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in the last video we defined internal energy as literally all the energy that's in a system it's kind of the most inclusive version at least in my head so that's my system it's some type of container and I have a bunch of particles in here it's literally the sum of the kinetic energies of all these particles if they had potential energies we'd throw that in there if they have electrical potential we'd throw that in in there if they have bonds with each other the energies in that bond we would throw it in there it's everything it's all inclusive and you know it's I told you in the last video it's not intuitive that you stands for internal energy but I kind of think it you know you it contains the universe of energies and you know that's just for me to memorize it don't think too deeply into what I just said but this is internal energy internal energy if you show me a system and if you show me a system it has some internal energy it's a function of its state I don't care how it got to that state but if you show me a system in a certain state maybe with a certain pressure or certain volume or at a certain temperature although if you give me pressure and volume that should be enough I can tell you what its internal energy is or if you especially if you tell me the type of molecule I have and things like that now we also said in the last video that because internal energy is all the energy of the system it can't be it can't be randomly created or destroyed it can just be transformed from one from one form to another so if I have a change in internal energy so if I have a change in internal energy it can only be due to well it can be due to more than what I'm describing but in our simple world where all of the energy in the system and maybe we're dealing with gases because that's normally what you deal with in a first-year chemistry course it's going to be the heat that could be added to the system plus the work done on the system plus the work done on the system and like I said in the last video sometimes they'll say instead of plus the work done on the system don't they say - this is the work that the system does either way and here I just want to make another side side let me discussion here because I decided to write it without the little Delta's here and the reason why I did that is if you were to write this equation which you will see you'll see it in textbooks teachers will do it nothing inherently criminal about that but I just do that because it clears in my mind what heat and what work are relative to internal energy if I were to write Delta U is equal to heat Delta Q plus Delta W to me this implies that at some point I had some amount of heat in my system and then I have a different amount of heat in my system and I took the difference between the two and I got a change in heat so this implies that heat is somehow an inherent an inherent macro state of the system and that's not the case I cannot look at this system until I could tell you how much I can tell you what the internal energy of this system is I can tell you its pressure I can tell you its volume I can tell you its temperature these are all macro states of the system I don't know how it got to this situation but I can tell you about it I cannot tell you what the heat is of this system and that might be a little unintuitive because if I tell you you know if I ask you hey I have a cup of coffee what's the heat of it you might say oh it's you know you might give me the temperature because in our everyday language we use things like heat and temperature interchangeably but in thermodynamics heat is a transfer of energy a way to think about it is if internal energy is your bank account right so you could say change in bank account change in bank account change in bank change in bank account and it really is like the bank the energy bank account of a system if you have a change in a bank account that's you you had some deposits or withdrawals and heat and work are really just deposits or withdrawals into our energy bank account heat is one kind maybe heat is like a wire transfer so you could say it's wire transfer wire transfers to your account transfers to your account plus I don't know plus check deposit so I'm just you know I'm just plus check deposits now it wouldn't make sense it makes a lot of sense to say you could say what is my value of my bank account or you could say what is my change in my bank account you take two snapshots of your bank account two different times but would it make sense to say you know I could say I wired transferred $10 right so I could say I could say this statement would be plus $10 and I could say that I wrote 20 dollars in checks minus 20 dollars in checks in which case my change in my bank account would be minus $10 now would it make sense for me to say change in wire transfer that implies that when I started off maybe my bank account had $100 in it and now it has 90 when it when my bank account had $109 in it did it have any wire transfer amount no wire transfer was how money it was was deposited or taken away from my account likewise it didn't have a checking deposit account so I can't really it just seems weird to me to say change in wire transfer is ten dollars or change in check deposit is $20 or minus 20 dollars what you say is I made a twenty ten dollar wire transfer and I and I paid twenty dollars in checks so I had a net change in my bank account of ten dollars likewise I say how much work was done to me or I did which is essentially a deposit or withdrawal of energy or I could say how much heat was given to me or how much heat was released which is another way of depositing or withdrawing energy from my energy bank account so that's why I like to stick to this and I like to stay away from this and like just like I said you can't say how much heat is in this system so someone will say oh how much heat isn't that so you cannot say that there is no heat state variable for that system you have internal energy the closest thing to heat we'll talk about in a future video is enthalpy enthalpy is essentially a way of measuring how much heat is in a system but we won't talk about that just now and you can't say how much work is in a system you can't say oh I have X amount of work in a system the system can do work or have work done to it but there is not a certain amount of work because that energy in the system could could be all used for work it could all be used for heat it could all be used for a ton of different things so you can't say those things and that's why I don't like treating them like state variables or state functions so with that said this is our definition let's do a couple of simple problems just to give you intuition and I really want to give you make you comfortable my real goal is to make you comfortable with you know when to know to use plus or minus on the work and the best way to do it is not to memorize a formula but just to kind of think about what's happening so let's say that I have some system here and it's a balloon and let's say that I have no change in internal let's say I have no change in internal energy internal energy is zero and for our purposes we can kind of view it as the kinetic energy of the particles haven't changed and let's say by expanding a bit by my balloon expanding bit I did some work I'll do this in more detail in the next video but let's say I do so the system does system does 10 joules of work my question is how much heat was added or taken away from the system how much heat was added or taken away so the way I can think about you don't even have to write the formula down or you can write it you could say look the internal energy the amount of energy in the system hasn't changed the system did 10 joules of work so that's energy going out of the system it did 10 joules so 10 joules went out in the form of work if the internal energy did not change then some energy then essentially 10 joules of energy had to go into the system 10 joules had to go into the system if it didn't the internal energy would have gone down by the amount of work we had so 10 joules and the only way if this is the network the only way that we're talking about that we can add energy outside of work is through heat so 10 joules of heat must have been added so we can write 10 joules of heat 10 joules of heat added added to system now let's look at that from the point of view of the actual formula if we have Delta U is equal to is equal to heat added plus work done to the system then we would say okay this was zero Oh two equal to the heat added to the system we remember in this way we're saying this is the heat done or the work done to the system right W is work done now the system did work to something else it didn't have work done to it to it so if the if if this is work done to the system and it did work then this is going to be a minus 10 minus 10 joules and then you solve both sides of this you add 10 to both sides and you get you get 10 is equal to Q which is exactly what we got up here but this can get confusing sometimes because you like oh did work it you know is this heat that the system did is this the heat is this heat that was added to the system or taken away the tenth the convention is all it tends to be that this is heat added heat added but then sometimes it's confusing is this the work done to the system or work done by and that's why I like just doing it this way if the system does work it loses energy if the system has work done to it it gains energy so let's do another problem I mean I could have done this exact same thing using the other formula you'll sometimes see Delta U is equal to Q minus the work that the system does does by the system done by the system work done by the system in this case once again change in internal energy was zero that is equal to heat added to the system minus the work done so - I told you at the beginning of the problem that the system did ten joules of work so minus the work done minus ten joules we get the same situation up here from two different formulas and we got ten is equal to Q either way the heat added to the system is 10 joules let's do one more let's say that I don't know cute like let's buy don't know let's say five joules of heat heat taken away from system taken away from system and let's say that one Joule of work done on system done on system so maybe we're compressing the balloon on the system what is our change in internal energy or let's say that our well let's just figure out our change so the way I think of it is five joules of heat taken away from the system that's going to reduce our internal energy by minus five and if one Joule of work is done on to the system we're putting energy into it so that'll be plus 1 so minus five plus one is going to be minus four or enter our change in internal energy is minus 4 joules now we could have done that a little bit more formally with the formula change in internal energy is equal to heat added to the system Plus work done on the system work done on the system so it's equal to heat added to the system we had five joules heat taken away so this is minus five Plus work done on the system we have one Joule of work done on the system and there we get once again - for now I am I could have written that same formula the other way I could have said change in internal energy is equal to heat added to the system minus the work that the system does I want to do this both ways because I don't want you get confused either way you see in in on problems or in school or maybe you take one class that doesn't one way in one class that does the other if you use it this way well is the heat added to the system we had heat taken away so it's minus 5 so minus the work that the system does how much this work does the system do well the system had one Joule of work done to it so did it did it set off minus one joules of work right so it's minus minus one I want to be clear when I use this formula this is system this is work done by system done by this is work done to done to the system had work done to it so it had minus 1 where joules of work done by the system so these become pluses and you get back to a minus 4 do whatever is intuitive for you for me this tends to be the most intuitive where you don't even use the formula you just think if I'm doing work I'm using up energy if I get work done to me I'm being handed over energy if I have heat taken away from me I'm giving away energy if I have heat added to me I have I'm getting energy see in the next video

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