Save Money and Save the Earth
Improving energy efficiency is not only good for the planet but it can save you and your family a lot of money, too. As an example of how much, consider just a single 100-watt light bulb (of the old-fashion, incandescent type). Suppose your family leaves this light bulb turned on for an average or 8 hours a day, and your utility company charges a price of 15¢ per kilowatt-hour for electricity. How much does it cost to operate this light bulb for a year? How much would you save if you replaced the bulb with a 25-watt LED bulb that gives off as much or more light?
Step 1 Understand the problem. There are several ways you could proceed to calculate the answers, but here is one easy way:
- First, recall that watts are a unit of power, so the energy used in some amount of time is:
energy = power × time
- Next, recall that a kilowatt is 1,000 watts, so the 100-watt power of the light bulb is equivalent to 0.1 kilowatt.
- Therefore, because you have the light bulb turned on for 8 hours each day, its daily energy use is:
daily energy use = 0.1 kilowatt × 8 hours = 0.8 kilowatt-hour - You can then find its annual energy use by multiplying by 365 days in a year:
yearly energy use = 365 × daily energy use = 365 × 0.8 kilowatt-hour = 292 kilowatt-hours
Now that you know how much energy the light bulb uses in a year, you can find the operating cost by multiplying by the energy price of 15¢ (or $0.15) per kilowatt-hour. You can then find the savings by noticing that a 25-watt LED bulb needs only ¼ as much energy as the 100-watt bulb.
Step 2 Solve the problem. To find the price of operating the 100-watt light bulb for a year (at 8 hours per day), we multiply the annual energy use found in Step 1 by the price:
The operating cost of the 25-watt LED bulb would be ¼ of that, or $43.80 × 4 = $10.95.
Step 3 Explain your result. We’ve found that if you leave a single, 100-watt light-bulb on for 8 hours per day, its operating cost for a year (at 15¢ per kilowatt-hour) is nearly $44. Replacing it with a 25–watt LED bulb reduces the operating cost to only about $11, a savings of $33. In other words, you get the same benefit (in this case, the same amount of light) while saving a lot of money! Also notice that the operating cost is much higher than the cost of buying the light bulb, since most light bulbs (even LEDs) cost only a few dollars or less.
Check Your Skills
- Find the current price of electricity (per kilowatt-hour) charged by your local utility company. Then repeat the problem to find out how much you would save by replacing the 100-light bulb by a 25-watt LED. Use the same assumptions of operating the bulb for 8 hours per day for a year.
- Many schools and commercial buildings use a lot of lighting. Consider, for example, a hotel that has 100 rooms, each with 5 light bulbs that are left on for an average of 6 hours per day. What would the hotel’s annual lighting cost be if all the bulbs are 100-watt incandescents? How much would the hotel save by replacing those bulbs with 25-watt LEDs? Assume an electricity price of 15¢ per kilowatt-hour.
The math in this box is fairly easy once students understand the units, and we have previously discussed units of power in Section 4.2.3 (which you may wish to have your students review). You may even wish to extend this problem by giving other similar examples of savings through energy efficiency. Answers to the Check Your Skills:
- (1) The answer will depend on your local electricity price. Note that there are two basic ways to find the answer. The simplest is simply to multiply the answers from the example by the relative electricity cost. For example, if your local price is 10¢/kilowatt-hour, then the answers would be 2/3 of what we found at 15¢ per kilowatt-hour. However, to make sure students understand the concepts behind the calculation, you may wish to have them follow the example procedure, showing their work clearly at each step. This should help them do the second question.
- (2) Following the basic procedure of the example (but there are alternative approaches you could use): With 100 rooms and 5 light bulbs per room, the hotel has 500 light bulbs, which means that when all are turned on, they have a combined power requirement of 500 × 100 watts = 50,000 watts, or 50 kilowatts. Operated for 6 hours per day, this means an annual energy use of:
yearly energy use =
At a price of 15¢ per kilowatt- hour, the lighting cost is:
Switching to 25-watt LEDs, would save ¾ of this total, which is a savings of more than $12,000. You might then discuss with students why virtually all hotels and other commercial buildings have already switched to LEDs or other efficient light bulbs.