After all the work we've been doing with fluids, you
probably have a pretty good sense of what pressure is.
Now let's think a little bit about what it really means,
especially when we think about it in terms
of a gas in a volume.
Remember, what was the difference
between a gas and a liquid?
They're both fluids, they both take the shape of their
containers, but a gas is compressible, while a liquid
is incompressible.
Let's start focusing on gases.
Let's say I have a container, and I have a
bunch of gas in it.
What is a gas made of?
It's just made up of a whole bunch of the molecules of the
gas itself, and I'll draw each of the molecules with a little
dot-- it's just going to have a bunch of molecules in it.
There's many, many, many more than what I've drawn, but
that's indicative, and they'll all be going in random
directions-- this one might be going really fast in that
direction, and that one might be going a little bit slower
in that direction.
They all have their own little velocity vectors, and they're
always constantly bumping into each other, and bumping into
the sides of the container, and ricocheting here and there
and changing velocity.
In general, especially at this level of physics, we assume
that this is an ideal gas, that all of the bumps that
occur, there's no loss of energy.
Or essentially that they're all elastic bumps between the
different molecules.
There's no loss of momentum.
Let's keep that in mind, and everything you're going to see
in high school and on the AP test is going to deal with
ideal gases.
Let's think about what pressure
means in this context.
A lot of what we think about pressure is something pushing
on an area.
If we think about pressure here-- let's pick
an arbitrary area.
Let's take this side.
Let's take this surface of its container.
Where's the pressure going to be
generated onto this surface?
It's going to be generated by just the millions and billions
and trillions of little bumps every time-- let
me draw a side view.
If this is the side view of the container, that same side,
every second there's always these little molecules of gas
moving around.
If we pick an arbitrary period of time, they're always
ricocheting off of the side.
We're looking at time over a super-small fraction of time.
And over that period of time, this one might end up here,
this one maybe bumped into it right after it ricocheted and
came here, this one changes momentum and goes like that.
This one might have already been going in that direction,
and that one might ricochet.
But what's happening is, at any given moment, since
there's so many molecules, there's always going to be
some molecules that are bumping into
the side of the wall.
When they bump, they have a change in momentum.
All force is change in momentum over time.
What I'm saying is that in any interval of time, over any
period or any change in time, there's just going to be a
bunch of particles that are changing their momentum on the
side of this wall.
That is going to generate force, and so if we think
about how many on average-- because it's hard to keep
track of each particle individually, and when we did
kinematics and stuff, we'd keep track of the individual
object at play.
But when we're dealing with gases and things on a macro
level, you can't keep track of any individual one, unless you
have some kind of unbelievable supercomputer.
We can say, on average, this many particles are changing
momentum on this wall in this amount of time.
And so the force exerted on this wall or this surface is
going to be x.
If we know what that force is, and we you know the area of
the wall, we can figure out pressure, because pressure is
equal to force divided by area.
What does this help us with?
I wanted to give you that intuition first, and now I'm
just going to give you the one formula that you really just
need to know in thermodynamics.
And then as we go into the next few videos, I'll prove to
you why it works, and hopefully give
you more of an intuition.
Now you understand, hopefully, what pressure means in the
context of a gas in a container.
With that out of the way, let me give you a formula.
I hope by the end of this video you have the intuition
for why this formula works.
In general, if I have an ideal gas in a container, the
pressure exerted on the gas-- on the side of the container,
or actually even at any point within the gas, because it
will all become homogeneous at some point-- and we'll talk
about entropy in future videos-- but the pressure in
the container and on its surface, times the volume of
the container, is equal to some constant.
We'll see in future videos that that constant is actually
proportional to the average kinetic energy of the
molecules bouncing around.
That should make sense to you.
If the molecules were moving around a lot faster, then you
would have more kinetic energy, and then they would be
changing momentum on the sides of the surface a lot more, so
you would have more pressure.
Let's see if we can get a little bit more intuition onto
why pressure times volume is a constant.
Let's say I have a container now, and it's got a bunch of
molecules of gas in it.
Just like I showed you in that last bit right before I
erased, these are bouncing off of the sides
at a certain rate.
Each of the molecules might have a different kinetic
energy-- it's always changing, because they're always
transferring momentum to each other.
But on average, they all have a given kinetic energy, they
keep bumping at a certain rate into the wall, and that
determines the pressure.
What happens if I were able to squeeze the box, and if I were
able to decrease the volume of the box?
I just take that same box with the same number of molecules
in it, but I squeeze.
I make the volume of the box smaller--
what's going to happen?
I have the same number of molecules in there, with the
same kinetic energy, and on average, they're moving with
the same velocities.
So now what's going to happen?
They're going to be hitting the sides more often-- at the
same time here that this particle went bam, bam, now it
could go bam, bam, bam.
They're going to be hitting the sides more often, so
you're going to have more changes in momentum, and so
you're actually going to have each particle exert more force
on each surface.
Because it's going to be hitting them more often in a
given amount of time.
The surfaces themselves are smaller.
You have more force on a surface, and on a smaller
surface, you're going to have higher pressure.
Hopefully, that gives you an intuition that if I had some
amount of pressure in this situation-- if I squeeze the
volume, the pressure increases.
Another intuition-- if I have a balloon,
what blows up a balloon?
It's the internal air pressure of the helium, or your own
exhales that you put into the balloon.
The more and more you try to squeeze a balloon-- if you
squeeze it from all directions, it gets harder and
harder to do it, and that's because the pressure within
the balloon increases as you decrease the volume.
If volume goes down, pressure goes up, and that makes sense.
That follows that when they multiply each other, you have
to have a constant.
Let's take the same example again, and what happens if you
make the volume bigger?
Let's say I have-- it's huge like that, and I should have
done it more proportionally, but I think you get the idea.
You have the same number of particles, and if I had a
particle here, in some period of time it could have gone
bam, bam, bam-- it could have hit the walls twice.
Now, in this situation, with larger walls, it might just go
bam, and in that same amount of time, it will maybe get
here and won't even hit the other wall.
The particles, on average, are going to be colliding with the
wall less often, and the walls are going to have a larger
area, as well.
So in this case, when our volume goes up, the average
pressure or the pressure in the container goes down.
Hopefully, that gives you a little intuition, and so
you'll never forget that pressure
times volume is constant.
And then we can use that to do some pretty common problems,
which I'll do in the next video.
I'm about to run out of time.
See you soon.