## 3 Results and Discussion
### Vapour and Liquid Water Heat Capacities  
Figure 4 plots the evolution of the reference enthalpy of vaporisation of water (Figure 4a) and the difference in internal energy between vapour and liquid water (Figure 4b) with temperature for the minimum pressure between saturated vapour pressure and 100 kPa. The source of the data is the NIST Chemistry WebBook [13]. The figure also plots the best linear fits \(\Delta h_{\text{LV}}=a+bT\), Equation (23), and \(\Delta u_{\text{LV}}=a^{\prime}+b^{\prime}T\), Equation (25), to the data in the mentioned range, where the fitting parameters have been found to be \(a=2500.9\) kJ/kg, \(b=-2.3989\) kJ/kg/K, \(a^{\prime}=2374.8\) kJ/kg and \(b^{\prime}=-2.8415\) kJ/kg/K. The squared Pearson correlation coefficient \(R^{2}\) obtained is nearly 1 for both \(\Delta h_{\text{LV}}\) and \(\Delta u_{\text{LV}}\) (Figure 4), which shows they are well represented with a linear fit. As mentioned, the difference in specific heat capacity between vapour and liquid water in isobaric conditions, \(c^{\text{V}}_{\text{P}}-c^{\text{L}}_{\text{P}}\), Equation (22), should be close to the identified coefficient \(b\), while the difference in isobaric conditions, \(c^{\text{V}}_{\text{V}}-c^{\text{L}}_{\text{V}}\), Equation (24), should be close to the identified coefficient \(b^{\prime}\). To illustrate the evolution of the specific heat capacities of liquid water and vapour with temperature, the values given by the NIST [13] for the range 0-150 \({}^{\circ}\)C are plotted in Figure 5. The figure includes values for isochoric and isobaric conditions at the minimum pressure between vapour saturation pressure and 100 kPa. Please note that, although the specific heat capacity of liquid water shows practically no dependence on pressure, that of water vapour does. For pressure conditions other than atmospheric, the corresponding specific heat capacity values can be obtained from the NIST [13], and an expression of the specific heat capacity of vapour as a function of pressure is found, for instance, in Vestfalova and Safarik [24]. Figure 3: Model selection results from information criteria for \(n=3\). Akaike weights _Aw_ from the Akaike information criterion (blue), and posterior model probabilities \(Bp\) from the Bayesian information criterion (orange). 1900 J/kg/K) correspond to the reference values between 0 and 15 \({}^{\circ}\)C. The vapour value specified for isochoric conditions (1428 J/kg/K) corresponds to the reference value at 11 \({}^{\circ}\)C. The vapour value given by [PERSON] et al. [17] (1620 J/kg/K) corresponds to the reference value in isochoric conditions at 121 \({}^{\circ}\)C although at saturation pressure. The vapour value given by [PERSON] and [PERSON] [12] (1900 J/kg/K) corresponds to the reference value in isobaric conditions at 15 \({}^{\circ}\)C.  
However, the main interest in this study of the consistency of the formulation with the modelling of water vaporisation is the difference between the specific heat capacities of liquid water and vapour. The difference between the reference values in Figure 5 as a function of temperature from 0 to 150 \({}^{\circ}\)C is plotted in Figure 6, for both isobaric (Figure 6a) and isochoric (Figure 6b) conditions. In addition, the fit coefficients \(b\) and \(b^{\prime}\) identified from Figure 4 and the differences obtained from the literature values in Table 2, which are constant with temperature, are included for comparison. Regarding the literature values (Table 2), all those given for isobaric conditions ([PERSON] and [PERSON] [7], [PERSON] et al. [14], [PERSON] and [PERSON] [15] and Gens [16] (p)), or corresponding to such conditions according to the values in Figure 5 ([PERSON] and [PERSON] [12]), are consistent with the difference between isobaric reference values, since they are contained in the range of reference values for the studied temperatures (Figure 6a). The literature values for isochoric conditions (Gens [16] (vol), [PERSON] et al. [17]) are also consistent with the isochoric reference values (Figure 6b).