Determine the U- Factor of the Following Roof Assembly

Question

Examlex · Accepted Answer

The Answer is To determine the U-factor of the roof assembly, we need to calculate the U-factor for both the opaque part and the skylight, and then find the weighted average based on their respective areas.

The U-factor is the inverse of the R-value, which is a measure of thermal resistance. The formula to convert R-value to U-factor is:

U-factor = 1 / R-value

First, let's calculate the U-factor for the opaque part of the roof:

U-factor (opaque) = 1 / R-value (opaque)
U-factor (opaque) = 1 / 35
U-factor (opaque) = 0.02857 (rounded to five decimal places)

Next, let's calculate the U-factor for the skylight:

U-factor (skylight) = 1 / R-value (skylight)
U-factor (skylight) = 1 / 2.0
U-factor (skylight) = 0.5

Now, we need to find the weighted average U-factor for the entire roof assembly. To do this, we multiply the U-factor of each part by its respective area and then divide by the total area of the roof.

Weighted U-factor = (U-factor (opaque) * Area (opaque) + U-factor (skylight) * Area (skylight)) / Total Area

Total Area = Area (opaque) + Area (skylight)
Total Area = 2,500 ft² + 100 ft²
Total Area = 2,600 ft²

Weighted U-factor = (0.02857 * 2,500 ft² + 0.5 * 100 ft²) / 2,600 ft²
Weighted U-factor = (71.425 + 50) / 2,600
Weighted U-factor = 121.425 / 2,600
Weighted U-factor ≈ 0.04670 (rounded to five decimal places)

Therefore, the weighted average U-factor for the entire roof assembly, taking into account both the opaque part and the skylight, is approximately 0.04670.

Determine the U- Factor of the Following Roof Assembly

Definitions: