## 3 Results and Discussion
### Results of 'Group A' Mixtures (Substances for Reducing the Critical Temperature)
The thermal efficiency depends on three dimensionless variables: the dimensionless main compression work, \(w_{mc}\)/\(w_{t}\), the dimensionless recompression work, \(w_{rc}\)/\(w_{t}\), and the dimensionless additional enthalpy supplied due to real gas conditions, \(\Delta\)h\({}_{pg}\)/\(w_{t}\). These terms depend on the thermodynamic properties of the working fluid in the  
Figure 6: Pressure vs enthalpy. Recompression Brayton cycle using pure s-CO\({}_{2}\) and U\(\Lambda\)total = 15,000 kW/K. recompression cycle. Further, \(\Delta\)h\({}_{\text{rg}}\) is the difference between the heat needed in a cycle working at real gas conditions and the heat needed in an ideal cycle [39]. It can be expressed by:  
\[\Delta\)h\({}_{\text{rg}}=\Delta\)h\({}_{\text{a}}+\Delta\)h\({}_{\text{T}t} \tag{2}\]  
where \(\Delta\)h\({}_{\text{T}t}\) is the enthalpy variation of the isothermal \(T_{t}\); this variable tends to zero when the turbine works at high temperatures. Thus, in these cases, Equation (1) can be approximated to:  
\[\eta_{th}=\frac{1\ -\ (1-\gamma)\cdot\frac{v_{\text{mc}}}{w_{\text{T}}}-\gamma \cdot\frac{w_{\text{tr}}}{w_{\text{T}}}}{1+\frac{\Delta\text{h}_{\text{g}}}{w _{\text{T}}}} \tag{3}\]  
The dimensionless variables \(w_{\text{mc}}/w_{t}\), \(w_{\text{rc}}/w_{\text{t}}\) and \(\Delta\)h\({}_{\text{a}}/w_{\text{t}}\) play an important role in the cycle efficiency. For this reason, the fluctuation of \(w_{\text{mc}}/w_{\text{t}}\), \(w_{\text{rc}}/w_{\text{t}}\) and \(\Delta\)h\({}_{\text{a}}/w_{\text{t}}\) of the s-CO\({}_{2}\) mixtures with respect to the pure s-CO\({}_{2}\) have been obtained using the next equations:  
\[\delta_{w_{mc}/w_{\text{t}}} = \frac{(w_{mc}/w_{\text{t}})_{\text{sCO2}_{\text{pure}}}-\ (w_{mc}/w_{\text{t}})_{\text{sCO2}_{\text{mixture}}}}{(w_{mc}/w_{\text{t}})_{ \text{sCO2}_{\text{pure}}}} \tag{4}\] \[\delta_{w_{\text{rc}}/w_{\text{t}}} = \frac{(w_{rc}/w_{\text{t}})_{\text{sCO2}_{\text{pure}}}-\ (w_{rc}/w_{\text{t}})_{\text{sCO2}_{\text{mixture}}}}{(w_{rc}/w_{\text{t}})_{ \text{sCO2}_{\text{pure}}}}\] (5) \[\delta_{\Delta\text{h}_{\text{a}}/w_{\text{t}}} = \frac{(\Delta\text{h}_{\text{a}}/w_{\text{t}})_{\text{sCO2}_{ \text{pure}}}-\ (\Delta\text{h}_{\text{a}}/w_{\text{t}})_{\text{sCO2}_{\text{mixture}}}}{( \Delta\text{h}_{\text{a}}/w_{\text{t}})_{\text{sCO2}_{\text{pure}}}}\] (6) \[\delta_{total} = \sum_{i}\delta_{i}=\ \delta_{w_{mc}/w_{\text{t}}}+\delta_{w_{\text{tr}}/w_{ \text{t}}}+\delta_{\Delta\text{h}_{\text{a}}/w_{\text{t}}} \tag{7}\]  
where \(\delta_{w_{mc}/w_{\text{t}}}\) is the variation of the dimensionless main compression work of the sCO\({}_{2}\)-mixtures respect to the pure s-CO\({}_{2}\), \(\delta_{w_{\text{rc}}/w_{\text{t}}}\) is the variation of the dimensionless recompression work of the sCO\({}_{2}\)-mixtures respect to the pure s-CO\({}_{2}\), \(\delta_{\Delta\text{h}_{\text{a}}/w_{\text{t}}}\) is the variation of the dimensionless additional enthalpy of the sCO\({}_{2}\)-mixtures respect to the pure s-CO\({}_{2}\), and \(\delta_{total}\) is the total variation of the dimensionless cycle work of the sCO\({}_{2}\)-mixtures respect to the pure s-CO\({}_{2}\). It has been observed that the cycle efficiency increases when \(\delta_{total}\) increases [40]. Therefore, the influence of the dimensionless variables \(w_{\text{mc}}/w_{\text{t}}\), \(w_{\text{rc}}/w_{\text{t}}\) and \(\Delta\)h\({}_{\text{a}}/w_{\text{t}}\) on the cycle efficiency can be displayed in Figure 5:0  
The adoption of s-CO\({}_{2}\) cycles is particularly promising for large-scale, high-temperature CSP plants [2]. Four factors are important for incorporating s-CO\({}_{2}\) into CSP plants: superior performance vs. steam Rankine cycles, the ability to integrate thermal energy storage, ultimate heat sink thermal  
Figure 5:1 Variation of the parameters \(w_{\text{mc}}/w_{\text{t}}\), \(w_{\text{rc}}/w_{\text{t}}\) and \(\Delta\)h\({}_{\text{a}}/w_{\text{t}}\) of the s-CO\({}_{2}\) mixtures with respect to the pure s-CO\({}_{2}\).