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Introduction to entropy

Introduction to entropy, and how entropy relates to the number of possible states for a system.

Video transcript

What I want to do in this video is start exploring entropy. When you first get exposed to the idea entropy it seems a little bit mysterious. But as we do more videos we'll hopefully build a very strong intuition of what it is. So one of the more typical definitions, or a lot of the definitions you'll see of entropy, they'll involve the word disorder. So it might be considered the disorder of a system. Now with just that definition in your head, I want you to pause this video and I want you to compare this system to this system. I want you to compare this room to this room, and ask yourself, which of these has more entropy. And then I want you to compare the moon here to the sun, and these clearly aren't at scale, the sun would be way more massive or way larger if I was drawing it to scale. But which of these systems has more entropy? Alright, so I'm assuming you've had a go at it. So when you look at these rooms you might say okay this room over here, this looks ordered, It's a clean room. And this over here looks disordered, it's a messy room. So if all you had is this definition, you'd say okay maybe this one is more disordered, maybe this one has more entropy. And you wouldn't be alone in thinking that. In fact, even in a lot of textbooks they'll use this analogy of a clean room verses a messy room. And the messy room somehow being indicative of having more entropy. But this isn't exactly the case. This form of disorder is not the same thing as this form of disorder. So let me make this very, very clear. So something being messy, does not equal entropy. To think about what disorder means in the entropy sense we're going to have to flex our visualization of muscles a little bit more, but hopefully it'll all sink in. Entropy, this kind of a disorder is more of the number of states that a system can take on. What do I mean by states of a system? Well if I have a container like this, and if I have four molecules that are bouncing around. So I have this magenta molecule, I have this blue molecule, I have this yellow molecule right over here, and then I have a green molecule. Well this would be a particular state, a particular configuration. But that system these molecules are bouncing around could take on other configurations. Or it could take on other states. Or maybe the yellow molecule is over here, they bounce around enough for the yellow molecule to get there, the blue molecule to get over here, maybe the pink molecule is now over here, and the green molecule is now over here. And so a system can take on a bunch of different states. I've just drawn two states for this system. But there could be many, many more states for this system. So each of these are a particular state for the system. So imagine this system where I have this box with the four molecules in it, and let's compare it to another system where I have a larger box. And let's say it has even more molecules in it. Let's say that it has two yellow molecules, let's say that is has a blue molecule, let's say that it has a green molecule, let's say that it has a magenta molecule, this is fun. Let's say it has a mauve molecule right over here. So this system that is larger, there's more places for the molecules to be and there's actually more molecules in it. This can actually take on more configurations or more states. I've just drawn one of them but there's many more. If you imagine these molecules all bouncing around in different ways there's many, many different states that it could take on. So the system without even knowing what the actual molecules are doing at that given moment in time, we would say that there's more possible states relative to this one, this has fewer possible states. And because this system over here has more possible states, more configurations, it would take more to tell you exactly where everything is. We would say that this has more entropy. So when we talk about disorder, we're really talking about the number of states something could have. And it makes sense that this thing you could imagine there's a lot more stuff moving around and a lot more different directions and they have a lot more space to move around. So it makes sense that the system as a whole has more entropy. So when we talk about entropy we're not talking about any one of the particular states, any one of the particular configurations, we're talking about the system as a whole without really knowing exactly where the molecules are. In this example with the rooms, we're just talking about particular states. Messy is a particular state, clean is a particular state. But we're not talking about the number of configurations that a room could actually have. In fact if this room is larger, this room actually could have more configurations. And if we're talking about the molecular level if this room was warm and this room were cold, and actually if this room is just larger, it's going to have more molecules in it. And those molecules are going to be in way more configurations that they could be arranged so there could be an argument that this actually has a higher entropy. And so using that same reasoning, let's go back to that comparison of the moon and the sun. Which of these would have more entropy? Well let's think about it. The sun is larger, it has way, way more molecules and those molecules are moving around way faster and they're hotter and they're moving past each other. While the moon is small, it's cold, it has fewer molecules. It's for the most part rigid, it doesn't have a very high temperature so these things aren't moving around a lot. It has way fewer states, way fewer configurations than the sun does. So the sun's entropy, if you view it as a system. If you view the sun as a system, it's entropy is way higher than the moon. It's entropy is much larger than the entropy of the moon. Think about it, how much information you would need. You would need a lot of information if someone wanted to tell you where every molecule or every atom on the moon is. But you would need even more to know where every atom or molecule for in a given moment on the sun is. If you're just looking at the sun, wow all these things are moving around and it's this huge volume. And they're very energetic and all of these molecules. So hopefully this starts to give you a sense of what entropy is. And you might say okay this is all fun intellectual discussion, what's the big deal? But the big deal is that to some degree you can describe the universe in terms of entropy. As we learn in the second law of thermodynamics, the entropy in the universe is constantly increasing. We are constantly moving to a universe with more possible states, which has all sorts of interesting implications.