First law of thermodynamics / internal energy

I've now done a bunch of videos on thermodynamics, both in the chemistry and the physics playlist, and I realized 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. And it's a good one. It tells us that energy-- I'll do it 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. 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 physics playlist, and we've done a bunch of this 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. 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 it's going to slow down a little bit more. And at this point it's 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 it'll start accelerating downwards. So here its velocity will look like that. And here its velocity will look like that. 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 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. It's moving, so it has energy. But then as we decelerate up here, we clearly have no 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 won't go into the math of it, but potential energy is just the potential to turn into other forms of energy. I guess that'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, 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. Then at the peak of where the ball is, it's all potential energy, the kinetic energy has 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 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 the mass of the ball, times the velocity of the ball, squared, over 2. That's the kinetic energy over here. And then I throw it. It all turns into potential energy. Then it comes back down, and turns into kinetic energy. But because of air resistance, I have a smaller velocity here. I have a smaller velocity than I did there. Kinetic energy is only dependent on the magnitude of the velocity. I could put a little absolute sign there to show that we're dealing with the magnitude of the velocity. So I clearly have a lower kinetic energy here. So lower kinetic energy here than 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 can go to the first law and say, oh, what happened? And the first law says, oh, Sal, it all turned into potential energy up here. And you saw it turned into potential energy because when the ball accelerated back down, it turned back into kinetic energy. But then I say, no, Mr. 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 the thermodynamics says, oh, well that's because you have air. And I'd say, well I do have air, but where did the energy go? And then the first law of thermodynamics says, oh, when your ball was falling-- let me see, that's the ball. Let me make the ball yellow. So when your ball was falling, it was rubbing up against air particles. It was rubbing up against molecules of air. 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. And essentially, if you think about it, if you go back to the macrostate/ microstate problem or descriptions that we talked about, 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 it was doing it on the way up as well. And so that kinetic energy that you think you lost or you destroyed at the bottom, of here, because your ball's going a lot slower, was actually transferred to a lot of air particles. It was a lot of-- to a bunch of air particles. 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 what we can say is, in general I transferred some heat to these particles. I raised the temperature of the air particles that the ball fell through by rubbing those particles or giving them kinetic energy. Remember, temperature is just a measure of kinetic-- and 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 you 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 that the first law of thermodynamics says, I still hold. You had a lot of kinetic energy, turned into potential, that turned into less kinetic energy. And where did the remainder go? It turned into heat. Because it transferred that kinetic energy to these air particles 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? And here we have something called the internal energy. The internal energy of a system. Once again this is a macrostate, or you could 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 a U. U for internal energy. Let me go back to my example-- that I had in the past, that I did in our previous video, if you're watching these in order-- of I have, you know, 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. The internal energy literally is all of the energy that's in the system. So it includes, and for our purposes, especially when you're in a first-year chemistry course, it's the kinetic energy of all the atoms or molecules. And in a future video, I'll actually calculate it for 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, they have some kinetic energy because they have some translational motion, if we look at the microstates. 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 its electrons are just jumping around anyway. So if they're individual atoms they can't rotate, but if they're 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-- well I'm doing it using a gas, and gases aren't good conductors-- but let's say I'm doing it for a solid. So I'm using the wrong tools. So let's say I have some metal. Those are my metal-- let me do more-- my metal atoms. And in that metal atom, I have, a bunch of electrons-- well that's the same color-- I have a bunch of-- let me use 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 literally every form of energy that exists here. 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 it has a lot of kinetic energy, but at this point right here, when it's about to go back, it's completely stationary for 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 actually harmonic motion. So in this case, internal energy also includes the kinetic energy for the molecules that are moving fast. But it also includes the potential energies for the molecules that are vibrating, they're 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. And for most of what we're going to do, you can assume that we're dealing with an ideal gas. Instead of, it 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 better, we're going to assume we're dealing with a monoatomic ideal gas. And maybe this is just 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. Let's just assume that they're not. They're just individual atoms. And 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, internal energy is everything. It's all of the energy inside of a system. If you said, what's the energy of the system? Its internal energy. So 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 an internal energy? It's 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 it 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 a very intuitive letter for heat, because heat does not start with Q, but the convention 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 maybe in the next video. It's equal to the heat added to the system, minus the work done by the system. And you could see this multiple ways. Sometimes it's written like this. Sometimes it's written that the change in internal energy is equal to the heat added to the system, plus the work done on the system. And this might be very confusing, but 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. But we're going to do it 100 different ways. But if you think about it, if I'm doing work I lose energy. I've transferred the energy to someone else. So this is doing work. Likewise, if someone is giving me heat that is increasing my energy, at least to me these are reasonably intuitive definitions. Now if you see this, you say, OK, 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. Or energy is being transferred into my system. 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 either of these. Because you're 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, heat transfer is another way for energy to go from one system to another, or from one entity to another. So if my total energy is going up, maybe heat is being added to my system. If my energy is going down, either heat is being taken away from my system, or I'm doing more work on something. I'll do a bunch of examples with that. And I'm just going to leave you with this video with some other notation that you might see. You might see change in internal energy is equal to change-- 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 it in a future video why that doesn't make a 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-- So sometimes a delta work, they just mean this means that work done by a system. So obviously if you have some energy, you do some work, you've lost that energy, you've given it 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 as change in heat. I'll just call this the heat added-- plus the work done onto the system. So this is work done to, this is work done by the system. Either way. And 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, and in the next video we'll really try to digest this internal energy formula 100 different ways.