Video: Finding the Power of an Electrical Appliance

A microwave is used for 5 minutes, during which time it is supplied with 180 kJ of energy. What is the power of the microwave?

02:14

Video Transcript

A microwave is used for five minutes, during which time it is supplied with 180 kilojoules of energy. What is the power of the microwave?

Okay, so we have this microwave. And clearly, something delicious is cooking inside. It’s being used for five minutes. We’re told that over this span of time, 180000 joules of energy is delivered to the microwave. The question is what’s the power of the microwave. To see what this is, let’s recall the relationship between power, energy, and time.

The equation connecting those three says this. It says that the power involved in a process is equal to the energy used divided by the time that the process took. In this scenario, we’re given both the energy used and the time elapsed. So we can substitute in those values now. The power of the microwave is equal to 180000 joules divided by five minutes.

Now, what we’ve written so far is true. But the units in this expression, particularly, on the right-hand side, aren’t what we want them to be. We can recall that the base units of energy are joules, the base units of time are seconds, and the base units of power are watts. In other words, we can see that one watt is equal to one joule of energy used up in one second.

When we go to calculate the power of the microwave, we would like to get our answer in units of watts. But in order to get that, we need to have the right-hand side in units of joules per second. We haven’t quite got there yet. We can see that our energy is currently in units of kilojoules not joules and our time is in minutes rather than seconds. Here’s what we can do about that.

We can recall in the first place that one kilojoule is equal to 1000 joules. That’s what the prefix kilo refers to. And we can also recall when it comes to time that one minute of time is equal to 60 seconds, where seconds of course is the time unit we’re interested in. If we take this information then and apply it to our fraction, we can write that our power is equal to the energy of 180 times 10 to the third joules divided by the time of five times 60 seconds.

And notice now that we’ve done this conversion, we have units of joules per second, in other words watts. When we calculate all this out, we find an answer of 600 watts. So that is the power of this microwave.