Question

In an electrically heated home, the temperature of the ground in contact with a concrete basement wall is 12.0 oC. The temperature at the inside surface of the wall is 19.1 oC. The wall is 0.11 m thick and has an area of 8.8 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

7.04 h

Step-by-step explanation:

First, we determine the power required to heat the wall solving the Fourier's Law equation as follows:

Thermal conductivity of concrete:

`k=2.5(J)/(smK)`

`(Q)/(\Delta t) =-kA(\Delta T)/(\Delta x)\\(Q)/(\Delta t) =-2.5(J)/(smK)*8.8m^2(12.0^\circ C-19.1^\circ C)/(0.11m)\\(Q)/(\Delta t) =1420 (J)/(s)=1.42 kW\\\\C=0.10 (\$)/(kWh)*1.42kWh= \$0.142\\\\h=(\$1)/(0.142)= 7.04 h`

Finally,we determine the cost of the energy required to heat the wall per hour. Then, to determine the hours of power equivalent to $1, we divide and get the number of hours.