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Video transcript

let's talk about the second law of thermodynamics this law is weird there's about ten different ways to state it which is one reason why it's weird let's start with one of the most common ways to stay it which is if you've got a cold object and a hot object heat will never be seen to flow spontaneously from a colder object to a hotter object so if you have these two sitting together maybe an ice cube and a hot piece of metal and you make them touch heats going to flow between them but we know what's going to happen the heats going to flow from the hot object to the cold object and never the other way at least not spontaneously you can force heat from a cold object to a hot object like we do with a refrigerator or a freezer but that's using a heat pump and those refrigerators and freezers are doing work to force that heat from the cold region into the hot region it won't do it spontaneously by itself you've got to force it to do it so what the second law says or at least one version of it is that that process will never be seen to happen in Reverse the heat will never be seen to flow from the cold object to the hot object now you might be thinking duh did we really need a law to tell us that but it's not so obvious because you can still conserve energy and momentum and all the other rules of physics and laws of physics by allowing heat to flow from the cold object to the hot object in other words let's say the cold object started with ten joules of thermal energy and the hot object started with its hotter so let's just say it has 30 joules of thermal energy you could imagine five joules of energy going from the cold object into the hot object which would leave you with five joules of energy for the cold object 35 joules of thermal energy for the hot object you still have 40 just like you did before you didn't break the law of conservation of energy it's just energy won't go that way so why why is thermal energy never seen to flow from the cold object to the hot object even though it satisfies every other known law of physics besides of the second law well before we answer that question I think it'd be useful to talk about an alternate version of the second law which looks something like this the total disorder will never be seen to decrease what do I mean by disorder imagine out a room and there were blue spheres and they're bouncing around wildly so these all have some velocity and random directions and when they strike a wall or each other they lose no energy so they keep bouncing around like crazy and then there's another section of the room with red spheres these are also bouncing around randomly they lose no energy they keep doing their thing except there's a divider in this room that doesn't allow the red spheres to go on to the blue sphere side and vice-versa these can't mix up so right now this is an ordered state because the Reds are separated from the blues so we say that this state has a certain amount of order to it but let's imagine we remove the divider now what's going to happen well you'll see these things mix up this blue sphere will move over here it'll bounce onto this side this red sphere will go over here they'll just keep getting mixed up and at some given moment you might find the spheres in some configuration like this they're still bouncing around but now they're all mixed up and we say that this state has a higher amount of disorder this is not ordered we say that this is more disordered which supports the second law the second law says if you let things do what they want to do spontaneously your system will go from the more ordered state to a more disordered state and you'll never see it go the other way we can stand in this room and wait but you're probably never going to see the blue spheres lineup all on the left side and the right Spears lineup on the right side with 12 total spheres maybe if you wait long enough a really long time you might catch it where all the red spheres are on one side and blues are on the other but imagine this imagine now instead of six reds and six blues there's 100 Reds a thousand Reds maybe 10 to the 23rd and Avogadro's number of reds and now they're all mixed up the odds of ever seeing them get back to this ordered state are basically zero the probability isn't exactly zero but the probability is very very low that you would ever see a disordered state with that many number of particles reassemble themselves into an ordered state so we kind of just know that from experience and what we've seen in our day-to-day lives but you still might be wondering how come how come we never see a disordered state go to an ordered state well it basically has to do with counting if you were to count all the possible ways of line the Reds over here on this side and the Blues on the left-hand side there'd be a lot of combinations that would satisfy that condition I mean you could swap this red with that red and this red with that red all on the right-hand side all these Reds could get swapped around and these blues as well they can get swapped around on the left-hand side you get a large number of variations that would satisfy the condition of Blues on the left Reds on the right but now I want you to ask yourself how many possibilities are there for having blues and reds spread out through the whole room well you could probably convince yourself there's more and it turns out there'll be a lot more now this red doesn't have to just maintain its position on the right-hand side somewhere this red can get swapped out anywhere over here I can swap a red with this blue and this blue with this red and this red with this red and this blue with this blue I can move them all over now that these spheres have the whole room through which they can mix the amount of states that will have blues and reds mixed throughout the whole room will vastly outnumber the amount of states that have just reds on one side and just Blues on the other side and this simple idea is the basis for the second law of thermodynamics roughly speaking the second law of thermodynamics hold because there are so many more disordered States than there are ordered States now I'm going to tell you something that you might not like this particular disordered state that I have drawn this exact one is just as likely as this exact ordered state in other words if I get rid of the barrier over here if you came in you'd be just as likely to find the room in this exact configuration as you were to find it in this exact configuration these two exact states are equally likely which sounds weird it makes you think well you're just as likely to find an order state than a disordered state but no this particular state is just as likely as this other particular state but there are so many more mixed-up States then there are separated states even though any particular state is just as likely since the mixed-up States vastly outnumber the separated states if you pick one at random it's going to be a mixed up state because there are so many more of them putting these all into a hat imagine writing down all the possible configurations of states ordered disordered in between you put them all into a hat you pull one out randomly any particular state is just as likely but since there's so many more disordered States you pick one out randomly it's probably going to be mixed up and if there's a large number of particles you're almost certain to find it mixed up so to help us keep these ideas straight we need some different terms physicists came up with a couple terms one is a macro state and a macro state is basically saying okay the particles are mixed up that's one possible macro state and we can be more precise we can say the Reds and the blues can be anywhere within the box another possible macro state would be to say that the particles are separated that is to say Reds are on this side anywhere on that side but on the right side and looser on the left side anywhere on the left side these terms are referring to a macro state and overall description of what you would see now there's another term a microstate and a microstate is a precise exact description of the nitty-gritty details of what every particle is doing within there if I just tell you the particles are mixed up you're not going to know exactly where they are similarly if I just tell you they're separated you're not going to know exactly where they are you'll know they're B on the right hand side the red ones will but you won't know maybe this red one moves down here maybe this red one moves up here the microstate is an exact description this red ones right here going a particular speed this blue ones right here going in particular speed if you specify the exact location blue right here blue right there going that fast red right here what you're describing to me is a microstate and so the second law another way of thinking about it there are more microstates for a disordered macro state than there are microstates for an ordered macro state and that's why we see systems go from order to disorder it's really just a statistical result of counting up the possible number of states so you might be wondering what does this have to do with heat going from hot to cold all this talk about microstates and macro States well it's not just position that can get disordered its velocities that can get disordered energy that can get disordered and that's more of like what's happening up here the positions of the hot molecules aren't necessarily moving over into the cold range but the energy over here is getting dissipated into the cold area so imagine it this way let's get rid of all this and imagine you had a room with a gas in it but this gas was kind of weird at this particular moment all the gas molecules on the right hand side we're moving really fast and all the gas molecules on the left hand side were moving really slow so the room was separated into a cold region and a hot region just like this energy is this is ordered or at least somewhat ordered it's more ordered than it's going to be if you wait a while this is all going to mix up you're going to have some fast-moving particles over here some slow ones over here it's all going to be blended together and so what would you say if you're standing in here at first you'd feel cold because these particles don't have a lot of energy then you start feeling warmer and warmer you'd say heat is flowing over to the left because you'd feel faster moving particles striking your body and so you'd rightly say that heat is moving from the right of this room to the left of this room it flows from the hot to the cold and that's what's happening up here heat flows from the hot to the cold you might object these are solids I said copper and an ice cube a copper atoms not going to make it over into the cold ice cube but the energy is gonna move so you can make the same argument over here don't allow these let's say these are the copper atoms moving around fast or at least jiggling in place rapidly when they bump into the slower moving water molecules in the ice cube they're going to give those water molecules some of their energy and this energy is going to become mixed up the energy will become disordered it will go from this ordered state where the high energy is over here and low energies here to a disordered state where the energy is distributed somewhat evenly so essentially what I'm saying is if you consider the macro state where the hot molecules are separated from the cold molecules there will be less microstates that satisfy that condition then there will be microstates that satisfy the condition for a macro state where the energy is mixed up and you're just as likely to find a fast-moving particle on the left as you are on the right this will have vastly more microstates many more possible ways of making up a mixed-up state then there are microstates that create a separate State I mean there's going to be a lot I'm talking a lot of microstates that satisfy this condition for this macro stay separated but there will be so many more microstates for the mixed-up case this dominates that's why you always see heat flow from a hot object to a cold object just because it's statistically inevitable with a large number of particles that you have here there are so many more ways of heat flowing from hot to cold then there are from cold to hot statistically speaking you just never see it go the other way energy will always at least spontaneously if you let it do it at once to energy is always going to dissipate and evenly distribute that's why it goes from the hot to the cold this energy is trying to get mixed up just because statistically there are so many more ways for that to happen now I need to tell you that there's actually a scientific term for the amount of disorder and we call it the entropy physicists use the letter s to denote the entropy and if you want to know the formula for the entropy you could look on Boltzmann's grave this is Ludwig Boltzmann he's got it on his gravestone how awesome is that the entropy s is K Boltzmann's constant times log this is actually natural log of W and W is the number of microstates for a particular macro state so you've got some configuration you want to know the entropy just look at what macro state it's in count up how many microstates are there for that macro state take log of it multiplied by Boltzmann's constant that gives you the entropy and there's a term for this w it's called the multiplicity because it's determining the multitude of microstates that satisfy the conditions for particular macro state now entropy is cool entropy is weird entropy is somewhat mysterious and still probably has secrets for us to unlock here I don't have time to go into all of them here but if you read up on it entropy has a role to play in the fate of the universe the beginning of the universe the arrow of time maybe our perception all kinds of facets of physics that are extremely interesting and entropy you always find this guy lurking around and one place you always find entropy is in the second law of thermodynamics because it allows us a third way to state the second law which is that the total entropy of a closed system will always be seen to increase technically if it's a reversible process the entropy could stay the same but honestly for all real world processes the entropy is going to increase for a closed system which is to say that the disorder increases
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