2: Evolution of atomic species: air: P = 1 bar \(-\) LTE. Comparison of our results with [PERSON] [5].  
By using our tool, the LTE compositions of air and argon plasmas were calculated at P = 1 bar. The choices for the temperature range and of the considered species were made with the aim of assisting with the comparison of our results against the works of other authors. The results validate our tool for atmospheric pressure.