I thought I'd film this video on a train. It's a weird train though; it hasn't moved for an hour. Also outside the window, it's just another window. Also, this side, it's just curtain. It's no train on that side. It's just train on this side. Anyway, this video is about entropy. And you've probably heard of entropy. Maybe you think of entropy as a measure of disorder. And you know that entropy is always increasing, so the disorder in the universe is always going up. This is like the popular one-line definition of entropy: that it's a measure of disorder. I'm not a big fan of it. I think it's kind of confusing, and it doesn't help with your understanding of what entropy really is. I know it's a popular definition, because it's like, you know, "the reason my room is always messy is because I'm constantly battling the universe's desire to increase in disorder." But there is a better definition than that. This definition goes back to why entropy was invented in the first place, and it's to do with how engines work and making engines more efficient. So, you know how an engine works: you put fuel in, you burn the fuel that creates heat, and then somehow this heat is turned into the movement of your engine. And that description is okay, but it's a lot more interesting than that. To illustrate the point I've brought an engine with me. This is a very special type of engine that you don't put fuel in! Yeah, that's right... Free energy, people. It's real! The big energy companies are liars. No. It's not. Sorry. This is an example of an external combustion engine, as opposed to an internal combustion engine. It's a Stirling engine. And you don't put fuel in; instead you burn your fuel on the outside. And this is such a finely engineered Stirling engine that it will run just off the heat of my hand. Okay, so that bottom plate now has had a bit of a chance to warm up. It's now about the same temperature as my hand, so I just need to give this flywheel a little kickstart. It should just keep going on its own. It's the little engine that could. If I get it to the same level as my face, then we'll both be in focus. To really get this thing going, you want to use something like a hot drink or a hand warmer. Looks like a little hot water bottle. Silly. Doesn't make any sense. It's not even a... Let me explain how a Stirling engine works: there are two plates here. The bottom one is hot because I'm heating it with a hand warmer, the top one is just at room temperature, and inside here's a block of foam. So, if I move the block of foam to the top, then the air inside the chamber is in contact with the hot plate in the bottom, so the air is warming up. When you heat up the air inside it expands, and that expanding air pushes this piston, here, so that pushes upwards which turns the wheel. When you turn the wheel, that's connected to the foam block, so the foam block is now at the bottom. And when the foam block is at the bottom and the air is in contact with the top plate, meaning the air cools down, meaning it contracts, meaning it pulls that piston back down. That turns the wheel some more, that pulls the foam back up to the top. So now the air is in contact with the bottom plate, so it's expanding because it's getting hot, which is pushing the piston, which is telling the wheel, which is pushing the foam down, and so on and so on and so on. So that is how a Stirling engine works. But the point is: it's not heat that you need; it's a difference in temperature. So in this case, there needs to be a difference in temperature between these two plates. In fact, you can run this Stirling engine on ice. So if you have the bottom plate colder than the top plate, you can make it work. And, there is no ice available on this train. So, I'm just going to reiterate that: it's not heat that you need to run an engine; it's a difference in temperature. Like, if both of these plates were really really hot, but the same temperature, it wouldn't run. So what's this got to do with entropy? Well, imagine you had two slabs of metal, and one was hot, one was cold; you touch them together. What do you expect to happen? You expect heat to flow from the hot slab to the cold slab, until the heat is evenly distributed between the two slabs, and once the heat energy is evenly distributed... that's the end. Nothing else happens. You never see it in reverse. If you have two slabs that are at the same temperature with evenly distributed heat, you don't spontaneously see one of the slabs stealing heat energy from the other until there's a difference in temperature. So, what if I put my Stirling engine between these two slabs? Well, heat would transfer between the slabs through the Stirling engine, causing the engine to turn. But once the energy is distributed evenly between the two slabs, then, the engine will stop turning because the two plates of the engine are now at the same temperature. And this is the really important bit: energy is only useful when it's clumped together. And when you use that energy, you're spreading it out, and once it's spread out, you can't use it anymore. It was during the industrial revolution that people became really interested in engines and how to make them more efficient. And it was here that the concept of entropy was born. It helped these early engineers to make their engines better. So my preferred one-line definition of entropy is that it's a measure of how spread out your energy is. And we've already heard that entropy always increases, so that means that energy is always spreading out. It's going from a clumped up state to a spread out state. And just as a side note: you can clump energy together locally, but it's always at the expense of energy spreading out somewhere else. For example, this is actually a reversible heat engine. So if I manually turn this wheel, I can cause one plate to get hot while the other gets cold. So I'm clumping the energy together on one side, but to run this wheel, I'm using my muscles, and my muscles are putting heat out into the universe, and entropy is increasing that way. So the overall effect is that entropy is increased, even though I'm creating a local decrease in entropy. So energy is always becoming more spread out and less clumped together. What that means is, in the future, eventually all the energy will be evenly spread out, and none of our engines will run, including our bodies, which are a kind of engine. They'll stop running. But it's not all bad news for us humans: fortunately, on Earth, there are loads of sources of clumped together energy that we haven't used yet. Clumped together energy that hasn't spread out. Things like coal, oil, and gas. When we burn those fuels, we're running our engines, and we're spreading the energy out. So, once we've burnt them, that's it. We can't use them anymore. The energy is spread out. So they will run out. They're non-renewable sources of energy. Fortunately, there is still one giant source of clumped together energy that we can use. And that's the Sun. So once the fossil fuels have run out, we can power our engines using things like solar panels. We can grow crops and make biofuels, and things like that. By the way, I'm not endorsing using up all the fossil fuels on Earth, because there are some terrible side effects from doing that. For example, pumping CO2 into the atmosphere. So, we should really be switching to that massive clump of energy, the Sun, sooner rather than later. Of course, all the energy in the Sun will eventually spread out as well, as will all the energy in the universe. And once all the energy in the universe is evenly spread out, nothing interesting can ever happen again. Do we need to worry about this? Well, this is called the heat death of the universe. And it's science's best guess at how the universe will end. But, it won't happen for another ten thousand trillion trillion trillion trillion trillion trillion trillion trillion years. So, why does entropy always increase? Well, it's actually a statistical phenomenon. Imagine you had a cardboard box. And you have a layer of ping-pong balls at the bottom: half of them are red; half of them are blue. And you painstakingly arrange them so all the red ping-pong balls are on one side, all the blue ping-pong balls are on the other side. Now, vigorously shake that box. All those ping-pong balls are going to fly around. Then let them settle again into a single layer, and you'll notice that the red ping-pong balls and blue ping-pong balls are randomly distributed throughout the layer. You won't find that you have, you know, all the red ping-pong balls on one side and all the blue ping-pong balls on the other side. And you probably just have an intuitive understanding of why. That seems obvious. But just to give it some statistical rigor: there is only one way to have all the ping-pong balls that are red on one side and all ping-pong balls that are blue on the other side. But, there are so many other possible arrangements: millions, billions, trillions of possible... I mean, gazillions of possible arrangements. Depending on how many ping-pong balls you've got of having them in that... in that layer. So, there's only one out of trillions that is that kind of clumped together state. So, clumped together is statistically unlikely. And when you scale that up to, you know, a box of atoms where you've got hot ones on one side and cold ones on the other, and they're all whizzing round, just by chance, they could all whizz over to one half of the box, leaving the cold ones on the other side. But it's so unlikely, that we never ever see it happen. And what's interesting is that you can look at time itself, the passage of time, the direction of time, the arrow of time, in terms of entropy. You can define a direction for time in terms of the spreading out of energy, in terms of the increase in entropy. So, there's an argument that time itself is a statistical phenomenon. This Stirling engine is made by Kontax. You can get it from stirlingengine.co.uk They ship worldwide. They've not sponsored the video or anything like that. I just think it's a wonderful engine. They sell other engines as well, so check out stirlingengine.co.uk So there you go: my preferred definition of entropy. I hope you enjoyed this video. 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Frank Lambert has written several of papers that explain why the disorder description of entropy is lacking and that advocate descriptions like the one in this video. Here is his website that has an archive of his papers. Its a great resource.
I think it's best to think of entropy as a statistical property that describes a state's likelyhood. Things are more likely to be in an even distribution as time progresses because there are more states that result in even distributions than those that don't.
We expect entropy to increase the same way we expect that dropping a box of Legos makes it scatter across the floor, instead of them falling in such a way that it makes a Lego building.
i mean entropy makes enough sense as dq/T, just the change in energy at a certain tempeature