## 2 Materials and Methods
### Measurement Methodology  
The measurement methodology, already set up in a previous work [30], is in compliance with ISO 16000-8 [18] and it is based on the decay method with the use of a single tracer gas. Among the various traces gases suggested by the standard (such as nitrogen, helium, argon, and carbon dioxide), CO\({}_{2}\) was chosen, due to its facility to be detected and to its suitable characteristics (chemically inert, non-toxic, without risk for health in the concentration ranged used, stable, unable to be absorbed by walls and furniture) [40]. The principle of decay method is based on marking the air in the ventilated room with the tracer gas and to evaluate the time necessary to replace the marked air with unmarked air. The tracer gas was supplied by a compressed tank of CO\({}_{2}\), with a critical orifice and a gas flow rate measurement device (Figure 3). The minimum flow rate and the duration of the CO\({}_{2}\) introduction were established in compliance with the standard [18] as a function of the volume of the room. In order to create a uniform gas concentration in the investigated volume, fans were switched on before each test; this procedure allowed to obtain a uniform concentration of the gas tracer in different points of the room volume, such as verified in the previous work [31]. The presence of people in the test room is a carbon dioxide source, so its concentration was recorded before the tracer gas introduction, in order to have a reference value for the MAA calculation; operators stayed outside the room during the measurements, but the limits of the European Agency for Safety and Health at Work (2010) were anyway considered. As the maximum concentration was reached, the decay started. The acquisition rate of the concentration of the gas tracer was generally 1 min; longer acquisition rates (2, 3, 5, and 10 min) were set when the decay was very long-lasting, especially in the configurations with the closed window. The CO\({}_{2}\) concentration was registered for a total time greater than the expected average age of air. We clarified this point. All the instrumentations were placed in a central position of the room, when possible, and in particular: \begin{table}
\begin{tabular}{c c c} \hline \hline
**Main Features** & **Case Study 1** & **Case Study 2** \\ \hline Location & Terni & Perugia \\ Room volume (m\({}^{3}\)) & 32.36 & 44.20 \\ Room surface (m\({}^{2}\)) & 11.31 & 16.37 \\ Window total surface (m\({}^{2}\)) & 2.49 & 2.16 \\ Window opening surface (m\({}^{2}\)) & 0.97 & 1.84 \\ Window frame total perimeter (m) & 10.10 & 7.45 \\ Window frame opening perimeter (m) & 5.48 & 6.50 \\ Window airtightness class (\(-\)) [37] & 1/2 & 4 \\ Reference air permeability at 100 Pa (m\({}^{3}\)/hm\({}^{2}\)) [37] & 50/27 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main features of the two investigated rooms. Figure 3: Tracer gas supplier: pressure adaptor (left) and flow meter (right). 1. A CO\({}_{2}\) pressurized tank was placed in a central position of the room;
2. The instrumentation for recording CO\({}_{2}\) concentration was placed at about 1.2 m of height;
3. The instrumentations for recording the indoor environmental conditions were placed next to the CO\({}_{2}\) pressurized tank and at 1.2-1.5 m of height;
4. The outdoor conditions were monitored by placing the instrumentations outdoor next to the window of the investigated room. After recording the gas concentration in a representative point during the decay time, the local mean age of air is obtained as follows [16], by solving the integral in the numerator by means of the trapezoid method:  
\[MAA\ =\ \frac{\int_{0}^{\infty}\varphi dt}{\varphi_{t=t0}}\ =\ \Delta I\left[\frac{ \varphi_{t0}}{2}\ +\ \varphi_{t0+1\Delta t}\ +\ \ldots\ +\ \varphi_{t0+(n-1)\Delta t}\ +\ \frac{\varphi_{t \epsilon}}{2}\right]\ +\ \frac{\varphi_{t-\epsilon}}{\lambda_{tail}}, \tag{1}\]  
where:  
1. MAA is the mean age of air;
2. \(\varphi\) is the tracer gas concentration;
3. \(\Delta\)t is the time acquisition rate;
4.