Calculating the Cost Effectiveness of Compact Fluorescent Lights (CFL) · Physics Playground

Example 20.8 from College Physics, 20.4 Electric Power and Energy

Calculating the Cost Effectiveness of Compact Fluorescent Lights (CFL)

If the cost of electricity in your area is 12 cents per kWh, what is the total cost (capital plus operation) of using a 60-W incandescent bulb for 1000 hours (the lifetime of that bulb) if the bulb cost 25 cents? (b) If we replace this bulb with a compact fluorescent light that provides the same light output, but at one-quarter the wattage, and which costs $1.50 but lasts 10 times longer (10,000 hours), what will that total cost be?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
To find the operating cost, we first find the energy used in kilowatt-hours and then multiply by the cost per kilowatt-hour.
Solution for (a)
The energy used in kilowatt-hours is found by entering the power and time into the expression for energy:

$E = Pt = (60 W) (1000 h) = 60,000 W \cdot h.$
20.35

In kilowatt-hours, this is

$E = 60 . 0 kW \cdot h.$
20.36

Now the electricity cost is

$cost = (60.0 kW \cdot h) ($0.12 /kW \cdot h) = $ 7.20.$
20.37

The total cost, including the cost of the bulb, will be $7.45 for 1000 hours (about one-half year at 5 hours per day).
Solution for (b)
Since the CFL uses only 15 W and not 60 W, the electricity cost will be $7.20/4 = $1.80. The CFL will last 10 times longer than the incandescent, so that the investment cost will be 1/10 of the bulb cost for that time period of use, or 0.1($1.50) = $0.15. Therefore, the total cost will be $1.95 for 1000 hours.
Discussion
Therefore, it is much cheaper to use the CFLs, even though the initial investment is higher. The increased cost of labor that a business must include for replacing the incandescent bulbs more often has not been figured in here.

0 of 4 steps open

How did it go?

Strategy

Solution for (a)

Solution for (b)

Discussion