Question

A homeowner wants some insulation blown into her attic. The original quote was for 16 cm of R-17 rated insulation. If she wants the attic insulated to R-44, what thickness (in cm) does she need to use

Answer 1

To achieve an R-44 rating in the attic, the homeowner needs to add approximately 5.82 cm of insulation.

Step-by-step explanation:

The R factor is a measure of the insulation's resistance to heat transfer. In this case, the homeowner wants to insulate the attic to an R-44 rating. The original quote was for 16 cm of R-17 rated insulation. To determine the thickness of insulation needed, we can use the fact that the R factor is directly proportional to the thickness of the insulation.

Let's assume that the original insulation has an R factor of 1 for every centimeter of thickness. Therefore, the original insulation has an R factor of 16. To achieve an R factor of 44, we need to find the additional thickness needed.

By using the formula R1 x D1 = R2 x D2, where R1 is the original R factor, D1 is the original thickness, R2 is the desired R factor, and D2 is the desired thickness, we can calculate the additional thickness needed:

16 cm x 16 = 44 x D2

Solving for D2, we get:

D2 = (16 cm x 16) / 44

Therefore, the homeowner would need to add approximately 5.82 cm of insulation to achieve an R-44 rating in the attic.

Answer 2

Answer: the value of the required thickness is 41.4 cm

Explanation:

Given that;

R1 = 17

R2 = 44

L1 = 16

L2 = ?

we know that, from thermal conductivity formula

P = 1 / R

P = k / L

1 / R = k / L

since k of a distinct material is constant,

we can take

L / R = constant

L1 / R1 = L2 / R2

L1R2 = L2R1

L2 = (L1 × R2) / R1

so we substitute

L2 = (16 × 44) / 17

L2 = 704 / 17

L2 = 41.4 cm

Therefore the value of the required thickness is 41.4 cm