Question

In an electrically heated home, the temperature of the ground in contact with a concrete basement wall is 11.2 oC. The temperature at the inside surface of the wall is 20.4 oC. The wall is 0.17 m thick and has an area of 7.0 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 ( 7) x (20.4 - 11.2) / (0.17 m)

=644 watts

1 dollar = 5 Kilowatt hours or 5000 watthours

so

Time for 1 dollar = 5000/644 =7.76 hours