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Current time:0:00Total duration:17:40

First law of thermodynamics / internal energy

Video transcript

I've now done a bunch of videos on thermodynamics posed both in the chemistry and the physics playlist and I realize that I have yet to give you or at least if my memory serves me correctly I have yet to give you the first law of thermodynamics and I think now is as good a time as any the first law of thermodynamics thermodynamics and it's a good one it tells us that energy energy I'll do it in in in this magenta color energy cannot be created or destroyed it can only be transformed from one form or another so energy cannot be created or destroyed only transformed only transformed so let's think about a couple of examples of this and we've touched on this when we learned mechanics and kinetics in our in our in our physics playlist and we've done a bunch of this in the in the chemistry playlist as well so let's say I have some rock that I just throw as fast as I can straight up maybe it's a ball of some kind so I throw a ball straight up that arrow represents its velocity vector right it's going to go up in the air maybe I let me do it here I throw a ball and it's going to go up in the air it's going to decelerate due to gravity and at some point up here the ball is not going to have any velocity so at this point it's going to slow down a little bit at this point is going to slow down a little bit more and at this points going to be completely stationary and then it's going to start accelerating downwards in fact it was always accelerating downwards it was decelerating upwards and then will start accelerating downwards so here it's velocity will look like that and here it's velocity you look like that and then right when it gets back to the ground if we assume negligible air resistance its velocity will be the same magnitude as the upward but in the downward direction so when we looked at this example and we've done this tons in the projectile motion videos in the chem in the physics playlist over here we said look we have some kinetic energy here and that makes sense I think to all of us energy intuitively means that you're doing something so kinetic energy energy of movement of kinetics right it's moving so it has energy but then as we decelerate up here we clearly have no kinetic energy zero kinetic energy zero kinetic energy so where did our energy go I just told you the first law of thermodynamics that energy cannot be created or destroyed but I clearly had a lot of kinetic energy over here and we've seen the formula for that multiple times and here I have no kinetic energy so I clearly destroyed kinetic energy but the first law of thermodynamics tells me that I can't do that so I must have transformed that kinetic energy I must have transformed that kinetic energy into something else and in the case of this ball I've transformed it into potential energy so now I have potential energy and I will go into the math of it but potential energy is just the potential the the potential to to turn into other forms of energy I guess it's the easy way to do it but the way to think about it is look the ball is really high up here and by virtue of its position in the universe it's if something doesn't stop it it's going to fall back down or it's going to be converted into another form of energy now let me ask you another question let's say I throw this ball up and let's say we actually do have some air resistance so I throw the ball up I have a lot of kinetic energy here so I have kinetic energy here then at the peak of the of where the ball is it's all potential energy it's the kinetic energies disappeared and let's say I have air resistance so when the ball comes back down the air was kind of slowing it down so it doesn't go so when it reaches this bottom point it's not going as fast as I threw it so when I reach this bottom point here my ball is going a lot slower than I threw it up to begin with and so if you think about what happened I have a lot of kinetic energy here I'll give you the formula the kinetic energy is a mass of the ball times the velocity of the ball squared over two that's the kinetic energy over here and then I throw it it all turns into potential energy and then it comes back down turns into kinetic energy but because of air resistance I have a smaller ASSA tea here I have a smaller velocity here than I did their kinetic energy is only depend on the magnitude of the velocity I could put a little no absolute sign there so that we're dealing with the magnitude of the velocity so I clearly have a lower kinetic energy here so lower kinetic energy lower kinetic energy here then I did here right and I don't have any potential energy left let's say this is the ground we've hit the ground so I have another conundrum you know when I went from kinetic energy to no kinetic energy there I could go to the first law and say oh what happened the first law says Oh salad it all turned into potential energy up here and then and you saw it turned into potential energy because in the ball accelerated back down and turn back into kinetic energy but now I say no mister first law of thermodynamics look at this point I have no potential energy and I had all kinetic energy and I had a lot of kinetic energy now at this point I have no potential energy once again but I have less kinetic energy my ball has fallen at a slower rate than I threw it to begin with and and the thermodynamic says oh well that's because you have air and not say well I do have air but where did the energy go and then the first law of thermodynamics says oh the the your your when your ball was falling the ball was Flemmi see let's see the the best the ball let me get the ball yellow so when your ball was falling it was rubbing up against air particles it was rubbing up against molecules of air right and right where the molecules bumped into the wall there's a little bit of friction friction is just essentially your ball made these molecules that it was bumping into vibrate a little bit faster it essentially if you think about it if we if you go back to the macro state microstate problem or descriptions that we talked about these balls this ball is essentially transferring its kinetic energy to the molecules of air that it rubs up against as it falls back down and actually was doing it on the way up as well and so that kinetic energy that you think you lost or you destroy it at the bottom of here because your balls going a lot slower was actually transferred to a lot of air particles it was a lot of to a bunch of air giggles now it's next to impossible to measure exactly the kinetic energy that was done on each individual air particle because we don't even know what their microstates were to begin with but we can say is in general I transferred some heat to these particles I raised the temperature of the of the of the of the of the air particles that the ball felt through by by by rubbing those particles or giving them kinetic energy remember temperature is just a measure of kinetic and it temperature is a macrostate or kind of a gross way or a macro way of looking at the kinetic energy of the individual molecules it's very hard to measure each of theirs but if say on average their kinetic energy is X you're essentially giving an indication of temperature so that's where it went it went to heat and heat is another form of energy so the first law of thermodynamics says I still hold you had Pinet you had a lot of kinetic energy turned into potential that turned into less kinetic energy and where did the the remainder go it turned into heat because it transferred that kinetic energy to these two these air particles or in the surrounding medium fair enough so now that we have that out of the way how do we measure the amount of energy that something contains measure the amount of energy and here we have something called the internal energy internal energy of a system once again this is a macro macro state or you can call it a macro description of what's going on this is called U for internal the way I remember that is that the word internal does not begin with the u U for internal energy internal energy U for internal energy and it literally is if I have let me go back to my example that I had in the past that I did in our previous video you're watching these in order of I have you know some gas in a say I have some gas with some movable ceiling at the top that's its movable ceiling that can move up and down we have a vacuum up there and I have some gas in here I have some gas in here the internal energy literally is all of the energy that's in this system so it includes and for our purposes especially when you're in a first-year chemistry course and it's the kinetic energy kinetic energy of all the atoms or molecules atoms or molecules and in a future video I'll actually calculate it for you know how much kinetic energy is there in a container and that'll actually be our internal energy plus all of the other energy so these atoms you know they have some kinetic energy because they have some translational motion if we look at the microstate if they're if they're just individual atoms you can't really say that they're rotating because what does it mean for an atom to rotate right because it's electrons or just jumping around anyway so if they're individual atoms they can't rotate but if there are molecules they can rotate if it looks something like that there could be some rotational energy there it includes that if we have bonds so I just drew a molecule the molecule has bonds those bonds contain some energy that is also included in the internal energy if I have some electrons let's say that this was not a let's well I'm doing it using a gas and gases aren't good conductors but let's say I'm doing it for a a solid oh I'm using the wrong tool so let's say I have a bunch of let's say I have some metal all right those are my metal let me do more my metal atoms and in that metal atoms I in that metal atom I have you know a bunch of electrons it's the same color I have a bunch of uses a suitably different color I have a bunch of electrons here and I have fewer here so these electrons really want to get here maybe they're being stopped for some reason so they have some electrical potential maybe there's a gap here you know where they can't conduct or something like that internal energy includes that as well that's normally the scope out of what you'd see in a first-year chemistry class but it includes that it also includes includes literally every form of energy that exists it also includes for example in a metal if we were to heat this metal up they start vibrating right they start moving left and right or up or down or in every possible direction and if you think about a molecule or an atom that's vibrating it's going from here and then it goes there then it goes back there it goes back and forth right and if you think about what's happening when it's in the middle point has a lot of kinetic energy but at this point right here when it's about to go back it's completely stationary for you know a super small moment and at that point all of its kinetic energy is potential energy and then it turns into kinetic energy then it goes back to potential energy again it's kind of like a pendulum or it's it's actually harmonic motion so in this case internal energy also includes it includes the the kinetic energy for the molecules that are moving fast but it also includes the potential energies for the molecules that are vibrating but it there at that point where they don't have kinetic energy so it also includes potential energy so internal energy is literally all of the energy that's in a system that's in a system and and and for most of what we're going to do you can assume that we're dealing with an ideal gas instead you know becomes a lot more complicated with solids and conductivity and vibrations and all that we're going to assume we're dealing with an ideal gas and even a better we're going to assume what we're dealing with in a monoatomic ideal gas so maybe this is just helium helium or neon one of the ideal gases they don't want to bond with each other they don't form molecules with each other or in in in you know well let's just assume that they're not they're just individual individual atoms right in that case the internal energy we really can simplify to it being the kinetic energy if we ignore all of these other things but it's important to realize the internal energy is everything it's all of the energy inside of the system it's it's it's it's you know it's it's if you said what's the energy system its internal energy so if in the the first law of thermodynamics says that energy cannot be created or destroyed only transformed so let's say that internal energy is changing so I have this system and someone tells me look the internal energy is changing so Delta U that's just a capital Delta that says what is the change in internal energy saying look if your internal energy is changing your system is either having something done to it or it's doing something to someone else some energy is being transferred to or away from it so how do we write that well the first law of thermodynamics or even the definition of internal energy says that a change in internal energy is equal to heat added to the system and once again very intuitive a letter for heat because heat does not start with Q but the convention is is to use Q for heat the letter H is reserved for enthalpy which is a very very very similar concept to heat we'll talk about that in the next video it's equal to the heat added to the system minus the work done by the system minus the work done by the system and you can see this multiple way sometimes it's written like this sometimes it's written that the change in enthalpy is equal to the heat added to the system plus plus the work done on the system and this might be very confusing but the you should just always and we'll really kind of look at this 100 different ways in the next video and actually this is a capital u let me make sure that I write that as a capital u we're gonna do it a hundred different ways but if you think about it if I'm doing work I lose energy I have transferred the energy to someone else so this is doing work doing work likewise if someone is giving me heat that is increasing my energy at least to me that these are reasonably intuitive definitions now if you see this you say okay how can I this must be if my energy is going up if this is a positive thing I either have to have this go up or work is being done to me work done to me done to me or energy is being transferred into my system and I'll become I'll give a lot more examples of what exactly that means in the next video but I just want to make you comfortable with each of these because our going to see them all the time and you might even get confused even if your teacher uses only one of them but you should always do this reality check when something does work it is transferring energy to something else right so if you're doing work it'll take away this is taking away your internal energy likewise if what heat transfer is another way for for energy to go from one system to another from one entity to another so if my energy my total energy is going up my Heat maybe heat is being added to my system if my energy is going down my energy is going down either heat is being taken away from my system or I am doing more work on something and I'll do a bunch of examples with that and I'm just going to leave you in this video with some other notations that you might see you might see change in internal energy is equal to change I shouldn't I keep writing a let me write it again change in internal energy capital u you'll sometimes see it as they'll write a delta Q which kind of implies change in heat but I'll explain in a future video well that doesn't make full sense but you'll see this a lot but you can also view this as the heat added to the system minus the change in work which is a little non-intuitive because when you talk about heat or work you're talking about transferring of energy so when you talk about change in transfer it becomes a little you know so sometimes the Delta work they just mean this means that work done work done by the system work done so obviously if you have some if you have some energy you do some work you've lost that energy you've given to someone else you'd have a minus sign there or you might see it written like this change in internal energy is equal to heat added I won't say even this kind of reads to me is change in heat I'll just call this the heat added plus the work the work done onto the system so this is work work done too this is work done by the system either way and you know you you shouldn't even memorize this you should just always think about it a little bit if I'm doing work I'm going to lose energy if work is done to me I'm going to gain energy if I lose heat if this is a negative number I'm going to lose energy if I gain heat I'm going to gain energy anyway I'll leave you there for this video in the next video we'll we'll really try to digest this internal energy formula in a hundred different ways