A 24-watt fluorescent light is left on for several hours during which time it is supplied with 432 kilojoules of energy. For how many hours was the light left on?
Let’s start by highlighting the important parts of the question. Firstly, we know that we’ve got a light and it’s a 24-watt light. It’s left on for several hours. And in that time, it’s supplied with 432 kilojoules of energy. What we’re asked to do is to find out how many hours the light was left on for. Now, we know that the light is a 24-watt light. But what does watt mean? If you’ll pardon the pun, a watt is a unit of measurement of power. Which means that here, we’re dealing with power as well as energy, which is what we’ve been told in the question, and time. So we need to find the relationship between the power of the light, the energy with which it’s supplied, and the amount of time for which the light is left on.
Well, if we look at the definition of power, we notice that it’s defined as the rate of energy transfer. This means that it is going to be dealing with all the quantities we’re looking for, because the rate of something simply means how much of that something is happening in a given unit of time. So when we say that the power is the rate of energy transfer, what we’re trying to say is that power is the amount of energy transferred per unit time. In symbols, we can write that as the power 𝑃 is equal to energy 𝐸 divided by time 𝑡. And happy days, this equation deals with the three quantities given to us in the question. So all we need to do is to rearrange it a bit to solve for the amount of time the light was left on for.
If we multiply both sides of the equation by the time divided by the power, we’re left with the time 𝑡 is equal to the energy 𝐸 divided by the power 𝑃. So all we need to do is to substitute our values in for the energy and for the power. And we should get an amount of time. One thing to notice though is that the energy is given to us in the question in kilojoules. We need to convert this to the standard unit of joules. Fortunately, this doesn’t take long. The prefix kilo simply means 1000. So one kilojoule simply means 1000 joules. And so 432 kilojoules simply mean 432 times 1000 joules. And that’s just 432000 joules. So now we can substitute that into our equation.
The time for which the light was left on is equal to 432000 joules divided by 24 watts. That ends up being 18000. And the unit is seconds because we use the standard units of joules for energy and watts for power. However, that’s not our final answer. If we read the question carefully, it wants the number of hours that the light was left on for. So we simply need to convert our time from seconds to hours. We know that every hour has 60 minutes in it. And every minute has 60 seconds in it. From this, we can find out the number of seconds in one hour. And that just happens to be 60 times 60 seconds. And that ends up being 3600 seconds. So if one hour is equivalent to 3600 seconds, then how many hours is equivalent to 18000 seconds? We can find this out simply by doing 18000 divided by 3600. That’s because the 3600 is equivalent to one hour. So we need to see how many lots of 3600 go into 18000. And that just happens to be exactly five.
So our final answer is that the light was left on for exactly five hours.