Reality Math
Dot Sulock, University of North Carolina at Asheville
Measuring Electricity II
1. Kilowatt-hours!
According to the US Energy Information Agency, a branch of the US Department of Energy
Electricity consumption by 107 million U.S. households in 2001 totaled 1,140 billion kWh.
Understanding this headline requires some additional learning because kilowatt-hours (kWh) are very different from (kilowatts) kW. We’ll have to study more about units of electricity to grasp the concept of kilowatt-hours and 1,140 billion kWh.
The difference between the rate of flow of electricity in kW and amounts of billable electricity in kWh is pretty confusing to most people. Suppose a lawyer makes $100/hr. That is a high rate of pay. It is like your household needing 4 kW instead of
1 kW. But to determine much money the lawyer will charge for her services, we need to know how many hours she has worked.
($100/hr) X (5 hours) = $500
(4 kW) X (5 hours) = 20 kWh.
(kilowatts ) X ( hours used) = kilowatt-hours (kWh)
So if your clothes dryer is using 4000 watts for 1 hour, you will have bought
(4 kW) X (1 hr) = 4 kWh of electricity.
Similarly, watts x hours = watt-hours. 1000 watt-hours = 1 kWh.
1. How many kWh of electricity would your 10-watt clock radio use in
(a) one day?
(b) one month?
(c) one year? Assume that it is always plugged in.
Electricity in North Carolina costs about 10 cents per kWh. If your flat-screen TV draws 120 watts when it is on, and it is on 8 hours a day (US national average according to The Economist) every day, let’s figure out what the electricity for the TV will cost each year.
Well the TV will be on (8 hours/day) (365 days a year) = 2920 hours every year
(120 watts) (2920 hours) = 350,400 watt-hours = 350 kilowatt-hours
(350 kWh) ($0.10 each) = $35 for the electricity for the TV for a year
2. (a) What would electricity for your clock radio cost annually?
(b) If your hot water heater uses 3000 watts when it is heating water and it is actually heating water 4 hours a day, how much would the electricity for hot water cost in a year?
(c) Why it is important to insulate your hot water heater, turn it off when you are out-of-town, and put a timer on it so you are not heating water all day long when you don’t need it?
2. CO2 Emissions from Generating Electricity
According to the US Environmental Protection Agency, producing electricity in the US produces on average 1.4 pounds of CO2 per kWh.
(US Environmental Protection Agency eGRID2006 Version 2.1, April 2007)
3. If your household uses 1 kW on the average all day and night, how many pounds of CO2emissions would your household be responsible for if your electricity was average US electricity
(a) per day?
(b) per year?
(c) Estimate each household’s electrical CO2 footprint in tons per year.
2000 pounds = 1 ton
3. Total Household Electrical Consumption in the US
“Electricity consumption by 107 million U.S. households in 2001 totaled 1,140 billion kWh.” US Department of Energy
4. (a) If each household uses 1 kW of electricity on the average all of the time, how many kWh does each house use in a year?
(b) If 107 million households use 1 kW of electricity on the average all of the time, how many kWh would they all use in one year? Give your answer in million kWh.
Did you find that 107 million households would be expected to use 937,320 million kWh?
5. (a) Write out 937,320 million kWh with all of its zeros.
(b) How many billion kWh is this?
Compare our estimate of kWh in 15(b) with the DOE data in the quotation. (c) Our estimate in (b) is how many kWh less than the actual residential electrical usage?
(d) Our estimate is what percent less than the real number?
6. Our estimate was made assuming that US households average 1 kW of electrical demand, and our estimate was too
(a) low or high?
(b) So do US households really use (more or less?) than 1 kW of electricity on average.
(c) Estimate the actual kW electrical flow of US households.
4. Light Emitting Diodes (LEDs)
7. A traffic light is always on. If it uses one of its 150-watt bulbs all the time (red, yellow, or green)
(a) how many kwh does one light use in one year?
(b)If electricity costs $0.10 per kWh, how much does the electricity for one traffic light cost per year?
8. Denver, Colorado replaced its 150-watt incandescent traffic light bulbs with light emitting diodes (LEDs) that used 14 watts each instead in 13,000 traffic lights.
(a) How many KWh does one of these LED traffic lights use in one year?
(b) How much does the electricity for an LED traffic light cost per year?
(c) How many dollars per year does Denver save from this switch?
5. Large Scale Electricity and CO2
According to the CIA World Factbook, the US produced 4.12 trillion kWh of electricity in 2010.
9. To estimate how many tons of CO2 were put into the atmosphere producing this electricity,
(a) At 1.4 lbs per kWh, about how many pounds CO2 was emitted?
(b) How many tons is this?
(c) Communicate. Round off your answer to (b) to one significant digit and use the word millions, billions, or trillions to explain your discovery in a clear sentence.
(d) Reflect. Give one adverse effect coming from all this CO2.
10. Determine how much CO2 emissions Denver saves with their new LED lights every year.
(a) How many kWh saved per light?
(b) How many kWh saved in total?
(c) About how manytons of CO2 kept out of the atmosphere every year?
11. Reflect. Give two benefits from using less electricity.
1