In an electrically heated home, the temperature of the ground in contact with a

Question

In an electrically heated home, the temperature of the ground in contact with a concrete basement wall is 12.3 °C. The temperature at the inside surface of the wall is 22.5 °C. The wall is 0.11 m thick and has an area of 8.1 m2. Assume that one kilowatt · hour of electrical energy costs $0.14. How many hours are required for one dollar's worth of energy to be conducted through the wall?
h In an electrically heated home, the temperature of the ground in contact with a concrete basement wall is 12.3 °C. The temperature at the inside surface of the wall is 22.5 °C. The wall is 0.11 m thick and has an area of 8.1 m2. Assume that one kilowatt · hour of electrical energy costs $0.14. How many hours are required for one dollar's worth of energy to be conducted through the wall?
h

Explanation / Answer

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 (8.1) x (22.5 - 12.3) / (0.11 m)

= 1276.85 watts

1 dollar = 5 Kilowatt hours or 5000 watthours so

Time for 1 dollar = 5000/1276.85 = 3.91 hours

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