Question

In this problem you will estimate the heat lost by a typical house, assuming that the temperature inside is Tin = 20°C and the temperature outside is Tout = 0°C. The walls and uppermost ceiling of a typical house are supported by 2 × 6-inch wooden beams (kwood insulation (kins = 0.04 W/(mK)) in between. The true depth of the beams is actually 5.625 inches, but we will take the thickness of the walls and ceiling to be Lwall interior and exterior covering. Assume that the house is a cube of length L = 9.0 m on a side. Assume that the roof has very high conductivity, so that the air in the attic is at the same temperature as the outside air. Ignore heat loss through the ground. The effective thermal conductivity of the wall (or ceiling) keff , is the area-weighted average of the thermal conductivities of the wooden beams and the fiberglass insulation that make up each of them. Allowing for the fact that the 2 x 6 beams 0.12 W/(mK)) with fiberglass 18 cm to allow for the are actually only 1.625 inches wide and are spaced 16 inches center to center, a calculation of this conductivity for the walls yields keff that the ceiling also has the same value of keff - 0.048 W/(mK). How much heat per second (H = Q/ΔT) is lost from the house due to heat conduction?