Question

The ceiling of a single-family dwelling in a cold climate should have an R-value of 28 ft² ·F°·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·K, and the thermal conductivity of silver is 428 W/m·K.

Answer 1

The thickness of insulator layer is given by

   ------- (1)

where R is the heat transfer resistance and k is the thermal conductivity

We have the R value but it is not in SI unit. to covert this.

1)For Polyeurethane foam

k=0.024 W/m·K and we have R=

substitite in Eq.(1)

2) For silver

k=428 W/m·K   and R is same as before

then

So there is a large change in thickness with thermal conductivity