## 3 Results and Discussion
### Spectroscopic Characterization
#### 3.3.2 Gas Temperature  
The gas temperature (\(T_{g}\)) in the plasma discharges is considered as close to the rotational temperature (\(T_{r}\)) [20]. This temperature describes the population of rotational states of the molecules. These states are mainly populated by collisions with the heavy particles. At the atmospheric pressures, the collision frequency is significantly high. Hence, prior to the instant photon emission, there is enough time to reach the equilibrium between the excited molecules and the gas particles.  
The theoretical emission intensity of the transition \(vJ^{\prime\prime}\to vJ^{\prime}\) corresponding to the vibro-rotational bands is given by [21]:  
\[I_{J^{\prime}J^{\prime\prime}}=D_{0}k^{4}Sexp\bigg{(}-\frac{E_{J^{\prime}}}{k_ {B}T_{r}}\bigg{)} \tag{7}\]  
where \(S\) is the oscillator strength, \(k\) is the wavelength, and \(k_{B}\) is the Boltzmann constant. \(E_{p}\) and \(D_{0}\) are the energy of the rotational level \(J^{\prime}\) and a coefficient that depends on the rotational partition function, \(Q_{r}\), respectively, and can be calculated by:  
\[\begin{array}{l}D_{0}=\frac{C(J^{\prime}+J^{\prime\prime}+1)}{Q_{r}}\\ E_{J^{\prime}}=B_{\
u}hcJ^{\prime}(J^{\prime\prime}+1)\end{array} \tag{8}\]  
where \(C\) is a constant and \(B_{\
u}\) depends on the vibrational state \(v\).  
Equation (7) can be used for the simulation of the bands, introducing the broadening of lines. In our case, where the instrument broadening was the predominant, a value of 0.108 nm was considered. The best fitting of this simulated spectrum to the experimental measurements permits to estimate the values of \(T_{rot}\). The SFCAIR [22] software was used as the source of coefficients of Equation (7) and for this fitting.  
Figure 10 shows an example of the fitting processes with the C\({}_{2}\)(\(d^{3}\Pi_{g}\), \(v=1\to a^{3}\Pi_{u},v=1\)) system to calculate the rotation temperatures for the C\({}_{4}\)H\({}_{10}\)/C\({}_{3}\)H\({}_{8}\) gas mixture at a 14 kV applied voltage, 18,000 rpm rotation frequency of the power electrode, and a 1 sLm gas flow rate.  
The variations of the rotational temperature as a function of the applied voltage, rotation frequency of the power electrode, and the gas flow rate are shown in Figure 11. As seen, the rotational temperature for the developed plasma reactor changes between 700-1300 K. These values are a good estimation of the gas temper  
Figure 10: Fitting of the simulated spectrum to experimental measures for determination of the rotational temperature using a C\({}_{2}\)(\(d^{3}\Pi_{g}\), \(v=1\to a^{3}\Pi_{u}\), \(v=1\)) band for C\({}_{4}\)H\({}_{10}\)/C\({}_{3}\)H\({}_{8}\) gas mixture at 14 kV applied voltage, 18,000 rpm rotation frequency, and 1 sLm gas flow rate.  
of the vibro-rotational levels follow the equilibrium (7). For separation of the equilibrium, these values could be overestimated.  
The gas temperature in the plasma reactor was increased by raising the applied voltages due to more energy being fed to the discharge medium while it was reduced by growing the rotation frequency and gas flow. As presented in the next section, this was due to the decrease in the energy of electrons in these conditions, and consequently the transfer to heavy particles decreased.