Watts and kilowatts - Math Central

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Question from Kenneth:

Hello:

Here is my question:

Find the kilowatt-hours of electricity used by a light bulb with a rating of 60 watts if the light is used for 10 hours.

The information in my textbook indicates the following: "An electric light bulb, for example, may be marked "60 WATT." This number is called the rating of the bulb.
It means that the bulb uses 60 watt-hours of electricity in one hour."

1. Is this the same as (60 watt-hours) / (1 hour) or (60 watts) / (1 hour) or neither?

2. I want to know how the different units cancel from the calculation. Here is my solution, but it is not totally correct.

If the bulb burns for 10 hours, it will use 600 watt hours of electricity. This equals 0.6 kilowatt hours.

10 hours X (60 watts) / (1 hour) = (600 watt-hours) / (1hour)
= (600 watt-hours) / (1 hour) divided by (1000 watts) / (1 kilowatt)
= (600 watt-hours) / (1 hour) X (1 kilowatt) / (1000 watts) = 0.6 kilowatts

The correct answer is 0.6 kilowatt-hours not 0.6 kilowatts.

I know that the 0.6 is correct, and I am sure that my solution is incorrect because the units do not cancel with kilowatt hours remaining as the unit in the answer.

Can you explain?

I thank you for your explanation.

We have two responses for you

Kenneth,

60 watt-hours of electricity in one hour means 60 watt-hours per hour or 60 watt-hours/hour. If the bulb burns for 10 hours that's

60 watt-hours/hour × 10 hours
= 600 watt-hours
= 600 watt-hours × 1/1000 kilowatts/watt
= 0.6 kilowatt-hours.

Harley

Hi Kenneth.

1. Is this the same as (60 watt-hours) / (1 hour) or (60 watts) / (1 hour) or neither?

The first. (60 watt-hours) / (1 hour) means the "hour" units cancel and you have 60 watts. That's a power rating.

Watts are a power unit, Watt-hours (literally, this is watts times hours) are an energy unit. Thus, energy is power times time (E = Pt)

A bulb is rated for a particular power (60 watts). If you run it for any period of time, it uses up energy (watt-hours, or kilowatt-hours if it is a particularly powerful bulb).

If it helps, think about power like speed and energy like distance. A vehicle can go a particular speed and a bulb can burn at a certain power. If you multiply that by time, you get the total distance travelled or the total energy consumed.

Power and energy really are quite different ideas and it is great that you are getting it straight!

Cheers,
Stephen La Rocque.

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