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# More on entropy

## Video transcript

I'm going to do one more video on entropy maybe I'll do more in the future but I thought I would at least right now do one more because I really want to make clear the idea of entropy is a macro state variable so let me write that down and S which is entropy is a macro state variable I'm going to write macro in bold red it's a macro state variable and I want to emphasize this and I talked a little bit about it in my previous video but I think even then I wasn't as exact as I needed to be and the reason why I want to say it's macros because there's a very strong temptation to point to particular microstates and say does this have higher entropy or lower entropy than another for example the the classic one even I did this you know you have a actually let me make up a bigger thicker lines okay so you have so you have this box that has a divider in it and we've gone through this multiple times let me draw the divider like right there okay so we say at first if we have a system where all of the molecules are over here so that's our first scenario and then our second scenario we studied this a lot we blow up the wall here we blow up the wall here and we actually calculated the entropy control okay let me copy it and then I'm going to paste it so let me put these next to each other all right so I have these two things and then the second time I blew away this wall let me blow it away okay let me erase the wall there and then we said once the system reaches equilibrium again remember for a system of these macro state variables like pressure like volume like temperature like entropy are only defined once the system is in equilibrium so once the system is in equilibrium again you know these particles are now allowing the same number of particles so maybe some let me erase some of these particle let me move them let me see if I can select some so whoops let me see I could select these particles and I could move them there so we'll have a more even that's not a good way to do it let me just redraw a set 1 2 3 4 5 6 7 8 particles let me erase what I have I'll make it with a more even distribution so then once I blow away the wall I might have 1 2 3 4 5 6 7 8 now the reason why I'm doing all of this is because there's a temptation to say that this state this state what I just drew you when I you know made sure to blow these away and draw 8 more I drew a microstate this is a microstate this is a microstate where actually any time someone is actually drawing molecules for you they're drawing a microstate they're drawing a microstate now I want to be very clear this microstate does not have more entropy than this microstate in fact microstates you don't have entropy you can't even entropy does not make sense what you can say is a system what you can say and I'm at this time I will draw it without the particles that if I have a container that is this big that contains so it has some volume so volume is equal to v1 its temperature is equal to t1 and it has 8 particles in it this has some entropy associated with it and what we can't say is if we were to double the size of this container if we were to double the size of this container which we did by blowing away that wall now all of a sudden our volume is equal to 2 times v1 if we say this is double our temperature is equal is still equal to t1 we saw that a few videos ago and we still have 8 molecules all we can say is because the entropy of this system is higher so now entropy is higher and I want to make this very clear because you never see it drawn this way people always want to draw the actual molecules but that confuses the issue that when you draw actual molecules you are showing a particular State for example this system if we were to look if we were to actually measure the microstate it could be is a very very infinitesimally small probability but all of the molecules all eight molecules might be right there I mean it's very easy it's it's almost you know you could read for the whole universe to come and go and it might not happen but there is some probability that happens so you can't assign entropy to a particular state all you can do is assign it to a particular system I want to be clear about that so even iYou know I talked about a clean and dirty room and all of that clean versus dirty room clean room dirty room and the point I was making is the entropy of a room is not dependent on its cleanliness or its dirtiness in fact you could kind of view these as each states of a room but even more these really aren't even states of the room because when a room is clean or room is static at a macro level they're static when they're when they're you know if you know if I have a a you know my books are lined like let me see you know sometimes people look at a deck of cards and say oh if I have all my cards stacked up like this or if I have all my cards that are all messy like that you know all messed up around that this has higher entropy and I want to make it very clear I mean maybe you can kind of make it knowledge but that's not the case these are both both of these systems are macro States for example I mean you know these aren't like this not like these cards are vibrating around any more than these cards are it's not like these can take on more configurations than these cards can so when you talk about entropy here you're trying to take a macro variable that's describing at a micro level and the cards themselves are not the micro level because they're not vibrating around continuously due due to some kinetic energy and whatever it's the cards molecules that are at the micro level and if these cards if you have the same you know mass of cards as you have here and if they're the same temperature the molecules in these cards can take on just as many states as the molecules in these cards so they're going to have the same entropy entropy is a macro state variable or macro state function that describes the number of states a system can take on so here I would view the cards as a system and we we care about is not the number of configurations the cards themselves can take on the cards aren't constantly vibrating and changing from one thing to another it's it's at the atomic level at the molecular level that as long as we are above absolute zero and which we pretty much always are things are going to be vibrating around continuously and continuously changing its state so it's almost impossible to measure the state and since it's impossible to measure the state we use something like entropy to say well how many states can we have and and I mean you know all of these things entropy whether we call it internal energy whether you look at entropy whether we look at pressure volume temperature these are all if you can think about some way these are shortcuts around having to actually measure what each molecule is doing and entropy you can kind of view it as a meta shortcut I mean temperature tells you average kinetic energy this tells you all of the energy that's in it this tells you you know how frequently the molecules are bumping against a certain area this tells you on average kind of where you know the outermost molecules are entropy is kind of a you can almost do it as a meta state variable it tells you how many states how many microstates can we take on so I just want to make this very clear because this is often confused and people there's a very very very strong temptation to point to a particular state and to say that that has higher entropy than another that somehow the you know this state is more entropic than that state that's not the case this system is more in tropic than this system then this half boxes has more volume if they have the same temperature and the same and and the if they have the same temperature with more volume then it's particles can take on more possible scenarios in any given moment in time anyway hopefully you found that a little bit useful I just want to make it very very very clear because this is often often often confused this is a macro state variable for a system where a system is composed of Mott these you know things that are bumping around randomly every you know millionth of a second they're changing state so you don't even you can't even it's very hard to even measure one of the microstates you can't point to a microstate and say oh this is higher entropy than another anyway see in the next video