Thermal energy, temperature, and heat | Khan Academy

I have two vessels of water. I start heating them with pretty much the same amount of heat; they are similar. What do we find? We find that the one which has less water starts boiling first. That's not very surprising. This means that the one which has less water, its temperature rises quicker, and it reaches the boiling point, that is, 100° C, much quicker than the other one. But the question is, why does this happen? Why is it that if you have less amount of water, its temperature shoots faster?

Well, to answer this question, we need to understand the difference between temperature, heat energy, and thermal energy, and that's exactly what we'll do in this video. So let's begin.

So let's start by asking ourselves, what is thermal energy? Well, thermal energy is basically the sum of kinetic energy of all particles. What does that mean? Well, for that, let's zoom into our water. We'll find water molecules, and these molecules are held together by intermolecular forces. Now, the forces are weak enough that the particles can actually move. They're all moving randomly. As a result of that, they have kinetic energy.

Now, there are different kinds of motion over here. So there is translatory motion where particles move from one place to another. Now, I've not drawn the arrow mark for all the particles because I don't want this to be too cluttered, but all particles can move. Some particles will move very slowly; other particles will move very fast, but there is kinetic energy because of that. But that's not it. Particles can also spin, so you have rotational kinetic energy. And particles can also vibrate; they can jiggle, so you get jiggling kinetic energy.

Now, you add all of that kinetic energy of all the molecules, all the particles over here; that total energy is what we call the thermal energy of that water. This is true for not just liquids; this is true for solids and gases as well. The only difference is, if you consider a solid, let's consider a solid like say ice, the big difference is that over here, particles, because of very strong intermolecular forces, particles are locked in space so they can't move from one place to another. But they can still vibrate. As a result of that, they do have kinetic energy, and so when it comes to solids, the thermal energy comes from the vibrational, the jiggling kinetic energy that they have.

What about gases? Well, in gases, they hardly have any intermolecular forces, so the particles are free to move about. Therefore, when it comes to gases, the thermal energy comes from the translational kinetic energy of the particles. But you can see in all the cases, thermal energy eventually comes from where? The kinetic energy of all the particles.

Okay, so that's thermal energy. What is temperature? Now, isn't it the same as thermal energy? It's not. Temperature is a measure of average kinetic energy of the particles, which means if you take the total energy of all the particles, which is basically thermal energy, divided by the total number of particles you have, you now get the average energy of each particle. That is a measure of what temperature is.

To see how different these two things are, let's take some numbers here. So let's say we have about 100 molecules of water over here. Now, of course, we both know that we're dealing with trillions and trillions of molecules, but let's just keep a simple number. So if here, if you have 100, let's say here you have, since you have more, you have about 300 molecules of water.

Okay, now if the average kinetic energy is two units, what does that mean? It means there will be some particles, some molecules, which will be moving with, which will be having more than two kinetic energy. Some particles will be having less than two kinetic energy. But if you average it out, you'll get two, and that represents the temperature. If this number is bigger, the temperature would be higher. If this number is smaller, the temperature would be lower.

Okay, now this water is at room temperature. I haven't started heating them yet. That means they should also have the same temperature, as this one, which means they should also have the same average kinetic energy. Because if it had any different kinetic energy, this water would be at a different temperature compared to this one. But that's not true. We right now have the same temperature, room temperature.

Okay, so now comes the question: what is the thermal energy here and here? Well, the thermal energy here would be, we have, on average, each molecule has two units of energy, but there are a total of 100 molecules. So the total energy would be 200. That represents the thermal energy here.

What's the thermal energy here? Again, each molecule, on average, has 2 units of energy, but there's a total of 300 molecules. Now, which means total would be 600 units of energy. So the thermal energy over here would be 600 units. Right in front of your eyes, you can see they have different thermal energy. This water has more thermal energy compared to this one, mainly because it has a lot more particles. But look, they have the same temperature, so you can see they're not the same thing.

This now brings us to the third and the final piece: heat energy. What is heat energy? Isn't it the same as thermal energy? No, heat energy represents the amount of thermal energy that is transferred. So whenever you are adding or removing thermal energy from an object, that's when we use the word heat. So in science, it doesn't make sense to say that this water has 600 units of heat energy. No, whatever water has is thermal energy. But if you add some thermal energy to it or you remove from some thermal energy from it, that's when we use the word heat. We say heat energy was added or heat energy was removed. So you don't have heat energy; you only have thermal energy.

And again, we'll take some numbers; it'll make a lot more sense. But before we do that, one question we could have is: how do you transfer energy? How do you transfer thermal energy? Well, it turns out there are actually three ways to do that.

The first one is conduction. This is where you transfer thermal energy without the particles themselves moving. For example, if we consider how heat energy is transferred in this vessel, let's look at the atoms of that vessel. The bottom of that vessel, the atoms at the bottom will have high thermal energy because it is directly in contact with the flame. But how does that thermal energy get transferred over here? Well, since the particles are mostly jiggling over here, remember it's a solid, so the thermal energy is mostly due to jiggling. Because the particles are jiggling, they're vibrating, they will come in contact and make the particles, you know, close to them jiggle. Next to them, jiggling, and then these particles will make the particles next to them jiggle, and so on and so forth. And that's how thermal energy is transferred, but the matter itself did not move. The particles did not move from one place to another. So without any matter motion, you have thermal energy transfer. That's what we call conduction.

But that's not it. There's a second kind of, there's a second way in which you can transfer thermal energy, which we call convection. This is kind of the opposite; here, matter moves from one place to another, and that's how thermal energy is transferred. Now, this cannot happen in solids because, in solids, remember, matter cannot move from one place to another, which means it can only happen in fluids—liquids and gases.

So for this, consider the water inside our vessel. And again, if you consider that the bottom of this is, let's say hot; it has high thermal energy, then this means the particles over here are moving with very high speeds and so they are farther apart and therefore they will have less density and so this part of water will now start rising up, making the rest of the cooler water to come down, and then that heats up, and then that rises up, and then the rest comes down. This is how, look, by making the matter move, the matter is moving, and as a result of that, thermal energy is being transferred. This can only happen in liquids and gases.

But there's a third one: that is radiation. Now, this is where the transfer of thermal energy can happen without any matter at all. This can happen in the vacuum of space using electromagnetic radiation. The best example of this is we receive heat from the Sun. Between the Sun and the Earth, there's a vacuum, so you cannot have conduction or convection. But what we do get is radiation, which can travel through space, and that's how we receive heat from the Sun.

So going back to our example, let's say we switch on the stuff and wait for some time. We'll transfer mostly the same amount of energy; it's the same stove and everything. So let's say we transferred about 300 units of energy. This is the heat energy that we transferred.

Okay, as a result of that, what happens to our thermal energy? Well, thermal energy will increase. This will go from 600 to 600 + 300: 900 units. This will go from 200 to 200 + 300: 500 units. So you can see, again, at any given moment of time, this has more thermal energy than this. But now comes the key moment: what is the new temperature? Well, the temperatures will be higher, but which one will be having more temperature? Will it be the same? Will it be different?

When you pause the video and think about it, okay? Remember, for temperature, I need to think about average kinetic energy. Now this has 900 units of energy, but that's divided among 300 molecules, 300 particles. So if you average it out, 900 divided by 300, you get about 3. So the temperature has increased because the average kinetic energy has increased from 2 to 3.

Okay, now let's look at over here. Although we have less thermal energy, 500 units, that's divided among only 100 molecules, 100 particles, which means if I divide it by 100, I get 5. The new average kinetic energy will be 5 units.

So you can see the average kinetic energy over here is higher; therefore, the temperature over here is higher. This makes sense, right? Because you have less molecules, less particles over here. When you distribute that energy, on average, each one ends up having more. That's why this one's temperature rises much quicker than this one, and that's the reason why that one eventually hits the boiling point earlier than this one.

So if you had to see the difference between the two in one picture, this picture kind of sums it up. If you add up all the kinetic energy of all the particles over here, it will be more here compared to over here because you have more particles over here to begin with. That's why this still has more thermal energy compared to this one. But think about the average. On average, the particles are moving pretty slowly over here, so it has less average kinetic energy, less temperature.

On average, the particles are moving very quickly over here, so on average, you have a much higher kinetic energy per particle, and therefore you have a higher temperature. Now here's something to think about: if you compare this vessel of water with the ocean, you would find that the ocean has way higher thermal energy compared to this one. Same idea. But this water in my kitchen is at a higher temperature; it's still hotter than the ocean because the average kinetic energy is higher than that in the ocean. That's incredible, isn't it?