On a cold winter day, the outside temperature is –5.0 °C while the interior of a well-insulated garage is maintained at 20.0 °C by an electric heater. Assume the walls have a total area of 75 m2, a thickness of 0.15 m, and a thermal conductivity of 0.042 W/(m • C°). What is the cost to heat the garage for six hours at these temperatures if the cost of electricity is $ 0.11/kWh? Note: 1 kWh = 3.6 × 106 J.

Question

On a cold winter day, the outside temperature is –5.0 °C while the interior of a well-insulated garage is maintained at 20.0 °C by an electric heater. Assume the walls have a total area of 75 m2, a thickness of 0.15 m, and a thermal conductivity of 0.042 W/(m • C°). What is the cost to heat the garage for six hours at these temperatures if the cost of electricity is $ 0.11/kWh? Note: 1 kWh = 3.6 × 106 J.

$ 0.61

$ 0.18

$ 0.44

$ 1.09

$ 0.35

Answer 1

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Answer 2

To determine the cost to heat the garage, we need to calculate the amount of heat transferred through the walls and then convert it to energy usage.

First, let's calculate the rate of heat transfer (Q) through the walls using the formula:

Q = (k * A * ΔT) / d

Where:
- Q is the rate of heat transfer (in watts, W)
- k is the thermal conductivity of the walls (in W/(m • °C))
- A is the surface area of the walls (in square meters, m^2)
- ΔT is the temperature difference between the inside and outside (in degrees Celsius, °C)
- d is the thickness of the walls (in meters, m)

Plugging in the values:
Q = (0.042 W/(m • °C) * 75 m^2 * (20.0 °C - (-5.0 °C))) / 0.15 m

Q = 0.042 * 75 * 25 / 0.15
Q = 787.5 W

Next, we need to convert the rate of heat transfer into energy usage. Given that the time is 6 hours, we can use the formula:

Energy (in joules) = Power (in watts) * Time (in seconds)

Since 1 hour = 3600 seconds:
Energy (in J) = 787.5 W * 6 * 3600 s
Energy (in J) = 170,100 J

Now, let's convert the energy from joules to kilowatt-hours (kWh):

Energy (in kWh) = Energy (in J) / (3.6 * 10^6 J/kWh)
Energy (in kWh) = 170,100 J / 3.6 * 10^6 J/kWh
Energy (in kWh) = 0.04725 kWh

Finally, we can calculate the cost:

Cost = Energy (in kWh) * Cost per kWh
Cost = 0.04725 kWh * $0.11/kWh
Cost = $0.00519825

Rounded to 2 decimal places, the cost to heat the garage for six hours at these temperatures is approximately $0.01.

Therefore, none of the given options match the correct answer.