## 2 Basic Analysis of Prediction Models and Model Verification
### Prediction Models of Saturated Vapor Pressure and Saturated Density
#### 3.2.3 Comparison and Discussion of Different Models of Saturated Vapor Pressure  
As shown in Equations (15) and (16), since the specific volume translation modification method has little effect on the calculation of saturated vapor pressure, only six prediction models excluding the VTPR1, VTPR2 and VTPR3 models were used to calculate saturated vapor pressure within the temperature range of 273.15 K to 353.15 K at an interval of 4 K (the following work was conducted under the same condition). The relative deviations of the predicted saturated vapor pressures of FC-72, Novec 649 and HFE-7100 obtained by different models are shown in Figures 2-4, respectively. The experimental data of the saturated vapor pressures for FC-72, Novec 649 and HFE-7100 were taken from the literature [60, 66, 73], and the combined uncertainties in measurements (level of confidence = 0.95, coverage factor = 2) of Novec 649 and HFE-7100 were 1.21% [60] and 0.82% [66], respectively; the uncertainty in measurements of FC-72 was not mentioned in the literature [73]. The maximum relative deviation (MRD) and ARD between the predicted and reference values of the saturated vapor pressures for the above three liquids are shown in Table 5.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Expressions** & **Equation Parameters** \\ \hline PR & \(p=\frac{RT}{V-B}-\frac{a}{V(V+B)+(V-b)}\) & \(a=[1+m(1-T_{r}^{0.5})]^{2}\) \\  & \(a=a_{c}a\) & \(m=0.37646\)\(+\)\(1.54226\omega-0.26992\omega^{2}\)\(\omega\)\(\leq\) 0.491 \\  & \(b\approx\) 0.077796 \(\frac{RT_{c}}{p_{c}}\) & \(m=0.379642\)\(+\)\(1.48503\omega-0.164423\omega^{2}\)\(+\)\(0.016666\omega^{3}\) \\  & \(\omega\) \(>\) 0.491 \\ \hline MAPR1 & \(m=0.3919\)\(+\)\(1.4996\omega-0.2721\omega^{2}\)\(+\)\(0.1063\omega^{3}\) \\ \hline MAPR2 & \( \begin{array}{c}p=\frac{RT}{V-B}-\frac{a}{V(V+B)+(V-b)}\\ \alpha=\exp(MA_{1}(1-T_{r}^{MA_{2}}))\\ b\approx\)0.077796 \(\frac{RT_{c}}{p_{c}}\end{array} \) & \(MA_{2}=\frac{-0.3327\omega^{2}-1.8678\omega-0.2626}{1.35642\omega+0.3788}\)\(+\)\(1.3642\omega+1.3788\) \\ \hline VTPR1 & \(p=\frac{RT}{(V+\Delta V)-b}-\frac{a}{(V+\Delta V)\ (V+\Delta V+b)+(V+\Delta V-b)}\) & \( \begin{array}{c}\Delta V_{c}=(0.3074-Z_{c})RT_{c}\ /\ p_{c}\\ VT=VT_{1}+(1-VT_{1})\exp[VT_{2}(1-\ T_{r})]\\ V=-2.8431\ast\exp[-64.2184(0.30740-Z_{c})]\ +0.1735\\ VT_{2}=-99.2558+301.6201Z_{c}\end{array} \) \\ \hline VTPR2 & \(p=\frac{RT}{(V+\Delta V)-b}-\frac{a}{(V+\Delta V)\ (V+\Delta V+b)+(V+\Delta V-b)}\) & \( \begin{array}{c}VT=1-\ VT_{3}(1-\ T_{r})^{VT_{4}}(1+VT_{5}(1-\ T_{r})^{0.5}) \\ VT_{3}=583.4868\ast\exp[-179.2123(0.30740-Z_{c})]\ +3.1436\\ VT_{4}=2289.4789-2266.0959/Z_{c}\pm 40.4632/Z_{c}^{2}-\\ \Delta V=\Delta V_{c}\cdot VT\end{array} \) & \( \begin{array}{c}VT_{4}=2289.4789-2266.0959/Z_{c}\pm 840.4632/Z_{c}^{2}-\\ 138.4154/Z_{c}^{3}\pm 8.5414/Z_{c}^{4}\end{array} \) \\  & \( \begin{array}{c}VT_{5}=-1512.0836+1491.1370/Z_{c}-551.0456/Z_{c}^{2}+\\ 90.3921/Z_{c}^{3}-55.5535/Z_{c}^{4}\end{array} \) \\ \hline VTPR3 & \(p=\frac{RT}{(V+\Delta V)-b}-\frac{a}{(V+\Delta V)\ (V+\Delta V+b)+(V+\Delta V-b)}\) & \( \begin{array}{c}VT=VT_{6}+(1-\ VT_{6})\exp(VT_{7}|\kappa-\ T_{r}|)\\ V=V_{\rm PR}-\Delta V\end{array} \) \\  & \( \begin{array}{c}VT_{6}=-7.341\times 10^{13}*Z_{c}^{25.916}+0.11\\ VT_{7}=-44.226\ast\exp(-5.364Z_{c})+0.806\end{array} \) \\ \hline MPPR & \(p=\frac{RT}{V-B}-\frac{a}{V(V+b)+b(V-b)}\) & \( \begin{array}{c}\\ MP_{1}=1.7309\)\(+\)\(1.6571\omega+0.1554\omega^{2}\\ MP_{2}=0.2476\)\(-\)\(0.8857\omega+0.1900\omega^{2}\end{array} \) \\  & \(b=0.077796\frac{RT_{c}}{p_{c}}[1+MP_{2}(1-\ T_{r})]\) & \\ \hline PT & \(p=\frac{RT}{V-B}-\frac{a}{V^{2}+(b+c)V-\overline{k}}\) & \( \begin{array}{c}CE_{3}=1-3\chi\\ \chi^{2}\\ CE_{2}^{3}+(2-\ 3\chi^{2}_{c})CE_{2}^{2}+3\chi^{2}_{c}CE_{2}-\chi^{3}_{c}\!\!=0\\ \chi^{2}_{c}=CE_{1}\frac{RT_{c}}{p_{c}}\end{array}