First law of thermodynamics / internal energy (video) | Khan Academy
This concept is best understood by looking at Law of Conservation of Energy Potential energy of oil or gas is changed into energy to heat a building. When a. Thermodynamics is the study of heat energy and other types of energy, such as work Both heat and work refer to processes by which energy is transferred to or from we can apply the ideal gas law to the above equation to get the following. A system possesses energy if it has the ability to do work. Work shifts energy from one system to another. thermal energy-- motion of particles of matter . in the relationship "potential" (potential energy) and "vis viva" (kinetic energy). Thomson incorporated several quotations from the King James Version of the Bible.
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 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.
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. 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 Walter the penguin gets bored in Antarctica, so he likes to run, jump, and then slide across the ice to a stop.
But Walter is a clever and curious penguin, so while he's sliding, he's thinking about energy conservation and he's confused, 'cause he knows that he starts off over here, with some amount of kinetic energy. But he knows that he ends over here with no kinetic energy since he slides to a stop.
So he wonders, how can energy be conserved, when he seems to be losing kinetic energy? Now if you would have asked this question when we dealt with forces, you would have said, "Oh, well obviously, this penguin is coming to a stop "'cause there must be some amount of friction "between the penguin and the ice. Well, the way we do it, is we just say that this force of friction is doing negative work on the penguin.
And we know the work is negative because the force of friction is directed in the opposite direction to the penguin's motion. The other way we could see this is that, we could just use the formula for work done by any force. That formula's f d cosine theta.
If we want to find the work done by the force of friction, we would plug in the force of friction for our force, the magnitude of it, times the distance the penguin slid to the right, and then this theta in cosine theta is always the angle between the force and the direction of motion.
So this penguin's sliding to the right, the forces directed to the left, you might think that's zero, but that's not zero. Think about it, the angle between leftward and rightward is not zero, that's actually degrees. So this angle would be right here, or pi radians. And cosine of is going to give you a negative one, so the work done by the force of friction on this penguin is going to be negative f k d.
Negative the force of friction, times the distance the penguin slid to the right. But this still doesn't answer Walter's question. Where did the kinetic energy go? Friction may have done negative work on this penguin, but where did that energy end up? And you probably have a good idea, 'cause when two surfaces rub together, some of that energy of motion is going to get transformed into thermal energy in those two surfaces.
In other words, this sheet of ice is going to have a little more thermal energy, it's going to heat up just a little bit. And Walter's feathery coat is going to heat up just a little bit, and they're going to have more thermal energy to end with, than what they started with.
Just like when you rub your hands together vigorously on a cold day to get warm, you're turning some of that kinetic energy into thermal energy that warms up your hands. And you might be like, "Alright, that's all well and good, "but how do we put this all together? And we can add the external work that was done, which we've just figured that out. We know the external work would be the work done by friction, so we'd have a minus, 'cause it was negative work, f k d, and it's negative again because this force is taking energy out of the system.
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But some people might object, they might say, "Wait a minute, we just said there was thermal energy "to end with, how come we didn't include that "in our final energy? In other words, Walter, and only his motional energy, his kinetic energy, was the only energy we were keeping track of, that's why we said that, initially, there was just Walter's kinetic energy. And this sheet of ice was external to our system, not part of our system, that's why it exerted a negative external work, removed the energy from the system, and Walter ended up with no kinetic energy.
But there's an alternate way to go about this calculation. You could say, "Alright, instead of just considering "Walter and Walter alone to be part of our system, "let's go ahead and include the ice as part of our system.
So an alternate way to solve these problems, is to use this same formula, but now, Walter and the ice are both part of our system. Our system would still start with the kinetic energy that Walter had at the beginning, that doesn't change. But now there would be no external work, not because force of friction isn't acting, there's still a force of friction, but that's an internal force between objects in our system.
So there's no external work done now. That might be a new or confusing idea to some people, so let me just say, if there's forces between objects within your system, then those forces cannot exert external work and they cannot change the total energy of your system. Only forces exerted on objects within your system from outside of your system, can change the total energy of your system.
So when this ice was not part of our system, it was exerting an outside external force on Walter, and the energy of our system changed.
We started with kinetic energy, we ended with no energy. But now that the ice and Walter are part of our system, this force of friction is no longer external.
It's internal, exerted between objects within our system, and so it does not exert any external work. It's just going to transform energies between different objects within our system. So that's why we write this zero here, there'd be no external work done if we choose the ice and Walter as part of our system. And this would have to equal the final energy, and we know where this energy ends up. It started with kinetic energy, and it ends as this extra thermal energy in the snow, and Walter's feathery coat.
So I could write that as e thermal.
But I know how much thermal energy was generated, this just has to equal the amount of work done by friction. So even though this work done is not external, it still transfers energy between objects within our system, so when we write that the work was negative f k d down here, we mean that the force of friction took f k d from something and turned it into something else, and that's all we need up here.
We need an expression for thermal energy. But if friction took f k d and turned it into something else, the thing it turned it into was the thermal energy so that value of f k d, that magnitude of the work done, was how much energy ended up as thermal energy. People might find that confusing, they might be like, "Wait a minute, why do we have this "with a positive here and not a negative? If you take energy from something, you're doing negative work on it. If I gave energy to something, I'd be doing positive work.
So this negative sign in the work done, just means that the force of friction took this much energy from something, and turned it into thermal energy. So when we want to write down how much thermal energy did we end with, well, we ended with the amount that we took. So we took f k d, the thermal energy ended with f k d. And I can still set this equal to the kinetic energy that Walter started with, and I get the same formula I ended up with over here, because I had to.