## 2 Materials and Methods
According to the novel method, the avoidable exergy destruction rate internally caused (\(\dot{E}^{AV,INT}_{D,k}\)) could be computed as the difference between the total exergy destruction of the investigated component (\(\dot{E}^{UN,k}_{D,k}\)), i.e., calculated under real operation conditions, and its exergy destruction (\(\dot{E}^{MIN,k}_{D,k}\)) evaluated under conditions at which its irreversibilities were reduced by improving its efficiency, taking into account that the remaining components were operating under real conditions  
\[\dot{E}^{AV,INT}_{D,k}=\dot{E}^{UN}_{D,k}-\dot{E}^{MIN,k}_{D,k} \tag{7}\]  
The avoidable exergy destruction within the k-th component, being caused by the avoidable irreversibilities occurring within the rest of the components (i.e., externally caused) \(\dot{E}^{AV,EXT}_{D,k}\), could be computed by subtracting the exergy destruction rate (\(\dot{E}^{MIN,rest}_{D,k}\)) within the k-th component under conditions at which the remaining components were working with reduced irreversibilities from the exergy destruction rate (\(\dot{E}_{D,k}\)) taking place within the k-th component under real operation  
\[\dot{E}_{D,k}^{AV,EXT}=\dot{E}_{D,k}-\dot{E}_{D,k}^{MIN,rest} \tag{8}\]  
It could be accepted that the avoidable endogenous and avoidable exogenous parts of exergy destruction (Equations (5) and (6)) allow the calculation of the same exergy destruction parts as the ones determined by the authors as avoidable internally and externally caused (Equations (7) and (8)). The schematic of the investigated vapor-compression refrigeration system, consisting of the compressor (CM), the condenser (CD), the throttling valve (TV), and the evaporator (EV), is illustrated in Figure 1.  
The analysis was performed for a refrigeration system having a cooling capacity of 100 kW [2]. Air was used as a secondary working fluid for the both the evaporator and condenser. The following assumptions were made [2]: (i) in the evaporator, air was cooled from \(-5\)\({}^{\circ}\)C down to \(-15\)\({}^{\circ}\)C; (ii) in the condenser, ambient air was heated from 20 \({}^{\circ}\)C up to 30 \({}^{\circ}\)C; (iii) the minimal temperature difference within the evaporator (i.e., between air and refrigerant) and within the condenser (i.e., between refrigerant and air) was 10 K. The real isentropic efficiency of the compressor was assumed to be 0.80 [2]. For evaluating the unavoidable exergy destruction rates (for applying the existing advanced exergy analysis methodology), the following assumptions were made: the unavoidable temperature differences in the evaporator and the condenser were equal to 0.50 K, whereas the unavoidable compressor efficiency was equal to 0.95. For a fair comparison of the two considered approaches, the same values of the component parameters were assumed for the calculation of internally and externally caused avoidable exergy destruction rates. For creating the theoretical cycle of the studied refrigeration system within the existing advanced exergy analysis methodology, the following assumptions were used [2]: (i) for both the evaporator and condenser, the minimal temperature differences were equal to 0 K; (ii) the compressor efficiency was equal to 1.0; (iii) an ideal expansion process was used for replacing the throttling valve. An ambient temperature equal to 20 \({}^{\circ}\)C was chosen as the reference point for the exergy analysis [23]. An open-source, web-based, interactive computing tool was developed [24] and applied for the advanced exergy analysis of the investigated refrigeration system. The tool was utilized by employing (i) a cloud service for developing notebooks using the object-oriented programming language Python and (ii) CoolProp [25], being a library for calculating the thermophysical properties of working fluids. Figure 1: Schematic of the investigated vapor-compression refrigeration system: 1–4—stream numbers.