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let me draw a good old PV diagram that's my pressure axis this is my volume axis just like that I have pressure and volume I showed several videos ago that if we start at some state here in the PV diagram right there and that I change the pressure and a volume to get to another state and I do it in a quasi-static way so essentially I'm always close to equilibrium so my state variables are always defined I could have some path that takes me to some other state right there and this is my path I'm going from the state to that state and we shade we say well if i we show that if I just did this the work done by the system is the area under this curve and then if I were to move back to the previous state and then if I were you know by some path just some random path that I happen to be drawing the work done to the system would be the area under this light blue curve so the net work done by the system ended up being the area inside of this path so this is something during a different color the net work done would be the area inside of this path when I go in this clockwise type of direction so this is the work the network write net work done by system done by system done by the system and now we also know so I mean so that's well we also know that if we're at some point on this PV diagram that our state is the same as it was before so if we go all the way here and then go all the way back all of our state variables will not have changed our pressure is the same as it was before our volume was the same as it was before because we went all the way back to that same point on the PV diagram and our internal energy is also the same point as it was before so our change in internal energy over this path you're going to have a different internal energy here than you had here when you go around the circle and you get back your change in internal energy is equal to 0 and we know that our change in internal energy we know that change in internal energy its defined as and this is from the first law of thermodynamics the heat added to the system so it's the heat added to the system minus the work done by the system now if we go on a closed loop on our PV diagram then what's our change in internal energy it's zero so we get 0 0 change in internal energy because we're at the same state is equal to the heat applied to the system minus the work done or and I've done this little little exercise multiple times I think this is probably the fourth or fifth time I'm doing it we get that the heat added to the system if we just add W to both sides is equal to the work done by the system so this area under this in between inside of this path I already said it's the work done by the system and if you don't remember even where that came from it was remember pressure times volume times change in volume is a little incremental change in work and that's why it relates to the area but we've done that multiple times I won't go there just yet but so if you have any area here some heat was added to the system some net heat right some some heat was added here and some heat was probably taken out here but you have some net heat that's added to the system and I use that argument to say why heat wasn't a good Oh isn't a good state variable because and I had a whole video on this that if I define some state variable let's just say heat content let's say I wanted to find some state variable heat content and I would say that the change in change in heat content would of course be equal to the change in heat and that's what I'm defining if I'm adding heat to the system my heat content should go up but the problem with that heat content state variable was that let's say over here I say that the heat content let's say that the heat content is equal to 5 now I just showed you that if we go on some path here and we come back and there's some area in this and in this little path that I took that some heat was added so let's say that this area and you know let's say that this area right here so this is Q is equal to the work done by the system let's say it's equal to 2 so every time if I start at heat content is equal to 5 that's just an arbitrary number and I were to do this entire path when I go back the heat content would have to seven and then when I go back and do it again my heat content would have to be nine and would have to increment by two every time I do this exact path it would have to increment by the amount of area that this path goes around so heat content can't be a state variable because it's dependent on how you got there it is a state variable and remember this in order to be a state variable if you're at this point you have to have the same value if your internal energy was ten here when you do the path and you come back your internal energy will be ten again that's why internal energy is a valid state variable it's dependent only on your state if your entropy was 50 here when you go back you do all sorts of crazy things and you come back to this point your entropy is once again 50 if your pressure here is I don't know if it's 5 atmospheres when you come back here your pressure will be 5 atmospheres your state variable cannot change based on what path you took if you're at a certain state that's all that matters to the state variable now this heat content didn't work and that's why we actually led into some videos where I divided by T and we got entropy which is was an interesting variation but that's still not satisfying what if we really wanted to develop something that could in some way be a state variable but at the same time measure Heat so obviously we're going to have to make some compromises because if we just do a very arbitrary kind of heat content variable then every time you go around this it's going to change so it's not a valid state variable so let's see if we can make up one so let's just make up a definition let's call my new thing that I'm going to try to maybe approximate heat let's call it h and just is a little bit of a preview we're going to call it enthalpy enthalpy and let's just define it I'm just playing around let's just define it as the internal energy plus my pressure times my volume plus pressure times volume so then what would my change would be might change in enthalpy B so my change in enthalpy will be of course the change of these things but I could just say that's my change in my internal energy plus my change in pressure times volume now this is interesting want to make a point here this by definition is a valid state variable why is it because it's the combi it's the addition of other state variables right at any point in my PV diagram and it's also true if I did diagrams that were entropy and temperature or anything that dealt with state variables at any point on my diagram U is going to be the same no matter how I got there P is by definition going to be the same that's why it's at that point V is definitely going to be at the same point so if I just add them up this is a valid state variable because it's just the sum of a bunch of other valid state variables so let's see if we can somehow relate this thing that we've already established as a valid state variable from the get-go from our definition this works because it's just the sum of completely valid state variables so let's see if we can relate this somehow to heat so we know what Delta U is is from from one of you know it's if we're if we're dealing with all of the internal energy or the change in internal energy I'm not going to deal with all the other chemical potentials and all of that it's equal to the heat applied to the system heat apply to the system minus the work done by the system all right let me put everything else there the change in l to enthalpy is equal to the heat applied minus the work done that's just the change in internal energy and plus Delta PV this is just from the definition of my enthalpy now this is starting to look interesting what's the work what's the work done by a system what's the work done by a system so I could write change in h or enthalpy is equal to the heat applied to the system minus what's the work done by a system if I have a if I have some system here it's got some piston on it you know if we're doing in a quasi-static I have those the classic pebbles that I've talked about in multiple videos when I apply heat or when I let's say I remove some of these pebbles so I am at a different equilibrium but what's actually happening when is the work being done you have some pressure being applied up here and this piston is going to be moving up and your volume is going to increase and we showed multiple videos ago that the work done by the system can be and kind of view this is the volume expansion work it's equal to pressure if we're pressure times change in volume times change in volume and then let's add the other part so this was our change in internal energy I had several videos where I show this and let me add the other part of the equation so our enthalpy our change in enthalpy can be defined by this now something interesting is going on I said that I wanted to define something because I wanted to somehow measure heat content my change in enthalpy will be equal to the heat added to the system if these last two terms cancel out if these if I can somehow get these last two terms to cancel out then my change in enthalpy will be equal to this if somehow these are equal to each other so under what conditions under what conditions are these equal to each other or another way under what conditions is Delta pressure times volume equal to pressure times Delta volume when does this happen when can I make this same because if I can make this statement then these two terms are equivalent right here and then my change in enthalpy will be equal to the heat added well the only way I can make this statement is if pressure is constant if pressure is constant constant constant pressure now why is that let's just think about it mathematically if this is a constant then if I just change you know if this is just five five times the change in something is the same thing as a change in five times that thing so it just mathematically works out you can work you could or if you if you view it another way if this is a constant if this is a constant you can just factor it out right I mean you could just say you know well if you if I said the change in 5x that would be you know you could say that's the that's equal to 5 times X final minus 5 times X initial and you could say that well that's just equal to 5 times X final minus X initial well that's just equal to 5 times the change in X it's just kind of almost too obvious for me to explain I think this you know sometimes when you over explain things it might become more confusing so this applies and the five I'm just doing this analogy for a constant so if pressure is constant then this equation is true so if pressure is constant if pressure is constant so this is a key assumption then so if we have if heat is being applied in a constant pressure system so we could write it this way so I'll write it multiple times because this is key if pressure is constant pressure is constant then our definition are our little thing we made up this enthalpy thing which we defined as internal energy internal energy plus pressure and volume then in a constant pressure system our change in enthalpy we just showed will be equal to is equal to the heat added to the system because all of this these two things become equivalent under constant pressure so I should write that this is only true when heat is added in a constant pressure system so how does this gel with what we did up here on our PV diagram what's happening in a constant pressure system let me draw our PV diagram that's P that's V let me make sure I mean right there this is P and this is V so what's happening in constant pressure we're at some pressure right there so if we're under constant pressure that means we can only move along this line so we could go from here to there and back to there or we can go from there to there back to there so we could go there all the way there and then go back but what do we see about this is there any area in this curve I mean there is no curve to speak up because we're staying in a constant pressure we've kind of squeezed out this diagram we've made the forward pass and the return Pat's the same exact path so because of this because of this you don't have that state problem right because no no net heat is being added to the system when you go from this point all the way to this point and then back to this point so because of that you can kind of see visually that enthalpy in a constant pressure when you're not moving up and down in pressure is the same thing as heat added so you might say hey Sal this was a bit of a promis-- constant pressure you know that's a big assumption to make why is this useful at all what's useful because most chemical reactions especially ones that occur in an open beaker or that might occur at sea level and that should be a big clue they occur at constant pressure you know if I just have if I'm sitting at the beach and I'm have my chemistry set and I have some beaker of something and you know and I'm throwing other stuff into it and you know I'm looking for a reaction or something it's a constant pressure system this is going to be atmospheric pressure one atmosphere I'm sitting at sea level so this is actually very useful for this is a very useful concept for everyday chemical experience it might not be so useful for engines because engines always have pressure changing but it's very useful for actual chemistry for actually dealing with you know what's going to happen to a reaction at at a constant pressure so what we're going to see is that this enthalpy you can kind of view it as the heat content when pressure is constant fact it is the heat content when pressure is constant so somehow we were it will not somehow I showed you how we were able to make this definition which by definition was a state variable because it was the sum of other state variables and if we just make that one assumption of constant pressure it all of a sudden reduces to the heat content of that system so we'll talk more in the future of measuring enthalpy but your scepter say if it's cop pressure is constant enthalpy is the same thing as it's really only useful when we're dealing with constant pressure but if we have pressure constant enthalpy can be imagined as heat content and it's very useful for understanding whether chemical reactions need heat to occur or whether they release heat so on and so forth see you soon

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