Question

One easy way to reduce heating (and cooling) costs is to add extra insulation in the attic of a house. Suppose a single-story cubical house already had 15 cm of fiberglass insulation in the attic and in all the exterior surfaces. If you added an extra 8.0 cm of fiberglass to the attic, by what percentage would the heating cost of the house drop? Take the house to have dimensions 10 m by 15 m by 3.0 m. Ignore air infiltration and heat loss through windows and doors, and assume that the interior is uniformly at one temperature and the exterior is uniformly at another.

(a) 20%
(b) 30%
(c) 40%
(d) 50%

Answer 1

To calculate the percentage by which the heating cost of the house would drop after adding extra insulation, we need to compare the heat transfer before and after the insulation. The rate of heat transfer is inversely proportional to the R-factor, which is a measure of thermal resistance. By calculating the initial and final heat transfer rates, we can determine the percentage decrease and thus the percentage by which the heating cost would drop.

Step-by-step explanation:

To calculate the percentage by which the heating cost of the house would drop after adding extra insulation, we need to compare the heat transfer before and after the insulation. The rate of heat transfer is inversely proportional to the R-factor, which is a measure of thermal resistance.

Initially, the R-factor of the house is the sum of the R-factors of the existing insulation and the exterior surfaces. After adding the extra insulation, the R-factor of the house becomes the sum of the R-factors of the existing insulation, the extra insulation, and the exterior surfaces.

Using the formula Q = ΔT/(R×A), where Q is the heat transfer rate, ΔT is the temperature difference between the inside and outside, R is the thermal resistance, and A is the surface area, we can calculate the initial and final heat transfer rates. Then, we can find the percentage decrease in the heat transfer rate which would indicate the percentage by which the heating cost would drop.

In this case, assuming the temperature difference is constant and the surface area of the house is 10 m × 15 m × 6 m (excluding the floor), we can calculate the initial and final heat transfer rates. The percentage decrease in the heat transfer rate would be the percentage by which the heating cost of the house would drop.