*2.2. Theoretical Fundamentals*

The enthalpy values were calculated by means of Equation (4), result of the substitution of Equation (2) and Equation (3) in Equation (1).

$$\mathbf{h} = (\mathbf{c}\_{\text{Pa}} \cdot \mathbf{t}) + \left[\mathbf{W} \cdot (\mathbf{L}\mathbf{o} + (\mathbf{c}\_{\text{PW}} \cdot \mathbf{t})) \right] \tag{1}$$

$$\text{MV} = 0.622 \cdot \text{(p}\_{\text{W}}/(\text{p} - \text{p}\_{\text{W}})) \tag{2}$$

$$\mathbf{p} = \mathbf{p}\_{\text{W}} / \mathbf{p}\_{\text{WS}} \tag{3}$$

$$h = \left( 1.004 \cdot t \left( ^\circ \text{C} \right) \right) + \left[ \begin{pmatrix} 0.622 \\ 0.622 \cdot \left[ \frac{0.7 \cdot t^{14.2928 - \frac{5291}{t \cdot \text{(\%)}}}}{1 - \left( q \cdot \text{e} \right)^{14.2928 - \frac{5291}{t \cdot \text{(\%)}}} \right] \\ 1 - \left( q \cdot \text{e} \right)^{14.2928 - \frac{5291}{t \cdot \text{(\%)}}} \end{pmatrix} \right] \tag{4}$$

Δh (KJ/kg)1...8760 = |he,1...8760 − hi,1...8760| (5)

$$
\Delta\text{h} \text{ (Kl/kg)} = \underline{\text{\chi}} \Delta\text{h} \text{ (Kl/kg)} \underline{\text{\chi}} \cdot \text{8760} \tag{6}
$$

where cpa is specific heat of dry air (1.004 KJ/kg ◦K); cpw is specific heat of water vapor (1.86 KJ/kg ◦K); t is temperature; ϕ is relative humidity (%); pw is partial pressure of water vapor in the air; pws is saturation vapor pressure; p is atmospheric pressure (1 bar); h is enthalpy (KJ/kg); he is outdoor air enthalpy (KJ/kg); hi is indoor air enthalpy (KJ/kg); L0 is latent heat of vaporization of water at 0 ◦C (2500.6 KJ/kg); and W is absolute humidity (kg of water/kg of dry air).

Following, the difference between both values is calculated in order to determine the energy that each envelope is equal to in each hour of the year. Last, the absolute values of these results were averaged. This average is the equivalent energy, the energy that can be isolated by each envelope (Equations (5) and (6)).

Taking this as a starting point, four approaches were designed. They allow us to analyze the possible links between the equivalent energy and the shape factor, the morphology, the location and the building materials. Both the information that was used for these calculations and the results are detailed in Appendix A (Table A4).
