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SAL: I've done a bunch of videos
where I use words like

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pressure and-- let me write
these down-- pressure and

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temperature and volume.

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And I've done them in the
chemistry and physics

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playlist. Especially the physics
playlist, but even in

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the chemistry playlist, I also
use words like kinetic energy.

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I'll just write e for energy.

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Or I use force and velocity.

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And you know, a whole bunch of
other types of, I guess,

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properties of things, for
better or for worse.

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And in this video what I want
to do is I want to make a

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distinction.

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Because it becomes important
when we start getting a little

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bit more precise, especially
when we get more precise in

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thermodynamics, or, I guess,
you know, the study of how

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heat moves around.

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So these properties right
here, these are

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properties of a system.

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Or we could call them
macrostates of a system.

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And these could be
macrostates.

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So for example, let me make it
clear, when I call a system,

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if I have some balloon like
this, and it has a little tie

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there and, you know, maybe
it has a string.

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This has these macrostates
associated with it.

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There is some pressure
in that balloon.

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Remember that's force
per area.

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There is some temperature
for that balloon.

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And there's some volume to
the balloon, obviously.

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But all of these, these help
us relate what's going on

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inside that balloon, or what
that balloon is doing in kind

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of an every day reality.

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Before people even knew about
what an atom was, or maybe

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they thought that there might
be such an atom but they had

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never proved it, they were
dealing with these

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macrostates.

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They could measure pressure,
they could measure

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temperature, they could
measure volume.

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Now we know that that pressure
is due to things like, you

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have a bunch of atoms
bumping around.

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And let's say that this is a
gas-- it's a balloon- it's

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going to be a gas.

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And we know that the pressure is
actually caused-- and I've

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done several, I think I did
the same video in both the

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chemistry and the physics
playlist. I did them a year

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apart, so you can see if my
thinking has evolved at all.

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But we know that the pressure's
really due by the

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bumps of these particles as they
bump into the walls and

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the side of the balloon.

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And we have so many particles
at any given point of time,

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some of them are bumping into
the wall the balloon, and

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that's what's essentially
keeping the balloon pushed

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outward, giving it its pressure
and its volume.

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We've talked about temperature,
as essentially

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the average kinetic energy of
these-- which is a function of

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these particles, which could
be either the molecules of

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gas, or if it's an ideal gas,
it could be just the

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atoms of the gas.

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Maybe it's atoms of helium or
neon, or something like that.

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And all of these things, these
describe the microstates.

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So for example, I could describe
what's going on with

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the balloon.

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I could say, hey, you know,
there are-- I could just make

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up some numbers.

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The pressure is five newtons
per meters squared, or some

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number of pascals.

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The units aren't what's
important.

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In this video I really
just want to make the

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differentiation between these
two ways of describing

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what's going on.

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I could say the temperature
is 300 kelvin.

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I could say that the volume
is, I don't know,

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maybe it's one liter.

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And I've described a system,
but I've described in on a

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macro level.

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Now I could get a lot more
precise, especially now that

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we know that things like atoms
and molecules exist. What I

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could do, is I could essentially
label every one of

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these molecules, or let's say
atoms, in the gas that's

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contained in the balloon.

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And I could say, at exactly this
moment in time, I could

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say at time equals 0, atom 1
has-- its momentum is equal to

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x, and its position, in
three-dimensional coordinates,

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is x, y, and z.

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And then I could say, atom
number 2-- its momentum-- I'm

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just using rho for momentum--
it's equal to y.

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And its position is a, b, c.

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And I could list every atom
in this molecule.

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Obviously we're dealing with a
huge number of atoms, on the

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order of 10 to the
20 something.

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So it's a massive list I would
have to give you, but I could

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literally give you the state of
every atom in this balloon.

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And then if I did that, I
would be giving you the

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microstates.

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Or I would give you a specific
microstate of the

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balloon at this time.

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Now when a system-- and I'm
going to introduce a word

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here, because this word is
important, especially as we

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go-- is in thermodynamic
equilibrium.

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So let me write that down.

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Equilibrium.

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We learned about equilibrium
from the

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chemistry point of view.

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And that tells you, that the
amount of something going into

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forward reaction is equivalent
to the amount going in the

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reverse reaction.

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And when we talk about
macrostates, thermodynamic

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equilibrium essentially
says that the

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macrostate is defined.

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That they're not changing.

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If this balloon is in
equilibrium, at time 1 its

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pressure, temperature, and
volume will be these things.

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And if we look at it a second
later, its pressure,

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temperature, and volume will
also be these things.

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It's in equilibrium.

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None of the macrostates
have changed.

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And actually, I'll talk about
in a second, in order for

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these macrostates to even be
defined, to be well defined,

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you have to be in equilibrium.

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I'll talk about that
in a second.

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Now, at second number, at time
equals 0, you might have this

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whole set of-- I went and
I listed 10 to the

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20th-something microstates of
all the different atoms in

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this molecule.

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But then if I look at these
gases a second later, I'm

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going to have a completely
different microstate right?

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Because all of these guys are
going to have bumped into each

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other, and given each other
their momentum.

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And all sorts of crazy things
could have happened in a

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second here, so I would have
a completely different

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microstate.

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So even though we're at
thermodynamic equilibrium, and

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our macrostate stayed the same,
our microstates are

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changing every gazillionth
of a second.

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They're constantly changing.

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And that's why, for the most
part, in thermodynamic, we

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tend to deal with these
macrostates.

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And actually most of
thermodynamics, or at least

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most of what you'll learn in
a first-year chemistry or

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physics course, it was devised
or it was thought about well

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before people even had a sense
of what was going on at the

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macro level.

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That's often a very important
thing to think about.

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And we'll go into concepts
like entropy and internal

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energy, and things like that.

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And you can rack your brain, how
does it relate to atoms?

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And we will relate them to
atoms and molecules.

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But it's useful to think that
the people who first came up

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with these concepts came up
with them not really being

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sure of what was going on
at the micro level.

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They were just measuring
everything at the macro level.

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Now I want to go back to this
idea here, of equilibrium.

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Because in order for these
macrostates to be defined, the

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system has to be
in equilibrium.

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And let me explain
what that means.

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If I were to take a cylinder.

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And we will be using this
cylinder a lot, so it's good

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to get used to this cylinder.

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And it's got a piston in it.

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And that's just, it's kind of
the roof of the cylinder can

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move up and down.

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This is the roof of
the cylinder.

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The cylinder's bigger, but let's
say this is a, kind of a

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roof of the cylinder.

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And we can move this
up and down.

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And essentially we'll just be
changing the volume of the

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cylinder, right?

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I could have drawn
it this way.

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I could have drawn it
like a cylinder.

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I could have drawn it like this,
and then I could have

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drawn the piston like this.

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So there's some depth here
that I'm not showing.

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We're just looking at the
cylinder front on.

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And so, at any point in time,
let's say the gas is between

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the cylinder and the floor
of our container.

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You know, we have a bunch of
molecules of gas here, a huge

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number of molecules.

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And let's say that we have
a rock on the cylinder.

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We're doing this in space
so everything above

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the piston is a vacuum.

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Actually just let me erase
everything above.

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Let me just erase this stuff,
just so you see.

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We're doing this in space and
we're doing it in a vacuum.

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Just let me write that down.

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So all of this stuff up here is
a vacuum, which essentially

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says there's nothing there.

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There's no pressure from here,
there's no particles here,

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just empty space.

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And in order to keep this-- we
know already, we've studied it

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multiple times, that this gas is
generating, you know things

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are bumping into the wall,
the floor of this

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piston all the time.

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They're bumping into
everything, right?

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We know that's continuously
happening.

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So we would apply some pressure
to offset the

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pressure being generated
by the gas.

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Otherwise the piston
would just expand.

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It would just move up and the
whole gas would expand.

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So let's just say we stick a
big rock or a big weight on

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top of-- let me do it in a
different color-- We put a big

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weight on top of this piston,
where the force-- completely

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offsets the force being
applied by the gas.

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00:10:02,100 --> 00:10:05,370
And obviously this is some force
over some area-- right,

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the area of the piston-- over
some areas so that we could

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figure out its pressure.

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And that pressure will
completely offset the pressure

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of the gas.

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But the pressure of the gas,
just as a reminder, is going

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in every direction.

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The pressure on this plate is
the same as the pressure on

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that side, or on that side, or
on the bottom of the container

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that we're dealing with.

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Now let's say that we were to
just evaporate this-- well

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let's not say that we
evaporate the rock.

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Let's say that we just evaporate
half of the rock

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immediately.

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So all of a sudden our weight
that's being pushed down, or

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the force that's being pushed
down just goes to half

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immediately.

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Let me draw that.

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So I have-- maybe I would be
better off just cut and

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pasting this right here.

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So if I copy and paste it.

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So now I'm going to evaporate
half of that rock magically.

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So let me take my eraser tool.

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And I just evaporate
half of it.

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And now what's going
to happen?

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Well, this piston is now
applying half the force.

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It can't offset the pressure
due to this gas.

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So this whole thing is going
to be pushed upwards.

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But I did it so fast. I did it
so fast. And you could try it.

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I mean, this would be truth
of a lot of things.

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If you had a weight hanging from
a spring, and you would

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just remove half the weight, it
wouldn't just go very, you

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know, nice and smoothly
to another state.

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What's going to happen is--
and let me see if I can do

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this using their cut and paste
tool-- it'll essentially,

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right when I evaporate half of
it, the gas is going to expand

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00:11:37,660 --> 00:11:39,945
a bunch, and then this weight
is going to come back down,

247
00:11:39,945 --> 00:11:41,590
it's going to spring
and go down.

248
00:11:41,590 --> 00:11:42,570
So let me do it again.

249
00:11:42,570 --> 00:11:45,260
It's going to expand, because
that gas is going to push up,

250
00:11:45,260 --> 00:11:46,750
and then it's going
to come back down.

251
00:11:46,750 --> 00:11:49,020
And then, it's just going to
oscillate a little bit.

252
00:11:49,020 --> 00:11:52,330
And then eventually it'll come
back to some stable and maybe

253
00:11:52,330 --> 00:11:53,490
it'll go back.

254
00:11:53,490 --> 00:11:56,680
It'll look, like right
about there.

255
00:11:56,680 --> 00:11:58,380
And let me fill this in.

256
00:11:58,380 --> 00:12:01,605
This shouldn't be white,
it should be black.

257
00:12:01,605 --> 00:12:04,605
Let me put some walls on
it, on the container.

258
00:12:04,605 --> 00:12:09,100


259
00:12:09,100 --> 00:12:11,240
So if we wait long enough,
eventually we'll get to

260
00:12:11,240 --> 00:12:14,720
another equilibrium state, where
this thing, the piston

261
00:12:14,720 --> 00:12:17,570
on top isn't, or the ceiling
isn't moving anymore.

262
00:12:17,570 --> 00:12:21,810
And now the gas has filled
this container.

263
00:12:21,810 --> 00:12:24,850
Now, at this point in time
we were in equilibrium.

264
00:12:24,850 --> 00:12:27,520
The pressure throughout
the gas was the same.

265
00:12:27,520 --> 00:12:29,960
The temperature throughout
the gas was the same.

266
00:12:29,960 --> 00:12:32,720
The volume was in a
stable situation.

267
00:12:32,720 --> 00:12:34,860
It wasn't changing from
second to second.

268
00:12:34,860 --> 00:12:38,050
So because of that, our
macrostates were well defined.

269
00:12:38,050 --> 00:12:47,530


270
00:12:47,530 --> 00:12:51,750
Now, when we wait long enough,
this thing will get to some

271
00:12:51,750 --> 00:12:53,600
stability where this
thing stops moving.

272
00:12:53,600 --> 00:12:56,440
When this thing stops moving
our volume stops changing.

273
00:12:56,440 --> 00:12:59,760
And hopefully our pressure will
start to become uniform

274
00:12:59,760 --> 00:13:00,800
throughout the container.

275
00:13:00,800 --> 00:13:02,290
And our temperature will
become uniform.

276
00:13:02,290 --> 00:13:05,240
And we'll now be a higher volume
or lower pressure,

277
00:13:05,240 --> 00:13:07,160
probably a lower temperature if
we assume that there's no

278
00:13:07,160 --> 00:13:08,870
other heat being added
to the system.

279
00:13:08,870 --> 00:13:12,580
And then we'll be well
defined again.

280
00:13:12,580 --> 00:13:14,140
So we could say what the
pressure, and the volume, and

281
00:13:14,140 --> 00:13:16,070
the temperature's going to be.

282
00:13:16,070 --> 00:13:18,880
But what about right when
I removed this rock?

283
00:13:18,880 --> 00:13:22,030
And this thing flew up and it
oscillated, and for a while

284
00:13:22,030 --> 00:13:24,080
the pressure at the top
was lower than the

285
00:13:24,080 --> 00:13:24,790
pressure down here.

286
00:13:24,790 --> 00:13:26,750
Maybe the temperature at the
top was lower than the

287
00:13:26,750 --> 00:13:27,930
temperature down here.

288
00:13:27,930 --> 00:13:29,740
The whole thing was in
a state of flux.

289
00:13:29,740 --> 00:13:31,440
It was not an equilibrium.

290
00:13:31,440 --> 00:13:34,390
And at that point, when we're--
let me let me draw

291
00:13:34,390 --> 00:13:37,110
that really-- so you know, when
we were in that state,

292
00:13:37,110 --> 00:13:39,140
where everything was just
crazy, right when we

293
00:13:39,140 --> 00:13:40,840
evaporated the rock.

294
00:13:40,840 --> 00:13:42,560
You know, we have a little
rock up here.

295
00:13:42,560 --> 00:13:44,490
Everything is going
up and down.

296
00:13:44,490 --> 00:13:48,320
Maybe the pressure up here
was lower than the

297
00:13:48,320 --> 00:13:53,820
pressure down here.

298
00:13:53,820 --> 00:13:55,610
Everything did not have
a chance to reach an

299
00:13:55,610 --> 00:13:56,560
equilibrium.

300
00:13:56,560 --> 00:13:58,950
At this state-- and this is
important, especially as we go

301
00:13:58,950 --> 00:14:03,570
into talking about things like
reversible reactions, and

302
00:14:03,570 --> 00:14:07,580
reversible processes, and
quasi-static processes.

303
00:14:07,580 --> 00:14:11,100
At this point in the reaction,
when we just did this, none of

304
00:14:11,100 --> 00:14:14,030
these macrostates were
well defined.

305
00:14:14,030 --> 00:14:16,350
You couldn't tell me what the
volume of this system is,

306
00:14:16,350 --> 00:14:18,720
because it's changing for every
second to second, or

307
00:14:18,720 --> 00:14:21,000
microsecond to microsecond,
it's fluctuating.

308
00:14:21,000 --> 00:14:23,110
You couldn't tell me what the
pressure of the system is,

309
00:14:23,110 --> 00:14:24,950
because it's changing
every second.

310
00:14:24,950 --> 00:14:27,300
You couldn't tell me what
the temperature is.

311
00:14:27,300 --> 00:14:31,380
Maybe the temperature could
be something there.

312
00:14:31,380 --> 00:14:32,880
It could be something there.

313
00:14:32,880 --> 00:14:34,900
All sorts of crazy things
are happening.

314
00:14:34,900 --> 00:14:37,500
So when the system is in
a state of flux, your

315
00:14:37,500 --> 00:14:40,670
macrostates are not
well defined.

316
00:14:40,670 --> 00:14:42,690
And I really want to hit
that point home.

317
00:14:42,690 --> 00:14:45,190
So me just draw that
in a diagram.

318
00:14:45,190 --> 00:14:47,450
Let me draw that in
a PV diagram.

319
00:14:47,450 --> 00:14:50,340
And we're going to use
these fairly heavily.

320
00:14:50,340 --> 00:14:53,300
So on my y-axis I'm going
to put pressure.

321
00:14:53,300 --> 00:14:57,500
In my x-axis I'm going
to put volume.

322
00:14:57,500 --> 00:15:00,720
So our initial state here, when
we had the rock sitting

323
00:15:00,720 --> 00:15:03,420
on top of the ceiling, this
movable ceiling or this

324
00:15:03,420 --> 00:15:07,100
piston, maybe we had
some well-defined

325
00:15:07,100 --> 00:15:08,090
pressure and volume.

326
00:15:08,090 --> 00:15:11,420
So my y, this is pressure
and this is volume.

327
00:15:11,420 --> 00:15:14,260
So this is where
we started off.

328
00:15:14,260 --> 00:15:15,800
So it was well defined.

329
00:15:15,800 --> 00:15:17,050
This is state 1.

330
00:15:17,050 --> 00:15:20,500
Let me label it right there.

331
00:15:20,500 --> 00:15:25,270
Now when we evaporated half the
rock, we eventually waited

332
00:15:25,270 --> 00:15:26,580
long enough, and this got
to an equilibrium.

333
00:15:26,580 --> 00:15:28,560
We got to state 2, and our
pressure volume and out

334
00:15:28,560 --> 00:15:30,310
temperature was well defined.

335
00:15:30,310 --> 00:15:32,670
And I'll just put it on
this pressure volume.

336
00:15:32,670 --> 00:15:35,630
So maybe this is state 2.

337
00:15:35,630 --> 00:15:37,500
We got down here.

338
00:15:37,500 --> 00:15:40,920
And just as an aside, I could
maybe put temperature as an

339
00:15:40,920 --> 00:15:42,690
extra dimension, but temperature
is completely

340
00:15:42,690 --> 00:15:45,420
determined by pressure and
volume, especially if we're

341
00:15:45,420 --> 00:15:47,030
dealing with an ideal gas.

342
00:15:47,030 --> 00:15:50,470
Remember, and we did this in
multiple videos, you have PV

343
00:15:50,470 --> 00:15:55,300
is equal to nRT.

344
00:15:55,300 --> 00:15:56,750
These are constants.

345
00:15:56,750 --> 00:15:58,260
The number of moles
isn't changing.

346
00:15:58,260 --> 00:16:01,710
This is the universal gas
constant, not changing.

347
00:16:01,710 --> 00:16:03,180
So if you know P and
V you know T.

348
00:16:03,180 --> 00:16:05,110
So that's the only two things
we have to plot.

349
00:16:05,110 --> 00:16:08,460
But I'll talk a lot more about
that in future videos.

350
00:16:08,460 --> 00:16:11,020
But the important thing to
realize is, I started off at

351
00:16:11,020 --> 00:16:14,750
this state, where pressure and
volume were well defined.

352
00:16:14,750 --> 00:16:17,980
I finished in this state, where
pressure and volume were

353
00:16:17,980 --> 00:16:19,210
well defined.

354
00:16:19,210 --> 00:16:20,810
But how did I get there?

355
00:16:20,810 --> 00:16:23,220
And because this reaction I
did, all of a sudden it

356
00:16:23,220 --> 00:16:25,960
happened super fast, and it was
essentially thrown out of

357
00:16:25,960 --> 00:16:27,210
equilibrium.

358
00:16:27,210 --> 00:16:33,640


359
00:16:33,640 --> 00:16:35,650
I don't know how I got here.

360
00:16:35,650 --> 00:16:38,960
The pressure and volume were
not well defined from going

361
00:16:38,960 --> 00:16:41,090
from that state to this state.

362
00:16:41,090 --> 00:16:43,500
Pressure, volume, and
temperature are only well

363
00:16:43,500 --> 00:16:50,580
defined if every intermediate
step is still almost in

364
00:16:50,580 --> 00:16:51,190
equilibrium.

365
00:16:51,190 --> 00:16:52,950
And we'll talk a lot more about
that in the next video.

366
00:16:52,950 --> 00:16:54,500
But I want to really make
this point home.

367
00:16:54,500 --> 00:16:57,390
It would be nice if we
could draw some path.

368
00:16:57,390 --> 00:17:02,240
We could say, we moved from some
pressure and volume to

369
00:17:02,240 --> 00:17:04,339
some other pressure and volume,
and we moved along a

370
00:17:04,339 --> 00:17:05,720
well-defined path.

371
00:17:05,720 --> 00:17:07,410
But we cannot say that.

372
00:17:07,410 --> 00:17:10,240
Because when we went from there
there, our definitions

373
00:17:10,240 --> 00:17:11,910
just disappeared for pressure
and volume.

374
00:17:11,910 --> 00:17:16,839
We cannot define those
macrostates in these

375
00:17:16,839 --> 00:17:19,000
intermediate non-equilibrium
states.

376
00:17:19,000 --> 00:17:21,560
Now, just as a little aside,
we could have defined the

377
00:17:21,560 --> 00:17:22,800
microstates.

378
00:17:22,800 --> 00:17:24,230
The microstates never change.

379
00:17:24,230 --> 00:17:27,950
At any given snapshot in time,
I could have listed every

380
00:17:27,950 --> 00:17:29,470
particle that's in this thing.

381
00:17:29,470 --> 00:17:31,310
And I could have given you
its kinetic energy.

382
00:17:31,310 --> 00:17:32,890
I could have given
you its position.

383
00:17:32,890 --> 00:17:34,780
I could have given
you its momentum.

384
00:17:34,780 --> 00:17:36,900
And there's no reason why I
couldn't have done that.

385
00:17:36,900 --> 00:17:39,920
So I could have actually
made a plot of

386
00:17:39,920 --> 00:17:41,270
one particular particle.

387
00:17:41,270 --> 00:17:43,980
And I could have said what its
kinetic energy, and over a

388
00:17:43,980 --> 00:17:46,170
course of time, is at any
given moment in time.

389
00:17:46,170 --> 00:17:47,110
And this is really important.

390
00:17:47,110 --> 00:17:50,690
So microstates are always
well defined.

391
00:17:50,690 --> 00:17:53,330
The microstate is what's exactly
happening to the atom

392
00:17:53,330 --> 00:17:56,970
in terms of its force and its
velocity and its momentum.

393
00:17:56,970 --> 00:18:01,800
While macrostates are only
defined, I should say well

394
00:18:01,800 --> 00:18:05,260
defined, when the system-- in
this case it's the balloon, in

395
00:18:05,260 --> 00:18:08,060
this case it's this piston on
top of this cylinder, this

396
00:18:08,060 --> 00:18:10,730
movable ceiling-- the
macrostates are only well

397
00:18:10,730 --> 00:18:13,700
defined when the system is in
equilibrium, or when you can

398
00:18:13,700 --> 00:18:16,390
essentially say, the pressure is
x, the pressure is the same

399
00:18:16,390 --> 00:18:16,920
throughout.

400
00:18:16,920 --> 00:18:19,950
Or the volume isn't changing
from moment to moment.

401
00:18:19,950 --> 00:18:23,000
Or the temperature is the
same thing throughout.

402
00:18:23,000 --> 00:18:25,870
Anyway, I'll leave you there and
we'll talk more about why

403
00:18:25,870 --> 00:00:00,000
I went through all this pain
in the next video.