If only conductive heat loss was significant for a house, then by what percentage would you lower the heat loss if the temperature was reduced inside from 70 F to 60 F when the outside temperature is 20 F?

Question

Physics

Jaslene Campos

29 June, 15:22

If only conductive heat loss was significant for a house, then by what percentage would you lower the heat loss if the temperature was reduced inside from 70 F to 60 F when the outside temperature is 20 F?

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Harley Boyle · Answer 1

Let's try and solve this using the heat conductivity equation. Q=-kA (ΔT) / (Δx)

Where Q represents heat loss, k represents thermal conductivity, A represents area of the wall, and x is the thickness of the wall.

We'll assume everything except Q and delta T is for this case only, 1.

Case 1 : 70 F - 20 F = 50 F. Q=-1*1 (50) / (1)

That's - 50. Negative because energy is being transferred outside. Assuming the same trend ...

Case 2 : 60F - 20F = 40F difference. I'm going to skip the calc. for this one, since it's pretty obvious. You're ending up with - 40 as the answer here.

Now, let's express the answer of Case 2 where the temp difference is - 40, as a percentage of Case 1.

-40-50*100=80

Therefore, you're lowering the heat loss by 20%.