## 3 Results and Discussion
### GC of the Exhaust Gas  
The results of the GC showed that hydrogen and carbon molecules, between the other species, were detected in the exhaust gas. These molecules were produced by the decomposition of the C4H10/C3H8 species in the plasma discharge. The conversion factors of these species were obtained using the following equations:  
\[ \begin{split}\text{C}_{4}\text{H}_{10}\text{ Conversion}&=\frac{\text{modes of C}_{4}\text{H}_{10}\text{ converted}}{\text{modes of C}_{4}\text{H}_{10}\text{ introduced}}\\ \text{C}_{3}\text{H}_{8}\text{ Conversion}&=\frac{\text{ modes of C}_{3}\text{H}_{6}\text{ converted}}{\text{modes of C}_{3}\text{H}_{8}\text{ entered}}\end{split}  \tag{2}\]  
where the moles of the converted hydrocarbons are calculated by the difference between the inlet and outlet concentrations obtained by the GC. The dependence of the conversions on the applied voltage, the electrode rotation frequency, and the gas flow rate are shown in Figure 4. The behaviors were similar to the peak intensity and the consumed power (see Table 1). The C4H10/C3H8 conversion grew with the applied voltage and the rotational frequency and decreased with the flow rate. This could mean that the decomposition of LPG species is also related to the number of current shocks formed in the reactor. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Applied Voltage (\& \(I_{p}\) (mA) & \(P\) (W) & \
\begin{tabular}{c} **Rotational** \\ **Frequency** \\ **(\(\times\)1000 rpm)** \\ \end{tabular} & \(I_{p}\) (mA) & \(P\) (W) &
\begin{tabular}{c} **Gas Flow** \\ **Rate (sLm)** \\ \end{tabular} & \(I_{p}\) (mA) & \(P\) (W) \\ \hline
10.5 & 30 & 182 & 9 & 45 & 360 & 1 & 52 & 375 \\
11.5 & 34 & 223 & 11 & 46 & 363 & 2 & 46 & 340 \\
12.5 & 38 & 268 & 13 & 47 & 366 & 3 & 40 & 317 \\
13.5 & 42 & 319 & 15 & 49 & 370 & 4 & 37 & 301 \\
14.5 & 49 & 398 & 18 & 52 & 375 & 5 & 33 & 285 \\ \hline \end{tabular}
\end{table} 
Table 1: Dependence of the averaged consumed power, \(P\), and the peak current on the voltage applied (stationary power electrode and 1 sLm), the rotational frequency (at 14 kV and 1 sLm), and the gas flow rate (at 14 kV and 18,000 rpm). Figure 4: The C3H8 and C4H10 conversions versus (**a**) different voltages applied on the stationary power electrode at 1 sLm gas flow rate, (**b**) rotational frequencies of power electrode at 14 kV applied voltage and 1 sLm gas flow rate, and (**c**) gas flow rates at 14 kV applied voltage and 18,000 rpm rotational frequency of the power electrode. The energy efficiency (\(\eta\)) of the LPG conversion in the developed reactor gives us an idea of the energy required for this conversion in the studied conditions. It is calculated from the number of moles of butane and propane converted by second, which can be obtained from the values of the conversion factors and the gas flow rate, divided by the consumed input power:  
\[\eta=\frac{\text{moles of C}_{4}\text{H}_{10}\text{ and C}_{3}\text{H}_{8}\text{ converted}/\text{s}}{P} \tag{3}\]  
Figure 5 shows the variations of the energy efficiency as a function of applied voltage, rotational frequency of the power electrode, and the gas flow rate. As can be seen, the energy efficiency of the reactor decreased by increasing the applied voltage while it grew at a higher rotation frequency of the power electrode and the gas flow rate. As mentioned, when the voltage grows, the number of filamentary shocks does also, and the consumed power and the LPG conversion increase consequently, but this study shows that the energy efficiency decreases for high applied voltage. This means that additional energy is not efficiently used for LPG decomposition. There are different processes that cause the energy lost in the plasma discharge, especially the joule heating and electron-heavy particle impacts, which result in all electron collisions not being effective for LPG conversion in the plasma. Thus, the exchange of kinetic energy between the electrons and the heavy particles largely determines the efficiency of the conversion.