Introduction to entropy

what I want to do in this video is start exploring entropy and when you first get exposed to the idea of 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 world they'll involve the word disorder so it might be considered to be the disorder of a system disorder 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 when you 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 if or way way WAY larger if I was drawing it to scale but which of these systems has more entropy all right so I'm assuming you've had a go at it and so when you look at these rooms you might say okay this room over here this looks this looks ordered it's a clean room and this over here it looks disordered it's a messy room disordered so if I if all you had is this definition you 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 versus a messy room in 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 let me make this very very clear so something being messy so messy messy does not equal entropy does not does not equal entropy to think about what disorder means in the entropy sense we're going to have to we're going to flex our visualization of muscles a little bit more but hopefully it'll all sick in sync in entropy this kind of 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 let's say that I have let's say that I have or molecules that are bouncing around so I have this magenta molecule I have this blue molecule I have this blue molecule I have this yellow molecule whoops trouble I have a 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 were bouncing around they 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 the green molecules now over here and so a system can take on a bunch of different states I've just drawn two states for the system B could there be many many many more States for the system so each of these are a particular state for the system so imagine this system where I have a this box with the four molecules in it and let's compare it to another system to another system where I have a larger box I have a larger box and let's say it has even more molecules in it let's say that it has let's say it has two yellow two of the yellow molecules let's say that it has a blue molecule let's say it has a green molecule let's say it has a magenta molecule this is fun let's say it has a moove 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 so this one over 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 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 more possible States more possible States relative to this one this has fewer possible States fewer fewer possible possible dates and because this system over here has more possible states more configurations it would take I would have to tell you more to tell you exactly where everything is we would say that this has more entropy so this has more 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 can kind of imagine it there's a lot more stuff moving around in 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 cleaning 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 if we light in front if we don't know the particular state it 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 gonna have more molecules in it and those molecules are going to be in way more configurations that they could be in range 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 the 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 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 that things aren't you know it's for the most part rigid it doesn't have a very high temperature so these things aren't moving around a lot so it has way fewer states way fewer configurations then 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 is way higher than the moon so entropy this entropy much larger much larger than then the entropy of the moon think about how much information you would need you would need a lot of information if someone wanted to tell you where every 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 Sun while all of these things are moving around and this this is 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 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