Question

In an electrically heated home, the temperature of the ground in contact with a concrete basement wall is 10.7 °C. The temperature at the inside surface of the wall is 23.9 °C. The wall is 0.15 m thick and has an area of 8.4 m2. Assume that one kilowatt · hour of electrical energy costs $0.12. How many hours are required for one dollar's worth of energy to be conducted through the wall?

Answer 1

Answer:

Fourier's laws

Explanation:

The problem can be solved if Fourier's laws for conductivity are applied as well,

$q = k A \Delta T / s$       (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))

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

s = material thickness (m, ft)

The thermal conductivity of concrete is k= 1.7

$q = (1.7 W/moC) *( 8.4) *(23.9 - 10.7) / (0.15 m)$

$q= 1256.64 watts$

Since

1 dollar = 5 Kilowatt hours or 5000 watthours so

Time for 1 dollar = 5000/1256.64 = 3.978 hours or  3 hours 58 minutes