## 5 Energy Requirement Estimation  
### Energy Calculations  
The inactivation of PPO in different fruits can be compared in terms of energy requirements. Equation (1) was used to calculate the energy for the thermal inactivation in fruit juice and puree. \[\text{Q}=\text{mC}_{\text{p}}\Delta\text{T} \tag{1}\]  
where Q is the specific heat energy required to heat the fruits samples (J), m is the mass of the fruits samples (kg), C\({}_{\text{p}}\) is the fruits heat capacity (J/kg.\({}^{\circ}\)C). \(\Delta\text{T}\) for thermal processing is the temperature difference between the final temperature and initial temperature, which was assumed to be 20 \({}^{\circ}\)C.  
In some studies, HPP combined with thermal treatment was applied for the inactivation of enzyme PPO, so Equation (1) was also used to estimate the energy requirement during the pre-heating of the sample before HPP treatment. For the sake of the estimation \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Fruit/Cultivar** & **Parameters** & **k (min\({}^{-1}\))** & **D-Value (min)** & **z-Value (\({}^{\circ}\)C)** & **E\({}_{\alpha}\) (kJ/mol)** & **References** \\ \hline Apple (_Malus domestica_ cv. Golden Delicious) & 64 \({}^{\circ}\)C & 0.036 & 28 & & & \\  & 656 W/cm\({}^{2}\) & & & 18 & 123 & [55] \\ juice & 67 \({}^{\circ}\)C & 0.056 & 18 & & & \\ \hline Pear (_Pyrus communis_ cv. Taylor’s Gold) & 460 W/cm\({}^{2}\) & & & & & \\  & 1.3 W/g & 0.356 & 7 & 50 & 40 & [28] \\  & 72 \({}^{\circ}\)C & & & & & \\ \hline Apple (_Malus domestica_ cv. Royal Gala) & 460 W/cm\({}^{2}\) & & & & & \\  & 1.3 W/g & 0.540 & 4 & 39 & 52 & [28] \\  & 72 \({}^{\circ}\)C & & & & & \\ \hline Strawberries (_Fragaria ananassa_ cv. Camarosa) & 460 W/cm\({}^{2}\) & & & & & \\  & 1.3 W/g & 0.483 & 5 & 80 & 25 & [28] \\  & 72 \({}^{\circ}\)C & & & & & \\ \hline Apple (_Malus domestica_ cv. Golden Delicious) & 60 \({}^{\circ}\)C & 0.178 & 13 & 19 & 105 & [60] \\ juice & & & & & & \\ \hline \hline \end{tabular}  
* Authors of paper [28,60] used an equipment with 24 kHz, while the other study’s frequency was 20 kHz.  
\end{table} 
Table 4: Kinetic parameters inactivation of PPO by Ultrasound *. energy calculation for HPP, the mass of the product treated was taken to be half of the maximum capacity of HPP chamber volume multiply with the density of water (assuming density of water is approximately the density of the sample) which is more industrial relevance considering the cost-effective capacity of HPP. The temperatures used to calculate the \(\Delta\)T was the temperature used before starting the HPP process, where the initial temperature was assumed at 20 \({}^{\circ}\)C to a final temperature before pressurisation that is associated to each treatment pressure. The temperature increase per 100 MPa for fruit juice and puree was assumed to be the same as pure water which is \(\sim\)3 \({}^{\circ}\)C [64]. The temperature increase due to heat of compression during pressurisation is 18 \({}^{\circ}\)C for a high pressure process at 600 MPa. In addition to the heat generated during the pressure come-up phase of the HPP cycle, the compression work (W\({}_{\text{compression}}\) in J) during pressurisation also needs to be calculated. The following Equation (2) is used to calculate the compression work during the pressurisation phase of the HPP cycle:  
\[\text{Wcompression}=\left[\int_{\text{P1}}^{\text{P2}}\text{PV}\beta\text{dP}- \int_{\text{T1}}^{\text{T2}}\text{PV}\alpha\text{dT}\right] \tag{2}\]  
\[\frac{1}{2}\ \beta\text{V}(\text{P}_{2}^{2}-\text{P}_{1}^{2})-\text{P}_{2} \text{V}\alpha(\text{T}_{2}-\text{T}_{1})\]  
where P1 and P2 are the initial and final pressure (Pa) during pressurisation, V is the volume of the chamber containing liquid water (m\({}^{3}\)), \(\beta\) is the isothermal compressibility of water at the average compression temperature, \(\alpha\) is the volume expansivity or thermal expansion coefficient of water, T2 \(-\) T1 is the adiabatic temperature increase during pasteurisation.