First and second laws of thermodynamics | Khan Academy

If you take a very hot coffee, say in a thermoflask, and keep it in a room, then you know that that coffee will automatically start cooling down all by itself until it reaches its room temperature. Right? But my question is why can't the RSE happen? Why can't a room temperature coffee automatically, all by itself, heat up?

I know that sounds like a silly question because we don't see that happening, but why not? Why doesn't this happen? It's questions like these that led us to discovering one of the most profound principles of thermodynamics, and that's exactly what we're going to learn in this video.

Now, before we start, because there's going to be a lot of energy transfer happening, it's important for us to be sure that we're talking about the same thing. One of the ways to do that is to define something called a system and a surrounding. Okay, so what exactly is a system? A system is basically a group of stuff that interests us. For example, if I draw a boundary around this coffee and call my coffee as a system, then all the molecules of that coffee now become part of my system.

Everything that is outside of that boundary, like say the molecules of air inside the thermoflask, the molecules of the thermoflask itself, and the table, and the room, and everything else becomes the surrounding. So you get it? So you have a system, you have a boundary, and then everything outside of that boundary is the surrounding. The boundary is imaginary, of course, but we can define our system however we want.

For example, another way I could have defined my system is by considering a boundary over here. Now I would say that look, everything inside the thermoflask, the coffee molecules, the molecules of the air over here, including the thermoflask itself, is now my system. That's my objects of interest, and everything outside of that now becomes the surrounding.

Okay, so we are completely free to define what our system is. Just to take another example, I could have also defined my system as a part of coffee and a part of the thermoflask, because I have shown over here, and again everything else becomes a surrounding. Now, this may not be the most useful one for us, but we can choose whatever we want.

Now, for the rest of this video, let us define this to be our system and the surrounding. Let's consider the thermoflask and all the molecules inside of the thermoflask. All of that will be our system, and everything else will be our surrounding.

All right, now let's look at what really happened when our coffee cooled down. Well, initially our system is at a very high temperature. This means the particles of that system, basically the molecules of the coffee and all of these over here, they have a very high average kinetic energy. Remember? That's what temperature is, right? But later on, our system cooled down. Our system's temperature decreased. That means the average kinetic energy of the particles must have become smaller.

This means this system lost some energy. Where did it go? Well, you can probably guess it. That must have flown into the surrounding. And here's the thing: if our system lost some amount of energy, our surrounding must have gained exactly that same amount of energy, right? Because energy can neither be created nor destroyed, isn't it? Guess what? That itself is what we call the first law of thermodynamics.

Okay, the first law of thermodynamics is basically energy conservation. You cannot destroy or create energy; energy must always be accounted for. So, in our case, when it comes to the system and surrounding, that basically means that energy lost or gained by the system should exactly equal the energy gained or lost by the surrounding.

Now, before we move ahead, one question that we could have is: when the system lost energy, its temperature drops significantly. Now the surrounding has gained the same amount of energy, so its temperature should shoot up significantly, right? So why doesn't the room just become hotter?

Well, the short answer is, yes, the surrounding has gained the same amount of energy, but remember the surrounding has way more molecules compared to the system. You have so many more molecules. And because, remember, the surrounding represents the air molecules over here, the molecules of this room, and so much more. Since our surrounding has way more molecules compared to the system, the energy, when you distribute it over all of these molecules, the average kinetic energy gained is almost negligible.

As a result of that, the temperature of the surrounding hardly changes. All right, now that brings us to our main question. If you have a high temperature system like our hot coffee, it can automatically cool down by transferring energy to its surrounding. Why can't the reverse happen? Why can't energy go from the surrounding to our room temperature system and increase its temperature?

The question to really ponder upon is: does this violate the first law of thermodynamics? Why don't you pause the video and just think about it. All right, let's see. As long as you made sure that the energy gained by my system is exactly equal to the energy lost by the surrounding, we are done. The first law of thermodynamics has no problems with it.

So you see, if we just think from the first law of thermodynamics, a hot coffee can cool down all by itself, and the reverse must also be possible. That's why we said it's not a silly question.

Now, since we know that this does not happen, that means there must be something else that's going on. There must be another law that could be preventing that from happening. What is that? That is the second law of thermodynamics.

And that says that entropy cannot decrease spontaneously. Now, I know this again brings up a lot of questions. So let's first try to understand what entropy is. There are many ways to think about entropy, but the way I like to think about it is it's a measure of how much your energy has spread out.

So what does this mean? To understand that, again let's consider a new system. This time let's consider the entire room and everything inside of it as our system. Let's assume that this system is isolated from its surrounding. Everything outside the room now becomes a surrounding. And let's assume that it's isolated; that means let's say that, you know, there is no energy transfer between the system and the surrounding.

We have insulated the whole thing, which is not really possible, but let's assume that. Okay, this means whatever happens inside my system, the energy must stay within the system. All right? The energy cannot escape anywhere; that's what we're assuming.

So now if we go back to initial conditions where the coffee was very hot, this particular coffee was very hot. Then look, that energy was concentrated over here. There was a lot of concentration of energy, and therefore we would say the entropy of our system was high. But then once that coffee cooled down, the total energy of my new system, this entire system, has stayed the same, right? Because the energy went from the coffee and the thermoflask into the room. The energy has not changed, but the energy is now more spread out.

Right? Therefore now the entropy has increased. So again, this means we started with low entropy because in the beginning we had some concentration of energy, and then we went towards high entropy because the energy got more spread out. The more spread out the energy gets, the higher the entropy becomes.

Okay, so now what is the second law saying? The second law says the entropy cannot decrease spontaneously. In other words, the energy cannot get concentrated spontaneously. Energy can spread out spontaneously; that can happen, but it cannot get concentrated spontaneously. That's what our second law of thermodynamics says.

So let's see if we can apply this over here. Right now, if you consider the situation, if you look at the entropy right now, the energy is pretty spread out compared to that. Initially, the energy was slightly more concentrated in the coffee. As a result, we started with a slightly lower entropy system, and as time passed by, the entropy increased. The energy got more spread out.

This happens until the temperature becomes equal. Once that happens, we say thermal equilibrium has been reached. That means after that, there won't be any significant energy flowing in or any energy flowing out, at least at a microscopic scale. So we have reached thermal equilibrium, and when that has happened, the energy has spread out. As a result, the entropy has increased.

That can happen according to the second law of thermodynamics. But why can't the reverse happen? Why can't the energy from our room just enter into our coffee? Well, if that happened, then look, the energy would get more concentrated. Therefore, the entropy would now decrease, and the second law says that cannot happen spontaneously. Entropy cannot decrease spontaneously; that's why the room temperature coffee cannot spontaneously become hotter.

What I find fascinating is that we take this for granted. I mean, we know that this cannot happen, but the reason is entropy. It's not that straightforward. That is pretty cool if you think about it, right?

And what's also cool is that this is the reason why heat always flows from a hot body to a cold body spontaneously, because that's how the entropy increases, and that's allowed. But the reverse cannot happen. If the heat were to flow spontaneously from a cold body to a hot body, then that would violate the second law of thermodynamics. The entropy would decrease; that is not allowed.

But anyways, this brings us to the last question. What about refrigerators? If you think about it, the inside of a refrigerator is pretty cold. Since the heat is flowing out of the refrigerator all the time, that means the heat is flowing from the cold region to a warmer region, a hotter region. So that's exactly opposite of what we said.

So does that break the second law of thermodynamics? No, because the keyword over here is spontaneously. We said this cannot happen spontaneously. A refrigerator does not do this spontaneously; it does it by using electrical energy. There's a heat pump over there which runs on electricity, and from using electricity, it is pumping the heat out.

So look, it's not happening all by itself; it's using electricity to do it. Therefore, that's fine. It's not a spontaneous process, so it's not breaking the second law. You can imagine if the power goes off, then the heat will start flowing back in, and all your food will get spoiled.

But now you might say, well wait a second, what about the entropy of the system? Well, now we need to be careful because, look, since we are drawing electricity, that means this system is no longer an isolated system. So an easier way to think about it would be, instead of plugging it to a socket, let's say the refrigerator was hooked up to a generator.

Now we can make sure we still have a completely isolated system. We don't need any energy from the outside. This is an electric generator. Let's say it uses diesel, and it converts into electricity. Now what would happen? Well, now think about it. Before we switch on the generator, the generator has some diesel in it. Diesel contains some energy; this is not thermal energy; it contains chemical energy.

But it is concentrated energy. That means initially there was a pocket of low entropy in this entire system, right? Okay, now what happens? Once we start running the generator, what happens to that low entropy chemical energy inside the diesel? Well, it eventually goes out as heat, ends up as thermal energy of all the particles over here, which means the energy has spread out, and as a result, look, the entropy has eventually increased.

Therefore, if you correctly account for all the energy sources, all of the energy within a system, you will find that the entropy will never decrease. Sure, it's possible to actively pump out heat and make sure that the entropy of one part of the system becomes lower, but as a consequence, you will find that the entropy of some other part of the system will always increase to ensure that the total entropy of the system never becomes smaller. It will only stay the same or it can only become larger.

There is no way to violate the second law of thermodynamics.