The north wall of an electrically heated home is 20 ft long, 10 ft high, and 1 ft thick and is made of brick whose thermal conductivity is k = 0.42 Btu/h•ft•°F. On a certain winter night, the temperatures of the inner and the outer surfaces of the wall are measured to be at about 62°F and 25°F, respectively, for a period of 8 h. Determine (a) the rate of heat loss through the wall that night and (b) the cost of that heat loss to the homeowner if the cost of electricity is $0.07/kWh.

Question

What will be an ideal response?

Answer 1

The inner and outer surface temperatures of the wall of an electrically heated home during a winter night are measured. The rate of heat loss through the wall that night and its cost are to be determined.

Assumptions 1 Steady operating conditions exist since the surface temperatures of the wall remain constant at the specified values during the entire night. 2 Thermal properties of the wall are constant.

Properties The thermal conductivity of the brick wall is given to be k = 0.42 Btu/h?ft°F.

Analysis (a) Noting that the heat transfer through the wall is by conduction and the surface area of the wall is, the steady rate of heat transfer through the wall can be determined from



Therefore, the cost of the heat loss through the wall to the home owner that night is $0.51.