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