Question

The roof of an electrically heated home is 6 m long, 8 m wide, and 0.25 m thick, and is made of a flat layer of concrete whose thermal conductivity is k= 0.8 w/m.°c. the temperatures of the inner and the outer surfaces of the roof one night are measured to be 15°c and 4°c, respectively, for a period of 10 hours. determine (a) the rate of heat loss through the roof that night and (b) the cost of that heat loss to the home owner if the cost of electricity is $0.08/kwh.

Answer 1

The rate of heat loss through the roof is 4.8 W and the cost of that heat loss to the homeowner is $0.0384.

Step-by-step explanation:

(a) Rate of heat loss through the roof:

To calculate the rate of heat loss through the roof, we need to use the formula for heat conduction:

Q = (k * A * ΔT) / t

Where:

• Q is the rate of heat loss
• k is the thermal conductivity of the concrete
• A is the area of the roof
• ΔT is the temperature difference between the inner and outer surfaces
• t is the time period

Plugging in the values:

Q = (0.8 * 6 * 8 * (15 - 4)) / 10

Q = 4.8 W

Therefore, the rate of heat loss through the roof is 4.8 W.

(b) Cost of heat loss:

To calculate the cost of heat loss, we need to convert the rate of heat loss from watts to kilowatts and then multiply by the cost of electricity:

Cost = (Q / 1000) * electricity cost * time

Plugging in the values:

Cost = (4.8 / 1000) * 0.08 * 10

Cost = $0.0384

Therefore, the cost of heat loss to the homeowner is $0.0384 for that night.