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Current time:0:00Total duration:14:37

Quasistatic and reversible processes

Video transcript

in the last video where we talked about macro states we set up this situation where I had this canister the cylinder and had this movable ceiling I call that a piston and the piston is being kept up by the pressure from the gas in the canister and it's being kept down by in the last example I had a a rock or weight on top and above that I had a vacuum so essentially there's some force per area or pressure being applied by the bumps of the particles into this piston and if this weight wasn't here let's say it assumes that the piston itself or this movable ceiling itself it has no mass if that weight wasn't there would just be pushed indefinitely far because there'd be no pressure from the vacuum but this weight is applying some force on that same area downwards so we're at some equilibrium point some stability and we plotted that on on this PV diagram right here I'll do it in magenta so that's our state one that we were in right there and then what I did in the last video I just blew away half of this block and as soon as I blew away half of this block obviously the force that's being applied by the block will immediately go down by half and so the gas will push up on it and it happened so fast that all of a sudden the gas is pushing up right when it happens the gas near the top of the canister is going to have lower pressure because it has less pushing up against it the molecules that are down here don't even know that I blew away this block yeah it's going to take some time and essentially the the gas is going to push it up and then maybe that it'll oscillate down and then push it up and oscillate down a little bit and it'll take some time eventually do we get to we get to another equilibrium state where we have a new probably or definitely lower pressure we definitely have a higher volume and if we weren't well I won't talk too much about it yet but we probably have a lower temperature as well and this is our new this is our new state and our macro straights pressure and volume are defined once we're at the new equilibrium so we're right here so my question in the last video was how did we get here is there any way to have defined a path to get from our first date where pressure and and volume were well defined because the system was in thermodynamic equilibrium to get to our second state and the answer was no because between this state and this state all hell broke loose I had different temperatures at different points in the in the mutton they in the system I could have had different pressure here then I had up here the volume might have been fluctuating for a moment-to-moment so when you're outside of equilibrium and I had written down it over I had written it down over there you cannot define or you can't say that those macro variables are well-defined so there was no path that you could say how we got from mere raíces how we got from state 1 to state 2 you could just say okay we were in some type of equilibrium so we were in state 1 then I blew away half the rock the pressure went down the volume went up the temperature also probably went down and so I ended up in this other state once I reached equilibrium and that's all fair and good but wouldn't it have been nice if there was some way if we could have said look you know there's some way that we got from this point to this point if we could perform my little rock experiment in a slightly different manner so that all this hell didn't break loose so that maybe at every point in between our my macro variables are actually defined so how could I do that remember I said that the macro variables the macro States whether it's pressure temperature volume and there are others but I say that these are only defined when we are in a thermodynamic equilibrium and that just means things are stopped they've reached a stability point that for example the temperature is consistent throughout the system if it's not consistent throughout the system I shouldn't be talking about it if the temperature is different here than it is up here I shouldn't say that the temperature of the system is X it's different at different points so I really can't make a well-defined statement about temperature similar for pressure or for or for volume because the volume is also fluctuating but if I perform that same experiment or that same process I should call it let me draw it again so I have my canister and instead of starting with a rock just one big rock draw this is my piston right here at the top of my is the movable ceiling of the cylinder and I have some gas inside of it instead of having just one big rock like I had over here how about I start with an equal weight of rock but let's say I have a bunch of small pebbles that add up to that same rock so this is a bunch of one you know just a just a pile of pebbles you can all you know maybe there's sand they're super super duper duper duper small right instead of just blowing away half of the sand all at once like I did with that rock over there and immediately jumping to that state and throwing the whole system into this undefined state of non equilibrium instead of doing that let me just do things very slowly and very gently let me just take out one grain of sand at a time all right so if I just take out one grain of sand and I do it and then I and then I wait and so I took out an infinitesimal amount of weight so what's going to happen well this this Pistons going to move up a little bit and let me draw that so let me copy and paste it so now my piston well since I just took out one little piece of sand the force pushing down will be a little bit less with the pressure pushing down will be a little less and so on my piston let me see if I can draw this it will have moved up let me erase it it will have moved up a very infinitesimal infinitesimally means an infinitely small infinitely small amount right it would have moved an infinitely small amount of time and so you wouldn't have thrown that system into this you know havoc that I did this last time right of course we haven't moved all the way here yet but what we have done is we would have moved from that point maybe to this this other point right here that's just a little bit just a little bit closer to there I've just removed a little bit of the weight so my pressure went down just a little bit my volume went up just a little bit temperature probably went down and the key here is I'm trying to do it in such small increments that as I do it my a system is pretty much super close to equilibrium it's not in this that I'm you know I'm just doing just slow enough that at every step it achieves equilibrium almost immediately or it's it's almost in equilibrium the whole time I'm doing it and then I do it again and do it again and I'll just draw my drawings a little less neat just for the sake of time all right let's say I remove another little little dot of sand that's infinitely small mass and now my my little piston will move with just a little bit higher and I have remember I have one less sand up here then I had over here and then my volume if my gas increases a little bit my pressure goes down a little bit and I've moved to this point here what i'm doing here is i'm setting up what's called a quasi-static process quasi-static process quasi-static process and the reason why it's called that is because almost static it's almost an equilibrium the whole time I'm just every time i move a grain of sand i'm just moving a little bit closer and obviously even a grain of sand the reality is if i were to do this in real life even a grain of sand on a small scale is going to wreak a little bit of havoc on my system this piston is going to was going to go up and out a little bit so i'll say oh let me just do even a small or grain of sand and do it even a little bit slower so that i'm always in equilibrium so as you can imagine this is kind of a theoretical thing if i did an infinitely small grains of sand and it just slow enough so that it just gently gently moved from this point to this point but we like to think of it theoretically because it allows us to describe a path because remember why don't why am i being so careful here why am i so careful to make sure that the state the system is in equilibrium the whole time when i get from there to there because our macro states are macro variables like pressure volume and temperature are only defined when we're in equilibrium so if i do this process super slowly and super small increments it allows me to keep my pressure and volume and actually my temperature of macro states at any point in time so i could actually plot a path so if i keep doing it small as well as well i could actually plot a path laughs to say how did I get from state 1 to state 2 on this on this PV diagram and you might say you know how this is this is all and I'll and I'll take a little step back here I always found this really confusing you know why do why are people you'll see a lot of a lot of talk and thermodynamic circles or even your book about you know this is it has to be a quasi-static process and you know I was just wanting you know why are people going through these pains to describe this process where you're removing sand after sand and the whole point is because you want to get as close to equilibrium the whole time you're doing it as possible so that your pressure and volume are defined the whole time the reality is in the real world you can never get something that's continuously defined but you can just do really really really small increments so each small increment you're at some equilibrium and if you're not happy with that you can do even smaller increments so at some point it's some limiting point you do have some type of continuous state change or while you're always in equilibrium it's almost an oxymoron because you're saying you're static you're saying that your your-your-your an equilibrium the whole time but clearly you are also changing the whole time you keep removing article little pieces of sand but you remove them just slow enough that all that crazy up-and-down motion and all of the flux and all of the weird temperature changes don't happen and it just you know just it just slowly slowly slowly creeps up and this isn't this is the reason why I'm even going through this exercise is because it's key when we start talking about thermodynamics and these PV diagrams and we'll start talking about Carnot engines and all of that that we'd be able to at least theoretically describe the path that we take on this PV diagram and we wouldn't have been able to do that if we can't assume that we're dealing with a quasi-static process now there's another term that you'll hear in thermodynamic circles that really I mean to me it really I don't know I had trouble comprehending it the first time I heard it called reversible reversible and sometimes these terms quasi static and reversible or used interchangeably but there is a difference quasi static reversible processes are quasi static and most quasi-static processes are reverse but there are a few special cases that aren't but the idea of a reversible process is something that happened so slowly so in this example I took off a grain of sand and I got to this state but if I assume that no friction when you know when this piston moved up a little bit in the real world let's say if these were you know this piston was metal when this rubs against the canister there'd be a little bit of friction generated and a little bit of energy would be dissipated as friction or heat but in a reversible process we're assuming the look this is frictionless when anything happens in the system when we go from this state right here let's say this is state a to state B so this is state a this is state B when we go from this state to this state one we're infinitesimally close to equilibrium the whole time so all of our macro states are well-defined and even more when we move from one state to the other there's no loss or dissipation of energy so those are two there's those are two important characteristics one infinitely close to equilibrium at all times and no loss of energy and the reason why that matters for a reversible process is because if we wanted if we were sitting in state B we could just add another grain of sand back in add another grade of sand back in push down this piston infinitely slow at an infinitely small increment and get back to state a right so that's why it's called reversible you could you could be at this point right here and take out a little bit of sand and get to this point right here but if you want since no energy was lost you could add a little bit of sand and get back to this point right here now the reality in the real world is if there is no such thing as a perfectly reversible process there will always be whenever you do anything there will always be some energy or heat loss to do lost to the process but so in the real world if I moved down here if I tried to put the sand back I would lose some energy and probably get to a little slightly different point but you don't have to worry about that the important takeaway from this video is that in that this situation I described there there was no intermediate macro state variables because our system was in flux it wasn't an equilibrium so if we wanted to get intermediate states we just have to essentially do this process it's or the and so slow I mean it theoretically would take you forever so we can only approximate it but the sand gives you an idea of what we're talking about and if we did it slowly with these infinitesimally small particles of sand then we can define the state at every point along the along the along the process and that's why we call it quasi static because at any point it's almost static it's almost an equilibrium so our pressure volume and temperatures can be defined and then if we add to that the notion that we haven't lost any heat when we're going in one direction or or another we could say it's reversible because if we took a piece of sand away we can always add a little a little bit of sand next now actually with that said let me give you the one example if maybe a quasi-static not actually I'll save that for a future video anyway hopefully you understand that these are these these are two concepts that used to really confuse me and hopefully this this this clears it up a little bit and I think more than what it is I think you know the first time I read about them like okay well what's the big deal the big deal is it allows you to define every your your macro States for every state in between these two states that you care about when you just did it as a regular kind of non quasi-static process in between you don't know what happened