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In an electrically heated home, the temperature of the ground in contact with a concrete basement wall is 10.1 oC. The temperature at the inside surface of the wall is 20.8 oC. The wall is 0.18 m thick and has an area of 8.9 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

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Answer:

17 hours

Explanation:

k = Thermal conductivity of concrete = 1.1 W/m┬░C

A = Area = [tex]8.9\ m^2[/tex]

l = Thickness = 0.18 m

[tex]\Delta T[/tex] = Change in temperature = 20.8-10.1

Power is given by

[tex]P=\dfrac{kA\Delta T}{L}\\\Rightarrow P=\dfrac{1.1\times 8.9\times (20.8-10.1)}{0.18}\\\Rightarrow P=581.961\ W[/tex]

Time required to produce 1 kWh

[tex]t=\dfrac{3600\times 10^3}{581.961}\\\Rightarrow t=6185.98153485\ s[/tex]

For one dollar

[tex]t=\dfrac{6185.98153485}{0.1}\\\Rightarrow t=61859.8153485\ s\\\Rightarrow t=\dfrac{61859.8153485}{60\times 60}\\\Rightarrow t=17.1832820412\ hours[/tex]

The time taken is 17 hours

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