Thermodynamics

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Note 1=

* probably think of entropy as a measure of disorder
* you know that entropy is always increasing so the disorder in the universe is always going up
	+ popular one-line definition of entropy that it's a measure of disorder
		- kind of confusing and it doesn't help with your understanding of what entropy really is
	+ 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
* better definition that goes back to why entropy was invented in the first place
	+ 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
		- somehow this heat is turned into the movement of your engine
	+ that description is okay but it's a lot more interesting than that
* let me explain how a Stirling engine works
* it's not heat that you need
	+ it's a difference in temperature
* 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 though 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 as a difference in temperature so what if I put my Stirling engine between these two stabs 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 clumped up stayed 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 clump 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 their 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 Sciences best guess at how the universe will end but it won't happen for another 10,000 trillion trillion trillion trillion trillion trillion trillion trillion years so why doesn't she 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 day 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 little ping-pong balls little 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 pink bubbles 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 always 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 the Stirling engine is made by contacts you can get it from Stirling engine 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 Stirling engine co uk so there you go my preferred definition of entropy I hope you enjoyed this video if you did then hit subscribe unless you're already subscribed in which case I'm not sure what happens when you press that button I don't gets there maybe there's only an unsubscribe button don't hit that that would be just it disaster personally master for me terrible for you as well I mean you would you might miss a video anyway I will see you next time

Note 2=
what will happen tomorrow is not random in other words it's at least somewhat predictable I mean not entirely to be sure but some things will happen for certain and other things definitely won't for example the Sun will rise water will still freeze at zero degrees Celsius and you won't become Michael Stevens we know this because everything in the universe is made of twelve fundamental particles and they interact in four predictable ways what if I were able to determine the positions and velocities of every single one of these particles in the universe well you would be the intelligence envisioned by Laplace who thought if you could really figure out where everything is and how fast it's moving you would know the entire future of the universe because you know how every particle interacts with every other particle wow so nothing would be unpredictable which means nothing would be random not even human behavior since we are made of the same fundamental particles as everything in the rest of the universe everything we will ever do or have ever done would be determined by the information in the state of the universe at any one time but what is information well it seems to be fundamentally about order the order of molecules in your DNA it contained the information needed to make you it is the order of zeros and ones streaming through the internet that contain all the information required to play this video it is the order of letters that makes a word on the order of words that makes a sentence that carries information so fundamentally information seems to be about order regularity that is until you really think about it I mean does every letter of a word carry the same amount of information no I mean after a cue you know almost for certain that the next letter will be a you after a th there will probably be an e so these letters carry very little information because you could predict them beforehand they are redundant in fact the founder of information theory Claude Shannon estimated the redundancy of English at about 75% which is why we can make sense of things like this so English can be compressed because it is not random it has patterns similarly video is compressible because of its regularities in each frame the pixels of similar color clustered together Plus from frame to frame most of the pixels don't change so you only need to record the ones that do change you can take advantage of this technique to create some trippy effects known as data moshing it's the application of the movement data from one video to the pixels of another it also means that an average video can be compressed to just one thousandth of its original size but what is the most you can compress something well anything that is not random any patterns or regularities can be reduced because they are predictable so you can continue shrinking a file down until what you're left with is totally random and that will contain all of the information of the original item but distilled pure information so pure information is randomness if you want to know how much information something contains you need to know how random it is and randomness is disorder what we also call entropy so information fundamentally is entropy this makes sense if you consider a string of binary digits for example this string is perfectly ordered it has very low entropy and it contains no information that's the state of an erased hard drive now this string contains slightly more information but again the regularities allow it to be easily compressed so the string that contains the maximum amount of information is just a random set of zeros and ones it has maximum entropy because it's totally disordered you could not predict any of those digits by looking at any of the other digits and if you wanted to send this information to someone you would have no other option but to send the whole string of digits there's no way to compress it but here's the thing about any object that contains maximum information for us as human beings carry no meaning for example a video containing maximum information we look like this it is just white noise the color of each pixel is independent of all the other pixels and they all change randomly this video could not be compressed because it's already totally random now a random sequence of DNA would not make an organism and a random string of letters does not generally make a word we are drawn to things that are neither perfectly ordered containing no information nor are they perfectly disordered containing maximum information somewhere in the middle we can recognize complex patterns and that is where we derive meaning in music poetry and ideas it is this search for meaning that leads us to propose scientific theories which if you think about it are really our way of compressing the universe for example general relativity our current theory of gravity compresses into one short equation everything from how an Apple falls to the earth to have a moon orbits the earth now all the planets orbit the Sun how the Sun orbits a supermassive black hole at the center of our galaxy now black holes form and behave and how the whole universe expands out from the Big Bang now that we have this theory the future is more predictable I mean we can predict eclipses thousands of years into the future so with all of our scientific theories does that mean that the universe is completely not random that it is perfectly predictable well let's assume for a second that Laplace was right and that knowing the state of the universe at any one time means you also know its state at every other time as well well that would mean that the information in our universe would be constant but if information is entropy that would mean the entropy of the universe is also constant and that does not appear to be the universe that we live in the second law of thermodynamics states that entropy in the universe increases with time or in other words things don't stir themselves apart but if entropy is going up that me the information in our universe is constantly increasing that makes sense because it would take more information to specify the state of the universe now then right after the Big Bang so where is this new information coming from my best bet is quantum mechanics quantum mechanics describes how the twelve fundamental particles behave and as spectacularly successful as it is it is only a probabilistic theory meaning that you cannot predict with absolute certainty where an electrons say will be at some later time you can only calculate probabilities of where you are likely to find it so when you do interact with it and locate the electron at a particular point you have gained information you now know something that you couldn't have predicted with certainty beforehand this drove Einstein crazy he said God does not play dice referring to this I mean he wished that we could compress our theory of quantum mechanics further so that we could really figure out where these particles were going to be but maybe the reason why we haven't been able to compress quantum mechanics further is because fundamentally it's random fundamentally new information is being generated every time a quantum event like that occurs in that case it could be these quantum measurements which are driving up the entropy of the universe they are creating new information all of the time and that means the disorder in our universe must go up this is what we observe as the second law of thermodynamics you know we often think about the second law as a curse as though everything which is ordered is going towards disorder but maybe I mean it's only in a universe where this law is obeyed that the truly unexpected can occur that the future can be actually undetermined for us really to have free will we need the second law of thermodynamics now you might think that these quantum events are too small to have any meaningful impact on the evolution of the universe but that is not true and that's because there are physical systems which are so deep so sensitive to the initial conditions that any tiny change will end up making a big difference later down the track that's called chaos but it's also known as the butterfly effect so you and I could be such physical systems chaotic systems and our free will could come from quantum events in our brains so it looks as though we live in a universe where the future is yet to be determined that is to say it's at least somewhat random but Derek what is the most random thing possible in the universe that's a good question Michael

Note 3=
I thought we talked about the laws of thermodynamics and maybe the second law in particular so there are four laws there are laws 1 2 3 and then this law 0 which I suspect was slotted in after the first 3 laws and it's actually sort of in some sense also the most trivial of them which is why it's probably called the zeroth law so the zeroth law just basically says if you've got three bodies call them a B and C if a and B are in thermal equilibrium with each other which is just a fancy way of saying they're the same temperature which means if you put them together no heat flows from one to the other so if a and B are in thermal iquilibrium and if a and C are in thermal equilibrium then B and C will be in thermal equilibrium it does seem fairly obvious it's it's a kind of a formal way of saying really there is only one definition of temperature and that there is no way you can actually come up with a system where temperature is defined in a funny way such that one of these bodies has some peculiar property such that its temperature as far as body a is concerned is one thing but its temperature as far as what you see is concerned is another thing and I think because it is sort of stating the obvious I think that's why it's a zeroth law so the first law is also fairly obvious in that it's basically sort of Restatement of the conservation of energy in thermodynamics there's kind of two sorts of energy that useful energy which is work so that's when you if you push something whatever that's that's sort of applying energy to it and that's useful energy and then the useless energy which is heat and what the service law says is that if you've got a body and you apply a certain amount of work to it so that's one sort of energy and then you add a certain amount of heat to it the total energy of that body will be whatever it was to start with plus the energy you added from the work plus the energy you added from the heat so it's really just a statement of the conservation of energy really so I mean there are kind of obvious laws but you have to start with the basic building blocks in order to build up the entire subject to certain thermodynamics and these are really the most fundamental building blocks the third is difficult to talk about until we introduce a concept of a thing called entropy which is to do with the disorder of a system and the third law is basically saying that as you cool a system down towards absolute zero the degree of disorder so this quantity entropy drops towards zero already stops to a very low value so classically it'll drop to zero there are some sorts of systems it'll just drop to a low value but it will decrease until you get to Absolute Zero and there will stop so second law has as various formulations the first formulations were put together really before this idea of entropy and disorder was invented and they were very kind of operational definitions of it so there are two classical statements of the second law of thermodynamics the first is one due to a guy called classiest who said that heat won't travel from our cold body to a hot body and that's sort of trivially known if you've just got a hot body and a cold body and you put them in contact with each other the heat will flow from the hot things or the cold thing so they'll end up at the same temperature they'll meet somewhere in the middle and so it's kind of obvious if you're just doing you know putting things in contact with each other but his statement is stronger than that which is there is nothing you can do to make heat flow from a cold body to a hot body without putting some work in so if you're prepared to inject some energy you can make hot things colder and colder and so if you know a fridge is an example where you pump heat after something which is already cold and add it to the air which is warmer so fridges you know in some sense they violate the purist view of this view but this law that you can't get eat trouble for something cold something hot but they'll get out is but you're putting work into you're allowed to it so if you've just got an isolated system you can't do it it's a one-way street and there's no way around it it's the important point that no matter how clever a machine you come up with you could never make it so it will extract the heat from the colder thing and add it to the hotter thing without having to put some work in along the way so that was Klaus elusive statement and then there's the other statement and that's that's in sometimes that's a sort of physicists statement because that's about you know heat flow and observations of what happens when you put bodies in contact with each other but the second version of this is due to Lord Kelvin and Kelvin statement is more of an engineer state this comes back to this fact that there are these two sorts of energy that's kind of useful energy you can do work with and this useless energy heat that you can't really do work with directly and Kelvin statement basically says that you can't turn heat directly into work you can't just take heat and turn it into into useful energy now of course again you do this as steam engine for example takes heat and turns it into work but in order to do that you have to have waste heat left over so his statement is that you can't again have a kind of fuel box where you just put heating at the top and the only thing that comes out is work you're always going to have to have heat going in work coming out but then some waste heat coming out as well there is a fundamental limit as to how little the amount of waste heat there is that you can get out of it and you can figure out what that limit is but but it's always a finite amount you can't you can never reduce that to some you know in completely an infinitesimal zero level those two things sound like completely different statements like they're talking about completely different things but it turns out they're exactly equivalent to one molar and I can show you if you like so what we're going to do this is by saying if one of these versions of the second law isn't true then the other one isn't true either so let's assume that's violate Klaus uses statement of the second law which specially says you can't get heat to flow from the cold body to the hot blade so let's assume we have a magic fridge which violates that law by actually allowing us to suck energy out of the cold body put it into the hot body without actually having to plug the fridge into the mains okay and then over here I'm going to just have a engine like a steam engine or something that which doesn't violate any of the laws at all and I'm going to take an amount of energy out of this hot body you two and because this isn't breaking any laws there has to be some waste heat from it so we're set it up so that amount of weight he is actually with q1 she's been loyal and happy so they yes exactly that's not violating any of the laws and we're going to get some work out of this which is just the difference between those two this is the first law again that says that you have to conserve energy overall so if we've got q2 flowing in and stay in the amount of work we get out of there which is the difference between the two now the neat part here is that what we've managed effectively to do if I just draw a box around this there's a lot here and so that's just going to be I'm going to stick all that on in a box and I'm not going to care what's inside that box and what that box is actually doing is it's taking an amount of energy well how much energy is coming in it's taking heat out of this body and taking an amount well q2 flowing out and choose one flowing back in so the amount of energy that's coming out of the top body is q2 minus q1 and this box and the only thing that's coming out of it is work to 2 minus q1 so this now violates kelvins version of the second law because actually with what we've always done in this process is we've taken an amount of heat out of the top body and turn it directly into work and kelvins latent of the law says you can't do that so that shouldn't be a surprise because we fill the box by breaking the rules we just wrote quote is wording of the rules exactly but what we're trying to show is that those two statements of the second law are the same as each other they really stating the same law and so indeed if they are the same law you'd expect if you broke one version of the law you'd break the other version of the laws as well but if there are actually different laws or the stating different things and that wouldn't necessarily be the case but that's kind of halfway there that shows that if we violate classicist version then we're violating kelvins version but to really show their equivalent we've also got the show if we violate kelvins version we're also violating cloudiest assertion care okay so kelvins version of the law says that you can't just turn energy into work so you can't just take heat and turn it directly into work that has to be a byproduct so let's violate that by coming up with a magical engine which directly turns energy turns heat into work an engine which yet which does nothing but take this useless energy heat and turn it directly is useful energy work and infinitely efficient steam engine so a real steam engine would be waste heat coming out of the but we're violating kelvins law here so we don't have to do that okay okay and then we're going to take that work and we're going to use it to power a fridge and that fridge will because this is now a proper fridge it's not violating class EEOC's law or anything we can get it to work so we plugged it into the mains and we can actually had use it to suck energy q2 out so we can figure out how much heats get to come out the other end it's just going to be the two lots of energy going in there's Q 1 and Q 2 so now if we just put a box around all this lock and say this is this is now my magic machine and I don't really want to look inside the box I just want to know what it's doing what's happening it's sucking an amount of energy Q 2 out of the cold and then on the hot side you've got q1 coming out on q1 plus q2 going in so the net amount of energy flowing into the hot is q2 so effectively we created a machine here where with nothing you know no export external wires or anything within that box it takes in any amounts of heat q2 from a cold body and adds it to a hot body and that violates klaus is his version of a second law so we've shown is that if kelvins versions of the second law isn't true then cloudy situation isn't true and it's a cloud uses version ii or isn't true then killed intuition the second law isn't true and so I just kind of finish it off so we've got these two laws kelvins version and classiest assertion and the sort of four possibilities they might both not be true one might be true and the other one might be false or the other way around or they both might be true and what we've ruled out by showing this is we've shown that if kill wins laws of is false thing then Claudius's has to be false to true if clouds this is version of the law is false then kelvins can't be true test to be false as well so we ruled out those two in the middle so the only two possibilities is they're either both wrong or they're both right and that's just another way of saying that they're saying exactly the same thing we haven't been able to prove that they're true but we've shown that if they with one of them is true the others true and it's one of those folks the other ones folks in other words they're kind of equivalent to each other signed up which will keep it in an orbit basically following following the earth around there used to be lots of science fiction stories about l-3 used to be a popular place to put the anti earth or you know if you're an evil genius that's where you put your hidden lair

Note 4=
professor Dave here let's learn the laws of thermodynamics science today explains the laws of thermodynamics help us understand why energy flows in certain directions and in certain ways a lot of the concepts described by thermodynamics seem like common sense but there is a layer of math beneath the intuitive level that makes them very powerful at describing systems and making predictions we won't get into the math but we should be able to describe these laws conceptually the first law described in the most basic way highlights conservation of energy energy is not created or destroyed it only changes forms from potential energy to kinetic energy to heat energy etc while we have found this to be untrue on the quantum level for chemists it does just fine however there seems to be a preferred direction in which energy flows from one form to another in order to understand why we look at the second law the second law introduces a new concept entropy entropy is quite difficult to understand but we can most easily describe entropy as disorder and the second law states that the sum of the entropy of a system and its surroundings must always increase in other words the entropy or the disorder of the universe is always increasing within a system there is also a tendency to go towards higher entropy the classic analogy is that your bedroom will over time become messy but it won't suddenly become neat another way to look at this is to say that entropy is a measure of how dispersed the energy of the system is amongst the ways that system can contain energy yet another way is to analogize entropic States to computer code let's take for example an ionic solid compared to the same substance as a liquid clearly the solid state is more ordered and the liquid state is more disordered or higher in entropy to describe the solid state using computer code you would need to include terms that describe the geometry of the lattice the intermolecular distances the precise configuration of every molecule and many other things but to describe the liquid state you would need to simply describe the volume of liquid and the shape of the vessel because the motion and configuration of the molecules are random that's far less information that needs encoding which is a way of rationalizing why increasing the entropy of a system is thermodynamically favorable we can look at all kinds of processes to highlight entropic influence heat will flow from a hot coffee cup into the table or your hand because the heat energy will be more disordered if more dispersed this is why heat spontaneously flows from hot to cold and not the other way around entropy the third law states that are perfectly crystalline solid at Absolute Zero has an entropy of zero as this is the most ordered state the substance can be in entropy is measured in joules per Kelvin note that entropy is not a measure of energy itself but of how energy is distributed within a system it is enthalpy the thermodynamic quantity we learned about before that is more accurately describing the energy of a system as we will see enthalpy and entropy intricately relate to tell us something about the Gibbs free energy of a system G or Gibbs free energy tells us whether a process will be spontaneous or not meaning if it will simply happen on its own change in Gibbs free energy is given by this equation which includes change in enthalpy change in entropy and temperature if Delta G is negative the process is spontaneous if positive it is non spontaneous so we can use this equation to see how a spontaneous process can be either enthalpically or entropically favorable or both but not neither for example if Delta H is negative which means exothermic and energetically favorable and delta s is positive which means an increase in entropy which is also favorable a negative minus a positive will always be negative or spontaneous if the opposite is true and both are unfavorable we have a positive minus a negative which will always be positive or non-spontaneous if only one of the two is favorable we have to do some math if Delta H is positive or endothermic that energetic unfavorability could be outweighed by the other term if the process is entropically favorable and since T is here this factor will increase with a larger T so entropically favorable processes are more likely to be spontaneous at higher temperatures conversely if it is energetically favorable but entropically unfavorable the entropic unfavorability will be minimized at lower temperatures this is a very important equation to understand because it describes all of the spontaneous processes in the universe there are those who incorrectly use entropy and the second law of thermodynamics to imply that order can't happen spontaneously but we just showed that in tropically unfavorable processes can be spontaneous at lower temperatures if they are energetically favorable an example of this is soap you need soap to wash nonpolar dirt and grime off your hands because they are immiscible with polar water molecules but soap molecules have polar heads and long nonpolar tails which allows them to spontaneously form structures called micelles these are spheres where the soap molecules orient themselves with the polar heads facing out in order to maximize ion dipole interactions with water molecules that bring the system to a lower energy and the nonpolar tails will all face in trapping the dirt by making a network of Vander Waals interactions the dirt trapped in the my cells washes away because the micelle as a whole is water-soluble due to the polar heads facing out that's how soap works and that's also how highly ordered structures can form spontaneously if by enthalpically favorable or energy storing processes in this way systems can defy entropy on the small scale but the second law does hold true in that the entropy of the universe is always increasing let's check comprehension thanks for watching guys subscribe to my channel for more tutorials and as always feel free to email me professor Dave explains at gmail.com