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Second Law of Thermodynamics

The Second Law of Thermodynamics: there can be no spontaneous transfer of heat from cold to hot.

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Video transcript

- [Voiceover] So I'm going to ask you what I think it is an interesting question. Have you ever sat in a room at room temperature, lets say it's around 70 degrees Fahrenheit. And watched a glass of liquid water spontaneously have ice in the middle? And I'm guessing that you have never seen that. Of course you wouldn't see ice spontaneously form, specially if the room is at 70 degrees Fahrenheit. If it's above the freezing temperature of water. But my question to you is, why not? Because that does not seem to defy any of the laws of physics, the Newtonian physics. Or even the first law of Thermodynamics. Lets just think about how that actually could occur. Lets imagine a bunch of water molecules, in their liquid state. So, I have a bunch of water molecules in their liquid state. I'm gonna do a good number of them. And, they have some temperature. Remember, temperature's just about average kinetic energy. But, each of these, are gonna have their own velocities, their own momentums. So, they're all going to be bouncing around in different ways. And, they have their hydrogen bonds between them. That's why water is liquid state at room temperature, as opposed to gas. You got some hydrogen bonds between them. But I'm not gonna get too fixated on that just yet. Now, you can imagine they're all bouncing around in random ways, but there is some probability that they interact just in the right way that maybe this molecule right over here is able to hit this one in the right way. So it transfers most of its momentum to the faster molecule. And so this one actually looses some of its momentum. And it slows down. And just as that's happening in the neighborhood of it, one of the other molecules is able to transfer most of its momentum to some other molecule. So it too slows down. So it too slows down. So they all have much smaller momentum. And then maybe this one, at the exact same time is able to do it. So it slows down, so it slows down here. And then the other ones that got the momentum transferred to them, they're all moving faster now. So lets say that one got their momentum transferred to it. That one got momentum transferred to it. That one got momentum transferred to it. That one got momentum transferred to it. And, this one got momentum transferred to it. And now, these molecules right over here, their momentum is small enough, their velocities are small enough, that the hydrogen bonds really take over and they're able to start forming some form of a lattice structure. They're getting cold enough, you could say, to actually freeze. So these are turning into ice. Why can't that happen? What I've just described, I'm just talking about things colliding and transferring their momentum. I'm talking about energy not being created or destroyed. So it seems to fit in with the first law of Thermodynamics. So it seems like, theoretically, maybe it is possible for ice to spontaneously form. Or maybe another way to think about it, maybe it is possible to start off with a system that is fairly uniform. It has an average temperature here. But maybe a cold pocket could form by the rest of it turning hot. So, maybe initially, all of the water is 70 degrees. So, everything I'm showing you is a neutral 70 degrees Fahrenheit. But maybe, there's some probability that spontaneously, I have no creation or loss of energy, but some of the energy from the middle gets put into the outside, so it warms up. So, let me do this in a different color. So maybe all of this water outside, maybe this is a top-down view of the water. Maybe all of this water heats up. Maybe all that water heats up. And all the water in the middle, cools down. But they have the same total, they have the same total kinetic energy. So I haven't created or lost energy, it's just happened to be that, spontaneously, I was able to transfer energy from the middle, outwards. And even as the middle got a little bit colder, I was able to transfer more and more energy from the cold, the cold water, to the hot water. And it gets ordered in this way. This is actually, it feels possible, due to some of the physics that we already know. But, some thoughtful folks, like these gentlemen here, this is Carnot, considered the father of Thermodynamics. Kelvin, Rudolf Clausius. They repeatedly observed, this doesn't seem to be happening in nature. Specially when you get to the characters like Kelvin and Clausius. They're saying, "hey look, it doesn't look like we're "observing transfer of heat "from cold to hot. "And, since we're not observing it, "lets just add our own Second Law of Thermodynamics". The Second Law of Thermodynamics is really based on empirical observation. And the Second Law of Thermodynamics, according to Rudolf Clausius, and I'm gonna paraphrase this, is that we don't see spontaneous, let me write this down. Second Law of Thermodynamics. He said, we don't see a spontaneous transfer of heat from cold areas to hot areas. So Second Law of Thermodynamics. So no transfer, no spontaneous. We can use work, like things like refrigeration equipment to make heat flow from cold to hot and cool something down. But no spontaneous transfer, transfer of heat, from cold to hot. And maybe I'll underline hot in orange right over here. And this was just really based on observation, because we don't spontaneously see this happening, we don't see the water randomly organizing itself into a hot region and a cold region, and getting so cold that maybe some of it will spontaneously freeze. What we do observe is that if I were to put ice water in the middle of a room at room temperature, I'm gonna see the other way. I'm gonna see transfer of heat from, let me draw a cup here. I'm gonna see transfer of heat from the warmer regions to the colder regions. So, these are ice cubes right over here. And, this is the water. This is the water right over here. We're gonna see the transferred heat the other way, from the cold regions, to the hot regions. Now, this was an empirical observation and it seemed to hold up to experimentation. But why do we actually see that? And it turns out, that there's some super, super, duper, duper, small probability that this could actually happen. Remember in real systems that we're talking about. And Thermodynamics is really the study of systems more than individual molecules that we're talking about. Any system we're talking about, we're talking about way more molecules, way more actors than just three molecules here. We could be talking about... Well, if you look at the number of molecules in a glass of water, you're looking at things with 20, 24, 25 zeros, depending on the size of your glass of water. So you're looking at a huge, huge number of molecules. And so statistically. And the didn't think about things statistically until Boltzmann comes along. But statistically, the odds of this happening are so low. Specially when you're thinking about, I'm not talking about just three molecules, I'm talking about way, way more than three molecules that you're just never going to actually see it. And you can think about this, if we were to allow ourselves to look at the molecular level of things. To not just look at the macro level. You could see why this is. So, if you, if you were to have some type of a container. Let me draw a container here. If you were to have a container. And you have, on the left-hand side, lets say you start with a bunch of molecules that are hot. So they have a high kinetic energy. So these are, these have a high average kinetic energy here. These molecules. And, on the right side of the container, you have, maybe some molecules. And maybe they're the same type of molecule, but they have low kinetic energy. So their temperature, on average they have a lower kinetic energy. They might have a few that have high kinetic energy. But on average, the have a lower kinetic energy. So we see that the, we see, that the temperature here is lower. So let me write this down. Right now where we're starting off, this has a lower temperature. While the left-hand side has a higher temperature. Now what's going to happen? These molecules, they can interact with each other. They're gonna bounce into each other. The things with high kinetic energy, they're gonna bump into the things with low kinetic energy. And all of these things are also going to get mixed together. But even if somehow you weren't mixing it, these things would be bumping into these and transferring their momentum. So, as time goes on you're going to have, you're going to have a system that looks more like this. Where all of them are going to have more of a medium, or on average, a medium kinetic energy. There's still gonna be differences in their kinetic energies, but they're not gonna be divided in this way between left and right. So you're gonna see it all mixed in, and you're gonna see that, neither the left of the right is going to have a higher temperature. And so what is the net effect? Well we had a transfer of energy from the hotter molecules to the colder molecules. So, that energy that we're talking about, that is heat. We use Q to denote the heat. We have a transferred energy from hot to cold. It's statistically unlikely, very unlikely, bordering on impossible, but there's an infinitely small chance it happens, it's just it wont be observed. Then you could go the other way, but that's not what we see. What we're talking about many, many, many, not even millions. Millions of millions of millions of millions of molecules. You're gonna see the ones with the higher kinetic energy on average mix in and transfer it to the ones with lower kinetic energy. And so that's why they were able to say "hey we don't see any spontaneous transfer of heat "from cold to hot". It is always going from, It is always going from hot to cold.