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.
