## 2 Materials and Methods
### Thermal Resistance Measurements  
The apparatus known as Small Hot Box [18] was used for measuring the thermal properties of the sample (Figure 2); it was designed, built, and calibrated by preliminary measurements at the University of Perugia (Laboratory of Environmental Control, Department of Engineering). The experimental apparatus consists of a hot chamber with external dimensions of \(0.94\times 0.94\times 0.50\) m\({}^{3}\): the walls are  
Figure 1: Glazing system with monolithic silica aerogel: investigated sample (supplied by Union College, Schenectady, NY, USA). made of wood panels (20 mm thick) and of an internal insulation layer of about 200 mm thickness, in order to minimize the heat flux. A constant temperature inside the hot room is ensured by an internal heating wire (maximum power 50 W). A closure wall, made as the hot chamber wall, allows to place the sample, thanks to an opening (300 \(\times\) 300 mm\({}^{2}\) dimensions, for a total area of 0.09 m\({}^{2}\)) in its central part. The Laboratory room represents the cold side of the system. The temperature of this room is constant, thanks to the presence of the HVAC plant and to the absence of walls adjacent to outdoor environment. The tests are carried out by the thermal flux meter methodology, maintaining a temperature difference between the sides (hot and cold) at least equal to 20 \({}^{\circ}\)C. A thermal flux meter installed in the central part of the sample measures the heat flux (\(q\)), while the surface temperatures are detected by eight thermo-resistances installed on the sample (four sensors each side). The thermal resistance (\(R\) in (m\({}^{2}\)K)/W) is calculated considering the mean surface temperatures of the hot and cold sides (\(T_{sH}\) and \(T_{sC}\), respectively) during the tests, in steady-state conditions, as:  
\[R=\frac{T_{sH}-T_{sC}}{q}\left[\frac{\text{m}^{2}\text{K}}{\text{W}}\right] \tag{1}\]  
By means of the precision values of the probes (\(\pm\) 5% for the thermal flux meter and \(\pm\) 0.1 \({}^{\circ}\)C for the thermo-resistances), an average measurement accuracy of about 5% is obtained for all the tests [19]. The thermal resistance (\(R\)) of the samples depends on the thermal conductivity and on the thickness of the monolithic aerogel and of the two float glasses. The thermal conductivity of the only aerogel layer (\(\lambda_{a}\)) was evaluated by using the Equation (2), assuming a thermal conductivity of the glass (\(\lambda_{g}\)) equal to 2.7 W/mK at about 38 \({}^{\circ}\)C (corresponding to 1 W/mK at 10 \({}^{\circ}\)C), 15 mm of aerogel (\(s_{u}\)), and 4.7 mm of glass (\(s_{g}\)):  
\[R=R_{a}+R_{g}=\frac{s_{a}}{\lambda_{a}}+2\cdot\frac{s_{g}}{\lambda_{g}}\left[ \frac{\text{m}^{2}\text{K}}{\text{W}}\right] \tag{2}\]  
A temperature of 38 \({}^{\circ}\)C was considered as the temperature of the glass because the Small Hot Box tests were carried out at two mean temperatures of the sample of about 38 \({}^{\circ}\)C and 41 \({}^{\circ}\)C (45/50 \({}^{\circ}\)C being the temperatures of the hot side and 20 \({}^{\circ}\)C of the cold chamber). These values are higher than the typical test conditions of 10 \({}^{\circ}\)C and 23 \({}^{\circ}\)C, to which the declared thermal values are usually referred. Figure 2: (**a**) Small Hot Box apparatus and (**b**) particular of the monolithic sample with the probes’ position (T = thermo-resistances, TF = thermal flux meter).