Video: Units of Energy

In this lesson, we will learn how to convert between the S.I. unit of energy, joules, and the units of energy more commonly used to describe energy production, such as the kilowatt-hour.


Video Transcript

In this video, we’re talking about units of energy. We’re going to learn how to account for energy in different measurement systems. And we’ll also learn what is the physical meaning behind these different units. What does it mean in the real world. But before we get into the units of energy, let’s consider what energy is by itself. Energy is something we all have experience with. For example, riding in a car, we experience energy due to motion. Or, say, warming our hands by a campfire, we experience heat energy. Or say that we pick up a stiff spring and we compress it with our hands. In order to hold the spring in that compressed position, we’ll experience potential energy. We see then that energy can take all different kinds of forms. But in each and every one of these forms, the energy involved has the capacity to do something. And, that is, it has the ability to do work.

Now, in physics, this word “work” has a special meaning. It refers to a situation where we’re applying some amount of force over some amount of distance. For example, say that we want to slide a box across the floor. In order to do so, we’ll need to exert a force on the box. We could label that force 𝐹. And then we’ll say that, thanks to the application of this force, the box moves along the floor. And say that we call that distance the box moves 𝑑. Well, in that case, the work done by this force 𝐹, and we can represent this work using the letter capital 𝑊, is equal simply to the force multiplied by the distance 𝑑.

Now, since this force 𝐹 did work on the box. Then we can say that whatever it was that supplied this force and maybe it was us pushing on the box had energy. That is, the ability to do work. Energy, then, is very closely related to work, which is equal to an applied force multiplied by the distance an object moves under that force. And here is just how closely these two terms are related. We can say that the energy applied to the box, we’ll call that 𝐸 sub ap. That that energy is equal to the work done on the box. After all, energy is the ability to do work. So the work done equals the energy applied. And going further, our relationship here says that work itself is equal to an applied force, we call that 𝐹, multiplied by the distance over which the force acts.

Now, taking a look at the far right side of these two equations, a force times a distance. Let’s remind ourselves what are the units of these terms. When it comes to the units of force 𝐹, we know that the base units of force in the SI system are newtons, abbreviated capital N. And we can recall that a newton can be further broken down into kilograms, meters, and seconds. One newton is equal to a kilogram times a meter per second squared. This is because a newton is defined as how much force is needed to accelerate a mass of one kilogram from rest to a speed of one meter per second over a time of one second.

In other words, say that we had a mass of exactly one kilogram sitting here on the surface. And we’ll say that this is a frictionless surface. Well, if this mass started from rest with an initial speed of zero, then one newton of force is the amount of force that would be needed to accelerate this kilogram mass. So that it acquires a speed of one meter per second. And that that acceleration takes place over an interval of one second. That is, pushing on this mass with one newton of force for one second gives it a final speed of one meter per second. That’s an overall force of one newton.

Anyway, that’s the SI unit of force, newtons. The SI unit of distance is the meter. This means that when we calculate the work done on an object or, for that matter, the energy applied to it. We’re going to get an answer with units of newtons times meters. And it turns out that this combined unit, a newton-meter, goes by another simpler name. A newton of force multiplied by a meter of distance is called a joule. It’s abbreviated using a capital J. And this is the unit that represents work done or energy applied. So then, when it comes to the units of energy, in the SI system, energy has these units, joules. Where a joule is a newton times a meter. Now, an important condition on all this, an important caveat, is that we’re talking about a specific unit system, the SI system. 99 percent of the time, that’s the system we use. But it’s not the only one out there.

To see why not, let’s clear a bit of space on screen. Imagine that we go to the hardware store to pick up a box of light bulbs. When we find some bulbs we like, we notice on the box is printed out this rating, 60 watts. This means that if we were to put one of these bulbs in a lamp, say in our house. Then that bulb as it shines would have a certain brightness that depends on how much energy the bulb is using up over an amount of time. So when it comes to light bulbs and other electrical appliances, it’s not just the energy that that appliance uses that we’re interested in. But how fast it uses up that amount. In other words, we’re talking about an energy usage rate. So when we look at a light bulb or say a microwave or a heater or some other electrical appliance, we won’t be told how many joules of energy the appliance uses. But rather we’ll be told how much energy the appliance uses per some amount of time. That’s the rate of energy use. The term for that rate, an amount of energy per an amount of time, is power.

Thinking about this definition, we see that it shows us there are two ways to increase or decrease power in any given situation. Say, for example, that we’re climbing up a staircase of stairs. In order to do this, in order to climb the stairs, it will take energy. We’re working against the force of gravity. And not only that, but our output of energy to climb the stairs will take place over some amount of time. This means that as we climb a staircase, we’re using some amount of power. Let’s say that, over a time of five seconds, we climb up to the second stair on the stairway of very large stairs. In order to do this, in order to get up to this new height, an height ℎ we could say above ground level, we had to use up energy. And we did it over a time of five seconds. So that implies some amount of power output.

Well, let’s say we started back at the bottom of the staircase. And now we wanted to expend more power. There are a couple of ways we could do that. One way would be to take the same amount of time as we took before, five seconds. But now, we climb to a higher height. We can call it ℎ two. In doing this, we’ve kept the amount of time the same. But we’ve increased the energy. And therefore, we’ve increased the power output. But another way to use more power is starting from the bottom to climb up to the same stair as we originally did. But take less time to do it. Say we do it in three seconds. In this case, we’ve kept our energy output the same as it was originally. But we’ve decreased the amount of time it took us to do it. And by doing this, we’ve increased our power output.

Now, if we take a look at the units in this equation, energy divided by time is equal to power. Working within the SI system, we know the units of energy are joules. And the units of time are seconds. When we divide one joule of energy by one second of time. That’s equal to what’s called one watt of power. This is the SI unit of power, named after James Watt. In addition to understand the units of this expression for power, let’s see what happens if we multiply both sides of the equation by time. When we do that on the left-hand side, this amount of time in the numerator cancels with the time in the denominator. And we see that energy is equal to power times time. And this makes sense if power is equal to energy divided by time. All we’ve done is algebraically rearranged this expression.

And this brings us back to our light bulbs and our electrical appliances that we use in our houses. The way that energy is described for appliances we use in our homes is in terms of an amount of power, in units of watts or kilowatts or gigawatts, multiplied by an amount of time, often a time of hours. When it comes to residential energy supply. The most common unit of energy used is a unit of power, called a kilowatt, which is 1000 watts, times an amount of time of one hour, 3600 seconds. And we can realize, based on our equation for energy, that it’s equal to an amount of power times an amount of time. That a kilowatt hour is an amount of energy, just like a joule is an amount of energy.

Now, taking a look at kilowatt hours. Here’s what that means practically. Say that we have a microwave in our house. And this particular microwave is rated at 1000 watts. That means that when it’s in operation, it’s using 1000 watts of power. Or, in other words, 1000 joules of energy every second. If we were to run this microwave continuously for one hour, I’m not sure why we would do that. But let’s just say we are. Then the total energy that the microwave would need would be 1000 watts of power times one hour of time. Or since 1000 watts is equal to one kilowatt. Over this time period, the microwave would use up a total of one kilowatt hour of energy. As strange as this unit kilowatt hours may seem.

For many of us on the outside of our house, there’s a meter that measures the electrical use of the house. And if we look closely at this meter, we’ll likely see that it measures energy use, that is, electrical energy, in units of kilowatt hours. It’s a way of understanding how long electrical appliances that require a certain amount of power are being powered. And indeed, electrical companies typically use this unit, kilowatt hours, to charge for their service.

So after all that, here’s where we stand. In the SI system, energy has units of joules. But in electrical applications, energy is measured in units of kilowatt hours. And this raises the question, how can we convert from one set of energy units to the other? In other words, how could we go from an amount of energy in kilowatt hours to an amount in joules. Or, in the opposite direction, joules to kilowatt hours. And the key to understanding these conversions in either direction is to understand how watts, joules, and hours are related.

We saw earlier that one watt, the unit of power, is equal to one joule divided by one second. Another way of saying it is that a watt is equal to a joule of energy transferred over a time of one second. So this means that, over here, in kilowatt hours, we can replace the watt with a joule per second. We now have a unit of kilojoules per seconds times hours. And what we want to do to the left side here is to have it read simply joules multiplied by some factor that we’ll call the conversion factor. So let’s see how we can do that.

Starting off, we can replace this kilo with 1000. That’s what that prefix means. A kilojoule per second is the same thing as 1000 joules per second. And next, let’s consider this time in hours. We know that there are 60 minutes in one hour. And there are 60 seconds in one minute. And that means there are 60 times 60 or 3600 seconds in one hour. If we replace one hour with 3600 seconds, then notice what happens to the units of seconds in the denominator and numerator. They cancel out with one another. Then we notice that if we take this value 3600 and we move it to the front and multiply it by 1000. Then when the dust settles, we wind up with this result of 3600000 joules. At this point, let’s remember what this number is. This is equal to one kilowatt hour of energy. We’ve just discovered that one kilowatt hour of energy is equal to 3600000 joules. And we can now write that out as an equation. So this, then, is how we’ll convert from one unit of energy, joules, to another, kilowatt hours.

Because electrical energy is most commonly measured in units of kilowatt hours, this particular conversion between kilowatt hours and joules will probably be the most useful to us. But we’re in no way limited to using this specific energy unit. For example, what if, instead of kilowatt hours, we had gigawatt hours. We know the prefix kilo refers to 1000 while the prefix giga refers to one billion. Or, instead of that, we could be talking about megawatt hours or even simply watt hours. All four of these are an expression of an amount of energy, typically in electrical context. And so long as we know how to work with the prefixes that they may have, we’ll be able to convert any one of these expressions into an expression of energy in joules. Knowing all this about units of energy, let’s get some practice now with these ideas through an example.

Which of the following is the correct definition of a watt-hour? A) A watt-hour is the amount of time it takes for a process to increase in power from zero watts to one watt. B) A watt-hour is a measure of the power of a process that is equivalent to the transfer of one joule of energy in one hour. C) A watt-hour is the amount of energy that an electrical device transfers in one hour. D) A watt-hour is the amount of energy transferred by a process that has a power of one watt and acts for one hour. E) A watt-hour is the amount of time it takes for a one-watt device to transfer one joule of energy.

Okay, considering these five options, we want to know which one offers the correct definition of a watt-hour. Now as a start point, we can recall that a watt is a unit of power. And that a watt, we can refer to it as capital 𝑊, is equal to one joule of energy transferred over a time of one second. So that’s a watt. But we’re talking about a watt-hour, a unit of power multiplied by a unit of time. To see just what this might mean, let’s take our equation for watts. Or a watt is a joule per second. And let’s multiply both sides of that equation by a time in seconds. When we do this, the time cancels out from the right-hand side. And we see that a joule of energy is equal to a watt of power multiplied by a second of time. Now this question is asking about watt-hours not watt-seconds. But the basic idea is the same. If we take an amount of power in watts and we multiply it by an amount of time. Then we’ll get an amount of energy.

All this tells us that a watt-hour is some amount of energy. And the fact that it’s an amount of energy rather than, say, an amount of time or an amount of power lets us cancel out some of our answer options. For example, option A says that a watt-hour is an amount of time. But we know that it’s not an amount of time. It’s an amount of energy. Option B says that a watt-hour is a measure of the power of a process. But again, a watt-hour is not an amount of power, but rather an amount of energy. So option B isn’t our choice either. Both options C and D describe a watt-hour as an amount of energy. So they’re at least correct that far. But then, as we continue on to option E, we see that this names a watt-hour as an amount of time. So we know this isn’t correct either.

It comes down then to options C and D. Let’s look at option C. This says a watt-hour is the amount of energy that an electrical device transfers in one hour. On the surface of it, this seems like a reasonable definition. It says that watt-hour is an amount of energy. That’s correct. And that it involves a process which lasts one hour. But there is something missing from this definition. And that is a description of the amount of power involved in the process. All option C tells us is that a watt-hour is an amount of energy. And it has something to do with the process that lasts one hour. But there’s a bit more to it.

Going onto option D, we see what this bit more is. It says a watt-hour is the amount of energy transferred by a process that has a power of one watt and acts for one hour. So it’s option D rather than option C which specifies both the amount of time, the hour, as well as the amount of power, one watt, that’s used. It’s this definition that correctly describes both the power as well as the time aspect of a watt-hour of energy. We see that it’s the amount of energy transferred by a process with the power of one watt that acts for one hour.

Let’s take a moment now to summarize what we’ve learned about the units of energy. Starting off, we saw that energy is the ability to do work. That is, to exert some amount of force over some amount of distance. Furthermore, the SI unit of energy is the joule, abbreviated capital J. And one joule is equal to a newton of force times a meter of distance. Along with this, we learned that energy, in joules, divided by time, in units of seconds, is equal to what’s called power, in units of watts. Based on this unit of power, energy in electrical applications is often measured in units of kilowatts, thousands of watts, times hours. Lastly, in converting between these two energy units of kilowatt-hours and joules, we saw that one kilowatt-hour is equal to 3600000 joules.

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