Question

In an electrically heated home, the temperature of the ground in contact with a concrete basement wall is 11.1 degrees Celsius. The temperature at the inside surface of the wall is 20.9 degrees Celsius. The wall is 0.19 m thick and has an area of 7.9 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?

a) 47 hours
b) 29 hours
c) 52 hours
d) 38 hours

Answer 1

The question asks for the amount of time it takes for one dollar's worth of energy to be conducted through a concrete basement wall, given certain temperature conditions and the wall's physical characteristics. By using the heat conduction formula and factoring in the cost of electricity, we can calculate the required time.

Step-by-step explanation:

To determine how many hours are required for one dollar's worth of energy to be conducted through the wall, first, we need to calculate the rate of heat transfer through the wall via conduction using the formula:

Rate of Heat Transfer (P) = κ×A×ΔT/L

Where:

• κ is the thermal conductivity of concrete (assumed to be 1.7 W/m·K),
• A is the area of the wall (7.9 m²),
• ΔT is the temperature difference across the wall (20.9°C - 11.1°C = 9.8°C),
• L is the thickness of the wall (0.19 m).

Once we have the power in watts, we convert it to kilowatts by dividing by 1000:

P (kW) = P (W) / 1000

Then, we can determine the cost per kilowatt-hour and hence the number of hours for one dollar's worth of energy:

Hours = $1 / (P (kW) × Cost per kWh)

Assuming a cost of $0.10 per kWh, we can insert the values to get the result. After calculating, we would find that the correct answer is a specified number of hours.