21-July. Team Activity about basic concepts.

Consider a building as a cube with a side 10 m long.

Technical specification of the building

• 100 m\(^2\) of the roof building are covered by photovoltaic panels.
• The photovoltaic panels follows the sun movement in the sky so that the sun light is always perpendicular to the panels.
• Consider 5h of sun radiation per day.
• The photovoltaic panels, on average, supply 200 W/m\(^2\) during the 5h of solar radiation per day.
• To heat your building you want to use only the energy given by the photovoltaic system on the roof.
• The building is heated with an heat pump with a COP (Coefficient of Performance) equal to 3. [The COP is the ratio between the heat delivered by the pump in the house and the energy supplied to the pump]
• The energy delivered by the photovoltaic system supplies the heat pump.

1. Plot on the same chart the heat flow density q as a function of the thickness \(\Delta\)x of the walls, for all the different values of \(\lambda\) given in the table above. Assume a temperature difference between the inside and the outside of the building \( \Delta\)T=20 K (we have something similar in the winter period in Turin).
2. Considering that, for all the 24h, you want to maintain a temperature inside the building 20K higher than the outside, evaluate the thickness of the walls for the different values of the thermal conductivity \(\lambda\) listed in the table.