The ceiling of a single-family dwelling in a cold climate should have an R-value of 25. To give such insulation, how thick would a layer have to be if it were made of each of the following materials?
(a) polyurethane foam (thermal conductivity k = 0.024 W/m · K)
To calculate the thickness of the insulation layer, we can use the formula:
R = (Thickness of insulation layer) / (Thermal conductivity)
Given that the desired R-value is 25 and the thermal conductivity of polyurethane foam (k) is 0.024 W/m · K, we can rearrange the formula to solve for the thickness:
Thickness of insulation layer = R * Thermal conductivity
Plugging in the values, we have:
Thickness of insulation layer = 25 * 0.024
Calculating further:
Thickness of insulation layer = 0.6 meters
Therefore, if you want to achieve an R-value of 25 using polyurethane foam with a thermal conductivity of 0.024 W/m · K, the insulation layer would need to be approximately 0.6 meters thick.