Question

In an electrically heated home, the temperature of the ground in contact with a concrete basement wall is 11.9 ^oC. The temperature at the inside surface of the wall is 21.7 ^oC. The wall is 0.12 m thick and has an area of 8.5 m². Assume that one kilowatt hour of electrical energy costs $0.10. How many hours are required for one dollar's worth of energy to be conducted through the wall?

Answer 1

Fourier's Law express conductive heat transfer as

q = k A dT / s (1)

where

A = heat transfer area (m2, ft2)

k = thermal conductivity of the material (W/m.K or W/m oC, Btu/(hr oF ft2/ft))

dT = temperature difference across the material (K or oC, oF)

s = material thickness (m, ft)

Assume K = 1.7 for concrete

q = (1.7 W/moC) x ( 8.5) x (21.7 - 11.9) / (0.12 m)

= 1180.08 watts

0.10 dollar = 1 kWh

So,

1 dollar = 1/0.1 = 10 Kilowatt hours or 10,000 watthours so

Time for 1 dollar = 10,000/1180.08 = 8.474 hours