## 2 Material and Methods  
### The Examined Systems  
The first examined system was a simple vapor compression cycle, which is depicted in Figure 1, and it was assumed to be the reference system (Ref). The working fluid was CO\({}_{2}\) (R744) and it operates in transcritical mode. The gas cooler outlet temperature (T\({}_{3}\)) was called, in this work, the heat rejection temperature level and it also can be symbolized as (T\({}_{c}\)). This system produces 100 kW of cooling and consumes work (W) in the compressor.  
The next examined system was the one with mechanical dedicated subcooling (M-SC), which produces 100 kW of refrigeration. This system uses CO\({}_{2}\) in the main cycle and R134a in the secondary cycle. This refrigerant was selected as a usual selection in the literature [24; 25]. In this system, there is the possibility to use photovoltaic panels, for example, in order to drive the secondary refrigeration cycle and to create an overall environmentally-friendly system. Figure 2 illustrates this system and it has  
Figure 1: The reference examined system (Ref) which is a simple transcritical refrigeration cycle.  
to be said that the condenser of the secondary system was assumed to operate at the same temperature level as the gas cooler outlet temperature. In other words, the temperature (T\({}_{3}\)) was assumed to be the same as the (T\({}_{33}\)), which is saturated liquid. This system consumes work in the primary cycle (W) and in the secondary cycle for the subcooling (W\({}_{\rm sc}\)). The temperature of the evaporator in the secondary system (T\({}_{11}\)) was assumed to be 5 \({}^{\circ}\)C lower than the temperature level (T\({}_{34}\)). Moreover, it has to be said that there was no superheating in the secondary cycle evaporator (or subcooler device).  
The last examined system is depicted in Figure 3, and it is the system with dedicated subcooling with the absorption chiller, which produces 100 kW of refrigeration. The detailed description of the absorption chiller is given in Appendix A. In this system, there is the possibility to use solar thermal collectors in order to drive the absorption chiller and to create an overall environmentally-friendly system. The absorption chiller is a single stage machine with an internal heat exchanger (70% effectiveness), which operates with the LiBr-H\({}_{2}\)O working pair. This machine was assumed to reject heat at the ambient (from the condenser and the absorber) at the temperature level (T\({}_{\rm c}\)), which is the same as the gas outlet temperature in every case. The absorption chiller evaporator temperature (T\({}_{\rm e,ach}\)) was assumed to be 5 \({}^{\circ}\)C lower than the (T\({}_{34}\)). Moreover, the minimum values of the (T\({}_{\rm e,ach}\)) were assumed to be 5 \({}^{\circ}\)C, because the refrigerant is water in the absorption chiller and it cannot operate at a lower temperature level due to the danger of freezing. This system operates by using a heat input in the generator (Q\({}_{\rm g}\)) and it does not consume work.  
The last step in this section is the presentation of the pressure-specific enthalpy (p-h) diagrams for the cycles in Figure 4. Figure 4a shows the p-h diagram for the reference cycle, while Figure 4b shows the same for the other cases with dedicated subcooling. It was obvious that the cooling capacity is higher in the cases with the subcooling because the distance between the state points (4) and (1) was greater in Figure 4b compared to the respective in Figure 4a.  
Figure 2: System with dedicated mechanical subcooling (M-SC).