Power
Power is the rate at which work is being done, or equivalently, the rate at which energy is being used (transformed from one form into another).
or, written more succinctly,
The SI unit of power is the unit of work or energy (Joules) divided by the unit of time (seconds). "Joules per second" isn't such a big mouthful, but it has nevertheless been given a special name, the Watt, abbreviated W.
You've probably heard of watts before, if for no other reason than changing a lightbulb. For old-style incandescent lightbulbs, 60W, 75W and 100W were the most typical brightnesses.
You have to be careful! We have two W's we'll be using a lot: W for "work", and W for "Watts".
Example 1 A typical household incandescent lightbulb has a power of 75 W. How much energy does such a bulb use in an hour?
Solution Because power = energy / time, energy = power · time.
1. Human metabolism, on average, uses about 100W of power.
(a) How much energy do you use in one day, in joules?
(b) Use the factor-label method to convert that energy from joules into food calories. (One food calorie is 4186 J.)
Other units
A common unit of power you may have heard of is the horsepower (hp).
1 hp = 746 W
A common unit of energy, often appearing on household electricity bills, is the kilowatt-hour — the total energy expended in one hour when used at a rate of 1000 Joules/sec.
Additional Problems
3. My hairdryer uses energy at the rate of 1200 Watts.
(a) If I dry my hair for 15 seconds (I don't have much hair) how much energy is used?
(b) If that amount of energy were used to lift a one-kilogram mass, how high could it go?
4. One model of the Ford F150 pickup truck can do work at the rate of 292 horsepower.
(a) How many watts is that?
(b) If you could use all that power to run 75-W lightbulbs, how many lightbulbs could you light?
(c) How much time would it take that truck to do 1.0 kW·hr of work?
5. A Gilded Sapphire hummingbird, with a mass of 4 grams, uses 0.40 watts of power in order to live. This is an average: it uses energy at a higher rate when flying (especially hovering) and less when resting at night.
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6. The power of a bumblebee in flight is about 0.02 watts.
(a) How much time will it take a flying bumblebee to use one joule of energy?
(b) How much time will it take a flying bumblebee to use one food calorie of energy?
7. My laptop computer uses about 65 watts when it is on.
(a) How much energy (in joules) does the computer use in 8.0 hours?
(b) How much is that, in kilowatt·hours?
(c) If the electric company charges 9.0 cents per kW·hr, how much money does it cost to run the computer for that time period?
(d) Electric companies typically release about 1.5 pounds of carbon dioxide into the atmosphere for each kW·hr of energy they produce. How much CO2 am I responsible for emitting if I leave the computer on for 8 hours?
8. The chemical energy in a gallon of gasoline is about 1.3x108 J. Humans need about 100 W of power to live. If you could get energy from gasoline instead of food, how long could you live on one gallon of gasoline?
9. Mr. Spock and his evil twin (who is identical to Mr. Spock in every way, except for the goatee and the evilness) both climb the same set of stairs. Mr. Spock climbs the stairs in 30 seconds, but the evil Mr. Spock takes 0.30 minutes.
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