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I've now done a bunch of videos
on thermodynamics, both

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in the chemistry and the
physics playlist, and I

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realized that I have yet to give
you, or at least if my

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memory serves me correctly, I
have yet to give you the first

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law of thermodynamics.

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And I think now is as
good a time as any.

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The first law of
thermodynamics.

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And it's a good one.

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It tells us that energy-- I'll
do it in this magenta color--

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energy cannot be created or
destroyed, it can only be

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transformed from one
form or another.

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So energy cannot be created or
destroyed, only transformed.

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So let's think about a couple
of examples of this.

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And we've touched on this when
we learned mechanics and

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kinetics in our physics
playlist, and we've done a

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bunch of this in the chemistry
playlist as well.

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So let's say I have some rock
that I just throw as fast as I

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can straight up.

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Maybe it's a ball
of some kind.

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So I throw a ball straight up.

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That arrow represents its
velocity vector, right?

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it's going to go
up in the air.

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Let me do it here.

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I throw a ball and it's going
to go up in the air.

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It's going to decelerate
due to gravity.

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And at some point, up here, the
ball is not going to have

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any velocity.

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So at this point it's going to
slow down a little bit, at

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this point it's going to slow
down a little bit more.

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And at this point it's going
to be completely stationary

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and then it's going to start
accelerating downwards.

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In fact, it was always
accelerating downwards.

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It was decelerating upwards,
and then it'll start

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accelerating downwards.

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So here its velocity will
look like that.

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And here its velocity
will look like that.

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Then right when it gets back
to the ground, if we assume

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negligible air resistance, its
velocity will be the same

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magnitude as the upward but
in the downward direction.

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So when we looked at this
example, and we've done this

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tons in the projectile motion
videos in the physics

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playlist, over here we said,
look, we have some kinetic

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energy here.

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And that makes sense.

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I think, to all of us, energy
intuitively means that you're

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doing something.

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So kinetic energy.

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Energy of movement,
of kinetics.

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It's moving, so it has energy.

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But then as we decelerate up
here, we clearly have no

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kinetic energy, zero
kinetic energy.

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So where did our energy go?

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I just told you the first law of
thermodynamics, that energy

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cannot be created
or destroyed.

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But I clearly had a lot of
kinetic energy over here, and

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we've seen the formula for that
multiple times, and here

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I have no kinetic energy.

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So I clearly destroyed kinetic
energy, but the first law of

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thermodynamics tells me
that I can't do that.

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So I must have transformed
that kinetic energy.

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I must have transformed
that kinetic energy

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into something else.

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And in the case of this ball,
I've transformed it into

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potential energy.

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So now I have potential
energy.

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And I won't go into the math of
it, but potential energy is

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just the potential to turn into
other forms of energy.

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I guess that's the easy
way to do it.

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But the way to think about it
is, look, the ball is really

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high up here, and by virtue of
its position in the universe,

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if something doesn't stop it,
it's going to fall back down,

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or it's going to be converted
into another form of energy.

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Now let me ask you
another question.

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Let's say I throw this ball up
and let's say we actually do

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have some air resistance.

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So I throw the ball up.

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I have a lot of kinetic
energy here.

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Then at the peak of where the
ball is, it's all potential

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energy, the kinetic energy
has disappeared.

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And let's say I have
air resistance.

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So when the ball comes back
down, the air was kind of

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slowing it down, so when it
reaches this bottom point,

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it's not going as fast
as I threw it.

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So when I reach this bottom
point here, my ball is going a

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lot slower than I threw
it up to begin with.

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And so if you think about what
happened, I have a lot of

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kinetic energy here.

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I'll give you the formula.

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The kinetic energy is the mass
of the ball, times the

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velocity of the ball,
squared, over 2.

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That's the kinetic
energy over here.

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And then I throw it.

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It all turns into potential
energy.

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Then it comes back down, and
turns into kinetic energy.

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But because of air resistance,
I have a

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smaller velocity here.

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I have a smaller velocity
than I did there.

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Kinetic energy is only dependent
on the magnitude of

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the velocity.

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I could put a little absolute
sign there to show that we're

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dealing with the magnitude
of the velocity.

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So I clearly have a lower
kinetic energy here.

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So lower kinetic energy here
than I did here, right?

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And I don't have any potential
energy left.

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Let's say this is the ground.

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We've hit the ground.

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So I have another conundrum.

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You know, when I went from
kinetic energy to no kinetic

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energy there, I can go
to the first law and

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say, oh, what happened?

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And the first law says, oh,
Sal, it all turned into

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potential energy up here.

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And you saw it turned into
potential energy because when

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the ball accelerated back down,
it turned back into

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kinetic energy.

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But then I say, no, Mr. First
Law of Thermodynamics, look,

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at this point I have no
potential energy, and I had

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all kinetic energy and I had
a lot of kinetic energy.

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Now at this point, I have no
potential energy once again,

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but I have less kinetic
energy.

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My ball has fallen at
a slower rate than I

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threw it to begin with.

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And the thermodynamics
says, oh, well that's

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because you have air.

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And I'd say, well I do
have air, but where

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did the energy go?

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And then the first law of
thermodynamics says, oh, when

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your ball was falling-- let
me see, that's the ball.

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Let me make the ball yellow.

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So when your ball was falling,
it was rubbing

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up against air particles.

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It was rubbing up against
molecules of air.

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And right where the molecules
bumped into the wall, there's

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a little bit of friction.

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Friction is just essentially,
your ball made these molecules

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that it was bumping into vibrate
a little bit faster.

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And essentially, if you think
about it, if you go back to

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the macrostate/ microstate
problem or descriptions that

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we talked about, this ball is
essentially transferring its

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kinetic energy to the molecules
of air that it rubs

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up against as it falls
back down.

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And actually it was doing it
on the way up as well.

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And so that kinetic energy that
you think you lost or you

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destroyed at the bottom, of
here, because your ball's

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going a lot slower, was actually
transferred to a lot

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of air particles.

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It was a lot of-- to a bunch
of air particles.

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Now, it's next to impossible to
measure exactly the kinetic

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energy that was done on each
individual air particle,

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because we don't even know what
their microstates were to

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begin with.

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But what we can say is, in
general I transferred some

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heat to these particles.

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I raised the temperature of
the air particles that the

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ball fell through by rubbing
those particles or giving them

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kinetic energy.

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Remember, temperature is just
a measure of kinetic-- and

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temperature is a macrostate or
kind of a gross way or a macro

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way, of looking at the
kinetic energy of

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the individual molecules.

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It's very hard to measure each
of theirs, but if you say on

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average their kinetic energy
is x, you're essentially

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giving an indication
of temperature.

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So that's where it went.

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It went to heat.

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And heat is another
form of energy.

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So that the first law
of thermodynamics

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says, I still hold.

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You had a lot of kinetic energy,
turned into potential,

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that turned into less
kinetic energy.

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And where did the
remainder go?

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It turned into heat.

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Because it transferred that
kinetic energy to these air

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particles in the surrounding
medium.

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Fair enough.

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So now that we have that out of
the way, how do we measure

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the amount of energy that
something contains?

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And here we have something
called the internal energy.

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The internal energy
of a system.

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Once again this is a macrostate,
or you could call

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it a macro description
of what's going on.

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This is called u for internal.

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The way I remember that is that
the word internal does

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not begin with a U.

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U for internal energy.

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Let me go back to my example--
that I had in the past, that I

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did in our previous video, if
you're watching these in

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order-- of I have, you know,
some gas with some movable

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ceiling at the top.

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That's its movable ceiling.

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That can move up and down.

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We have a vacuum up there.

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And I have some gas in here.

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The internal energy literally is
all of the energy that's in

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the system.

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So it includes, and for our
purposes, especially when

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you're in a first-year chemistry
course, it's the

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kinetic energy of all the
atoms or molecules.

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And in a future video, I'll
actually calculate it for how

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much kinetic energy is
there in a container.

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And that'll actually be our
internal energy plus all of

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the other energy.

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So these atoms, they have some
kinetic energy because they

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have some translational motion,
if we look at the

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microstates.

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If they're just individual
atoms, you can't really say

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that they're rotating, because
what does it mean for an atom

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to rotate, right?

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Because its electrons are just
jumping around anyway.

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So if they're individual atoms
they can't rotate, but if

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they're molecules they can
rotate, if it looks

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something like that.

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There could be some rotational
energy there.

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It includes that.

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If we have bonds-- so I
just drew a molecule.

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The molecule has bonds.

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Those bonds contain
some energy.

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That is also included in
the internal energy.

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If I have some electrons, let's
say that this was not

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a-- well I'm doing it using a
gas, and gases aren't good

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conductors-- but let's say
I'm doing it for a solid.

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So I'm using the wrong tools.

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So let's say I have
some metal.

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Those are my metal-- let me do
more-- my metal atoms. And in

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that metal atom, I have, a
bunch of electrons-- well

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that's the same color-- I have
a bunch of-- let me use a

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suitably different color--
I have a bunch

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of electrons here.

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And I have fewer here.

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So these electrons really
want to get here.

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Maybe they're being stopped for
some reason, so they have

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some electrical potential.

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Maybe there's a gap here, you
know, where they can't conduct

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or something like that.

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Internal energy includes
that as well.

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That's normally the scope out
of what you'd see in a

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first-year chemistry class.

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But it includes that.

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It also includes literally
every form of energy that

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exists here.

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00:10:52,060 --> 00:10:54,870
It also includes, for example,
in a metal, if we were to heat

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00:10:54,870 --> 00:10:57,910
this metal up they start
vibrating, right?

252
00:10:57,910 --> 00:11:00,520
They start moving left and
right, or up or down, or in

253
00:11:00,520 --> 00:11:01,690
every possible direction.

254
00:11:01,690 --> 00:11:04,760
And if you think about a
molecule or an atom that's

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00:11:04,760 --> 00:11:09,420
vibrating, it's going from here,
and then it goes there,

256
00:11:09,420 --> 00:11:10,960
then it goes back there.

257
00:11:10,960 --> 00:11:12,330
It goes back and forth, right?

258
00:11:12,330 --> 00:11:14,750
And if you think about what's
happening, when it's in the

259
00:11:14,750 --> 00:11:17,240
middle point it has a lot of
kinetic energy, but at this

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00:11:17,240 --> 00:11:19,670
point right here, when it's
about to go back, it's

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00:11:19,670 --> 00:11:23,550
completely stationary for
a super small moment.

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00:11:23,550 --> 00:11:25,360
And at that point, all
of its kinetic energy

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00:11:25,360 --> 00:11:26,590
is potential energy.

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00:11:26,590 --> 00:11:27,910
And then it turns into
kinetic energy.

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00:11:27,910 --> 00:11:29,490
Then it goes back to potential
energy again.

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00:11:29,490 --> 00:11:30,940
It's kind of like a
pendulum, or it's

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00:11:30,940 --> 00:11:33,010
actually harmonic motion.

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00:11:33,010 --> 00:11:37,010
So in this case, internal
energy also includes the

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00:11:37,010 --> 00:11:38,990
kinetic energy for the molecules
that are moving

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00:11:38,990 --> 00:11:42,110
fast. But it also includes the
potential energies for the

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00:11:42,110 --> 00:11:44,530
molecules that are vibrating,
they're at that point where

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00:11:44,530 --> 00:11:45,470
they don't have kinetic
energy.

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00:11:45,470 --> 00:11:47,450
So it also includes
potential energy.

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00:11:47,450 --> 00:11:52,000
So internal energy is literally
all of the energy

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00:11:52,000 --> 00:11:54,810
that's in a system.

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00:11:54,810 --> 00:11:58,270
And for most of what we're going
to do, you can assume

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00:11:58,270 --> 00:12:00,190
that we're dealing with
an ideal gas.

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00:12:00,190 --> 00:12:02,710
Instead of, it becomes a lot
more complicated with solids,

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00:12:02,710 --> 00:12:05,580
and conductivity, and vibrations
and all that.

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00:12:05,580 --> 00:12:07,900
We're going to assume we're
dealing with an ideal gas.

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00:12:07,900 --> 00:12:09,910
And even better, we're going to
assume we're dealing with a

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00:12:09,910 --> 00:12:11,850
monoatomic ideal gas.

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00:12:11,850 --> 00:12:15,850
And maybe this is just
helium, or neon.

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00:12:15,850 --> 00:12:16,990
One of the ideal gases.

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00:12:16,990 --> 00:12:18,430
They don't want to bond
with each other.

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00:12:18,430 --> 00:12:21,250
They don't form molecules
with each other.

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00:12:21,250 --> 00:12:23,880


288
00:12:23,880 --> 00:12:25,010
Let's just assume that
they're not.

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00:12:25,010 --> 00:12:32,030
They're just individual atoms.
And in that case, the internal

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00:12:32,030 --> 00:12:35,340
energy, we really can simplify
to it being the kinetic

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00:12:35,340 --> 00:12:37,380
energy, if we ignore all
of these other things.

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00:12:37,380 --> 00:12:39,690
But it's important to realize,
internal energy is everything.

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00:12:39,690 --> 00:12:44,430
It's all of the energy
inside of a system.

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00:12:44,430 --> 00:12:45,880
If you said, what's the
energy of the system?

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00:12:45,880 --> 00:12:48,280
Its internal energy.

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00:12:48,280 --> 00:12:52,390
So the first law of
thermodynamics says that

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00:12:52,390 --> 00:12:56,230
energy cannot be created or
destroyed, only transformed.

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00:12:56,230 --> 00:12:59,630
So let's say that internal
energy is changing.

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00:12:59,630 --> 00:13:03,140
So I have this system, and
someone tells me, look, the

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00:13:03,140 --> 00:13:06,370
internal energy is changing.

301
00:13:06,370 --> 00:13:09,070
So delta U, that's just a
capital delta that says, what

302
00:13:09,070 --> 00:13:10,730
is the change an internal
energy?

303
00:13:10,730 --> 00:13:14,600
It's saying, look, if your
internal energy is changing,

304
00:13:14,600 --> 00:13:17,310
your system is either having
something done to it, or it's

305
00:13:17,310 --> 00:13:18,780
doing something to
someone else.

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00:13:18,780 --> 00:13:20,430
Some energy is being
transferred to it

307
00:13:20,430 --> 00:13:22,540
or away from it.

308
00:13:22,540 --> 00:13:24,950
So, how do we write that?

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00:13:24,950 --> 00:13:27,360
Well the first law of
thermodynamics, or even the

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00:13:27,360 --> 00:13:29,920
definition of internal energy,
says that a change in internal

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00:13:29,920 --> 00:13:35,810
energy is equal to heat added to
the system-- and once again

312
00:13:35,810 --> 00:13:40,810
a very intuitive letter for
heat, because heat does not

313
00:13:40,810 --> 00:13:43,380
start with Q, but the
convention is

314
00:13:43,380 --> 00:13:45,490
to use Q for heat.

315
00:13:45,490 --> 00:13:49,520
The letter h is reserved for
enthalpy, which is a very,

316
00:13:49,520 --> 00:13:51,530
very, very similar
concept to heat.

317
00:13:51,530 --> 00:13:54,720
We'll talk about that maybe
in the next video.

318
00:13:54,720 --> 00:13:59,250
It's equal to the heat added to
the system, minus the work

319
00:13:59,250 --> 00:14:00,500
done by the system.

320
00:14:00,500 --> 00:14:03,790


321
00:14:03,790 --> 00:14:05,180
And you could see this
multiple ways.

322
00:14:05,180 --> 00:14:06,760
Sometimes it's written
like this.

323
00:14:06,760 --> 00:14:10,550
Sometimes it's written that the
change in internal energy

324
00:14:10,550 --> 00:14:18,440
is equal to the heat added to
the system, plus the work done

325
00:14:18,440 --> 00:14:19,730
on the system.

326
00:14:19,730 --> 00:14:21,960
And this might be very
confusing, but you should just

327
00:14:21,960 --> 00:14:25,020
always-- and we'll really kind
of look at this 100 different

328
00:14:25,020 --> 00:14:25,990
ways in the next video.

329
00:14:25,990 --> 00:14:27,440
And actually this
is a capital U.

330
00:14:27,440 --> 00:14:29,680
Let me make sure that I write
that as a capital U.

331
00:14:29,680 --> 00:14:31,270
But we're going to do it
100 different ways.

332
00:14:31,270 --> 00:14:35,400
But if you think about it, if
I'm doing work I lose energy.

333
00:14:35,400 --> 00:14:37,790
I've transferred the energy
to someone else.

334
00:14:37,790 --> 00:14:41,360
So this is doing work.

335
00:14:41,360 --> 00:14:45,090
Likewise, if someone is giving
me heat that is increasing my

336
00:14:45,090 --> 00:14:48,380
energy, at least to me these
are reasonably intuitive

337
00:14:48,380 --> 00:14:48,980
definitions.

338
00:14:48,980 --> 00:14:54,950
Now if you see this, you say,
OK, if my energy is going up,

339
00:14:54,950 --> 00:14:57,750
if this is a positive thing, I
either have to have this go

340
00:14:57,750 --> 00:15:00,340
up, or work is being
done to me.

341
00:15:00,340 --> 00:15:05,730


342
00:15:05,730 --> 00:15:09,220
Or energy is being transferred
into my system.

343
00:15:09,220 --> 00:15:11,930
I'll give a lot more examples of
what exactly that means in

344
00:15:11,930 --> 00:15:12,880
the next video.

345
00:15:12,880 --> 00:15:14,030
But I just want to make
you comfortable

346
00:15:14,030 --> 00:15:15,120
with either of these.

347
00:15:15,120 --> 00:15:16,520
Because you're going to see
them all the time, and you

348
00:15:16,520 --> 00:15:18,200
might even get confused
even if your teacher

349
00:15:18,200 --> 00:15:19,970
uses only one of them.

350
00:15:19,970 --> 00:15:22,050
But you should always do
this reality check.

351
00:15:22,050 --> 00:15:25,100
When something does work, it
is transferring energy to

352
00:15:25,100 --> 00:15:27,310
something else, right?

353
00:15:27,310 --> 00:15:30,120
So if you're doing work, it'll
take away, this is taking

354
00:15:30,120 --> 00:15:32,340
away, your internal energy.

355
00:15:32,340 --> 00:15:36,780
Likewise, heat transfer is
another way for energy to go

356
00:15:36,780 --> 00:15:40,180
from one system to another, or
from one entity to another.

357
00:15:40,180 --> 00:15:45,680
So if my total energy is going
up, maybe heat is being added

358
00:15:45,680 --> 00:15:46,730
to my system.

359
00:15:46,730 --> 00:15:51,210
If my energy is going down,
either heat is being taken

360
00:15:51,210 --> 00:15:55,450
away from my system, or I'm
doing more work on something.

361
00:15:55,450 --> 00:15:57,690
I'll do a bunch of examples
with that.

362
00:15:57,690 --> 00:15:59,000
And I'm just going to leave you
with this video with some

363
00:15:59,000 --> 00:16:01,050
other notation that
you might see.

364
00:16:01,050 --> 00:16:05,030
You might see change in internal
energy is equal to

365
00:16:05,030 --> 00:16:09,850
change-- let me write it again--
change in internal

366
00:16:09,850 --> 00:16:11,290
energy, capital U.

367
00:16:11,290 --> 00:16:14,360
You'll sometimes see it as,
they'll write a delta Q, which

368
00:16:14,360 --> 00:16:17,060
kind of implies change
in heat.

369
00:16:17,060 --> 00:16:18,820
But I'll explain it in a future
video why that doesn't

370
00:16:18,820 --> 00:16:21,240
make a full sense, but you'll
see this a lot.

371
00:16:21,240 --> 00:16:24,670
But you can also view this as
the heat added to the system,

372
00:16:24,670 --> 00:16:28,020
minus the change in work,
which is a little

373
00:16:28,020 --> 00:16:30,240
non-intuitive because when you
talk about heat or work you're

374
00:16:30,240 --> 00:16:32,000
talking about transferring
of energy.

375
00:16:32,000 --> 00:16:33,790
So when you talk about change
in transfer it becomes a

376
00:16:33,790 --> 00:16:36,470
little-- So sometimes a delta
work, they just mean this

377
00:16:36,470 --> 00:16:41,580
means that work done
by a system.

378
00:16:41,580 --> 00:16:44,750
So obviously if you have some
energy, you do some work,

379
00:16:44,750 --> 00:16:46,760
you've lost that energy, you've
given it to someone

380
00:16:46,760 --> 00:16:48,610
else, you'd have a
minus sign there.

381
00:16:48,610 --> 00:16:52,060
Or you might see it written like
this, change in internal

382
00:16:52,060 --> 00:16:58,120
energy is equal to heat added--
I won't say even this

383
00:16:58,120 --> 00:16:59,860
kind of reads to me
as change in heat.

384
00:16:59,860 --> 00:17:06,690
I'll just call this the heat
added-- plus the work done

385
00:17:06,690 --> 00:17:07,630
onto the system.

386
00:17:07,630 --> 00:17:15,160
So this is work done to, this
is work done by the system.

387
00:17:15,160 --> 00:17:16,020
Either way.

388
00:17:16,020 --> 00:17:19,040
And you shouldn't even memorize
this, you should just

389
00:17:19,040 --> 00:17:20,410
always think about
it a little bit.

390
00:17:20,410 --> 00:17:22,348
If I'm doing work I'm going
to lose energy.

391
00:17:22,348 --> 00:17:24,699
If work is done to me I'm
going to gain energy.

392
00:17:24,700 --> 00:17:27,920
If I lose heat, if this is a
negative number, I'm going to

393
00:17:27,920 --> 00:17:29,290
lose energy.

394
00:17:29,290 --> 00:17:31,710
If I gain heat I'm going
to gain energy.

395
00:17:31,710 --> 00:17:33,440
Anyway, I'll leave you there
for this video, and in the

396
00:17:33,440 --> 00:17:37,010
next video we'll really try to
digest this internal energy

397
00:17:37,010 --> 00:17:39,410
formula 100 different ways.

398
00:17:39,410 --> 00:00:00,000