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After all the work we've been
doing with fluids, you

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probably have a pretty good
sense of what pressure is.

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Now let's think a little bit
about what it really means,

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especially when we think
about it in terms

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of a gas in a volume.

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Remember, what was
the difference

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between a gas and a liquid?

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They're both fluids, they both
take the shape of their

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containers, but a gas is
compressible, while a liquid

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is incompressible.

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Let's start focusing on gases.

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Let's say I have a container,
and I have a

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bunch of gas in it.

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What is a gas made of?

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It's just made up of a whole
bunch of the molecules of the

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gas itself, and I'll draw each
of the molecules with a little

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dot-- it's just going to have
a bunch of molecules in it.

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There's many, many, many more
than what I've drawn, but

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that's indicative, and they'll
all be going in random

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directions-- this one might be
going really fast in that

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direction, and that one might
be going a little bit slower

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in that direction.

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They all have their own little
velocity vectors, and they're

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always constantly bumping into
each other, and bumping into

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the sides of the container, and
ricocheting here and there

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and changing velocity.

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In general, especially at this
level of physics, we assume

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that this is an ideal gas, that
all of the bumps that

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occur, there's no
loss of energy.

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Or essentially that they're all
elastic bumps between the

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different molecules.

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There's no loss of momentum.

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Let's keep that in mind, and
everything you're going to see

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in high school and on the AP
test is going to deal with

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ideal gases.

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Let's think about what pressure

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means in this context.

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A lot of what we think about
pressure is something pushing

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on an area.

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If we think about pressure
here-- let's pick

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an arbitrary area.

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Let's take this side.

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Let's take this surface
of its container.

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Where's the pressure
going to be

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generated onto this surface?

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It's going to be generated by
just the millions and billions

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and trillions of little
bumps every time-- let

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me draw a side view.

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If this is the side view of the
container, that same side,

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every second there's always
these little molecules of gas

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moving around.

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If we pick an arbitrary period
of time, they're always

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ricocheting off of the side.

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We're looking at time over a
super-small fraction of time.

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And over that period of time,
this one might end up here,

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this one maybe bumped into it
right after it ricocheted and

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came here, this one changes
momentum and goes like that.

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This one might have already been
going in that direction,

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and that one might ricochet.

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But what's happening is, at
any given moment, since

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there's so many molecules,
there's always going to be

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some molecules that
are bumping into

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the side of the wall.

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When they bump, they have
a change in momentum.

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All force is change in
momentum over time.

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What I'm saying is that in any
interval of time, over any

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period or any change in time,
there's just going to be a

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bunch of particles that are
changing their momentum on the

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side of this wall.

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That is going to generate force,
and so if we think

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about how many on average--
because it's hard to keep

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track of each particle
individually, and when we did

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kinematics and stuff, we'd keep
track of the individual

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object at play.

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But when we're dealing with
gases and things on a macro

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level, you can't keep track of
any individual one, unless you

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have some kind of unbelievable
supercomputer.

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We can say, on average, this
many particles are changing

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momentum on this wall in
this amount of time.

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And so the force exerted on this
wall or this surface is

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going to be x.

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If we know what that force is,
and we you know the area of

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the wall, we can figure out
pressure, because pressure is

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equal to force divided
by area.

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What does this help us with?

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I wanted to give you that
intuition first, and now I'm

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just going to give you the one
formula that you really just

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need to know in thermodynamics.

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And then as we go into the next
few videos, I'll prove to

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you why it works, and
hopefully give

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you more of an intuition.

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Now you understand, hopefully,
what pressure means in the

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context of a gas
in a container.

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With that out of the way, let
me give you a formula.

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I hope by the end of this video
you have the intuition

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for why this formula works.

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In general, if I have an ideal
gas in a container, the

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pressure exerted on the gas-- on
the side of the container,

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or actually even at any point
within the gas, because it

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will all become homogeneous at
some point-- and we'll talk

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about entropy in future videos--
but the pressure in

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the container and on its
surface, times the volume of

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the container, is equal
to some constant.

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We'll see in future videos that
that constant is actually

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proportional to the average
kinetic energy of the

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molecules bouncing around.

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That should make sense to you.

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If the molecules were moving
around a lot faster, then you

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would have more kinetic energy,
and then they would be

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changing momentum on the sides
of the surface a lot more, so

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you would have more pressure.

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Let's see if we can get a little
bit more intuition onto

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why pressure times volume
is a constant.

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Let's say I have a container
now, and it's got a bunch of

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molecules of gas in it.

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Just like I showed you in that
last bit right before I

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erased, these are bouncing
off of the sides

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at a certain rate.

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Each of the molecules might
have a different kinetic

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energy-- it's always changing,
because they're always

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transferring momentum
to each other.

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But on average, they all have
a given kinetic energy, they

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keep bumping at a certain rate
into the wall, and that

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determines the pressure.

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What happens if I were able to
squeeze the box, and if I were

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able to decrease the
volume of the box?

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I just take that same box with
the same number of molecules

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in it, but I squeeze.

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I make the volume of
the box smaller--

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what's going to happen?

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I have the same number of
molecules in there, with the

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same kinetic energy, and on
average, they're moving with

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the same velocities.

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So now what's going to happen?

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They're going to be hitting the
sides more often-- at the

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same time here that this
particle went bam, bam, now it

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could go bam, bam, bam.

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They're going to be hitting
the sides more often, so

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you're going to have more
changes in momentum, and so

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you're actually going to have
each particle exert more force

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on each surface.

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Because it's going to be hitting
them more often in a

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given amount of time.

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The surfaces themselves
are smaller.

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You have more force on a
surface, and on a smaller

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surface, you're going to
have higher pressure.

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Hopefully, that gives you an
intuition that if I had some

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amount of pressure in this
situation-- if I squeeze the

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volume, the pressure
increases.

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Another intuition-- if
I have a balloon,

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what blows up a balloon?

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It's the internal air pressure
of the helium, or your own

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exhales that you put
into the balloon.

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The more and more you try to
squeeze a balloon-- if you

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squeeze it from all directions,
it gets harder and

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harder to do it, and that's
because the pressure within

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the balloon increases as you
decrease the volume.

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If volume goes down, pressure
goes up, and that makes sense.

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That follows that when they
multiply each other, you have

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to have a constant.

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Let's take the same example
again, and what happens if you

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make the volume bigger?

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Let's say I have-- it's huge
like that, and I should have

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done it more proportionally, but
I think you get the idea.

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You have the same number of
particles, and if I had a

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particle here, in some period
of time it could have gone

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bam, bam, bam-- it could have
hit the walls twice.

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Now, in this situation, with
larger walls, it might just go

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bam, and in that same amount
of time, it will maybe get

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here and won't even hit
the other wall.

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The particles, on average, are
going to be colliding with the

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wall less often, and the walls
are going to have a larger

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area, as well.

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So in this case, when our volume
goes up, the average

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pressure or the pressure in
the container goes down.

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Hopefully, that gives you a
little intuition, and so

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you'll never forget
that pressure

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times volume is constant.

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And then we can use that to do
some pretty common problems,

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which I'll do in
the next video.

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I'm about to run out of time.

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See you soon.

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