The ceiling of a single-family dwelling in a cold climate should have an R-value

Question

The ceiling of a single-family dwelling in a cold climate should have an R-value of 33 ft^2 middot F degree middot h/Btu. To give such insulation, how thick would a layer of (a) polyurethane foam and (b) silver have to be? The thermal conductivity of polyurethane foam is 0.024 W/m middot K, and thermal conductivity of silver is 428 W/m middot K. (a) Number Units (b) Number Units By accessing this Question Assistance, you will learn while you earn points based on the Point Potential policy set by your instructor.

Explanation / Answer

1 ft^2.F.h/Btu=0.1761 m^2.K/W

so R=33 *0.1761 m^2.K/W=5.8113 m^2.K/W

as R=L/k

where L=thick ness, k=thermal conductivity

part a:

for polyurethene foam:

L=R*k=5.8113*0.024=0.1395 m=13.95 cm

part b:

silver:

L=R*k=5.8113*428=2487.2364 m

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