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Let's say I have a balloon.

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And in that balloon I have a bunch of

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particles bouncing around.

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They're gas particles, so they're floating freely.

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And they each have some velocity, some kinetic energy.

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And what I care about, let me just draw a few more, what I

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care about is the pressure that is exerted on the surface

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of the balloon.

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So I care about the pressure.

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And what's pressure?

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It's force per area.

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So the area here, you can think of it as the inside

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surface of the balloon.

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And what's going to apply force to that?

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Well any given moment-- I only drew six particles here, but

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in a real balloon you would have gazillions of particles,

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and we could talk about how large, but more particles than

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you can really probably imagine-- but at any given

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moment, some of those particles are bouncing off the

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wall of the container.

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That particle is bouncing there, this particle is

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bouncing there, this guy's bouncing like that.

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And when they bounce, they apply force to the container.

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An outward force, that's what keeps the balloon blown up.

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So think about what the pressure is going to be

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dependent on.

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So first of all, the faster these particles move, the

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higher the pressure.

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Slower particles, you're going to be bouncing into the

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container less, and when you do bounce into the container,

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it's going to be less of a ricochet, or less of a change

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in momentum.

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So slower particles, you're going to

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have pressure go down.

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Now, it's practically impossible to measure the

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kinetic energy, or the velocity, or the direction of

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each individual particle.

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Especially when you have gazillions

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of them in a balloon.

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So we do is we think of the average

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energy of the particles.

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And the average energy of the particles, you might say oh,

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Sal is about to introduce us to a new concept.

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It's a new way of looking at probably a very familiar

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concept to you.

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And that's temperature.

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Temperature can and should be viewed as the average energy

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of the particles in the system.

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So I'll put a little squiggly line, because there's a lot of

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ways to think about it.

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Average energy.

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And mostly kinetic energy, because these particles are

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moving and bouncing.

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The higher the temperature, the faster that these

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particles move.

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And the more that they're going to bounce into the side

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of the container.

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But temperature is average energy.

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It tells us energy per particle.

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So obviously, if we only had one particle in there with

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super high temperature, that's going to have less pressure

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than if we have a million particles in there.

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Let me draw that.

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If I have, let's take two cases right here.

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One is, I have a bunch of particles with a certain

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temperature, moving in their different directions.

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And the other example, I have one particle.

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And maybe they have the same temperature.

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That on average, they have the same kinetic energy.

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The kinetic energy per particle is the same.

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Clearly, this one is going to be applying more pressure to

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its container, because at any given moment more of these

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particles are going to be bouncing off the side than in

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this example.

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This guy's going to bounce, bam, then going to go and

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move, bounce, bam.

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So he's going to be applying less pressure, even though his

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temperature might be the same.

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Because temperature is kinetic energy, or you can view it as

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kinetic energy per particles.

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Or it's a way of looking at kinetic energy per particle.

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So if we wanted to look at the total energy in the system, we

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would want to multiply the temperature times the number

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of particles.

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And just since we're dealing on the molecular scale, the

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number of particles can often be represented as moles.

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Remember, moles is just a number of particles.

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So we're saying that that pressure-- well, I'll say it's

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proportional, so it's equal to some constant,

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let's call that R.

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Because we've got to make all the units work out in the end.

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I mean temperature is in Kelvin but we eventually want

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to get back to joules.

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So let's just say it's equal to some constant, or it's

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proportional to temperature times the number of particles.

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And we can do that a bunch of ways.

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But let's think of that in moles.

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If I say there are 5 mole particles there, you know

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that's 5 times 6 times 10 to the 23 particles.

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So, this is the number of particles.

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This is the temperature.

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And this is just some constant.

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Now, what else is the pressure dependent on?

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We gave these two examples.

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Obviously, it is dependent on the temperature; the faster

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each of these particles move, the higher pressure we'll

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have. It's also dependent on the number of particles, the

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more particles we have, the more pressure we'll have. What

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about the size of the container?

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The volume of the container.

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If we took this example, but we shrunk the container

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somehow, maybe by pressing on the outside.

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So if this container looked like this, but we still had

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the same four particles in it, with the same average kinetic

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energy, or the same temperature.

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So the number of particles stays the same, the

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temperature is the same, but the volume has gone down.

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Now, these guys are going to bump into the sides of the

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container more frequently and there's less area.

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So at any given moment, you have more force and less area.

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So when you have more force and less area, your pressure

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is going to go up.

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So when the volume went down, your pressure went up.

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So we could say that pressure is inversely

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proportional to volume.

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So let's think about that.

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Let's put that into our equation.

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We said that pressure is proportional-- and I'm just

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saying some proportionality constant, let's call that R,

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to the number of particles times the temperature, this

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gives us the total energy.

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And it's inversely proportional to the volume.

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And if we multiply both sides of this times the volume, we

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get the pressure times the volume is proportional to the

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number of particles times the temperature.

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So PV is equal to RnT.

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And just to switch this around a little bit, so it's in a

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form that you're more likely to see in your chemistry book,

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if we just switch the n and the R term.

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You get pressure times volume is equal to n, the number of

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particles you have, times some constant times temperature.

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And this right here is the ideal gas equation.

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Hopefully, it makes some sense to you.

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When they say ideal gas, it's based on this little mental

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exercise I did to come up with this.

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I made some implicit assumptions when I did this.

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One is I assumed that we're dealing with an ideal gas.

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And so you say what, Sal, is an ideal gas?

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An ideal gas is one where the molecules are not too

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concerned with each other.

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They're just concerned with their own kinetic energy and

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bouncing off the wall.

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So they don't attract or repel each other.

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Let's say they attracted each other, then as you increased

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the number of particles maybe they'd want to

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not go to the side.

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Maybe they'd all gravitate towards the center a little

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bit more if they did attract each other.

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And if they did that, they would bounce into the walls

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less and the pressure would be a little bit lower.

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So we're assuming that they don't attract

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or repel each other.

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And we're also assuming that the actual volume of the

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individual particles are inconsequential.

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Which is a pretty good assumption, because they're

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pretty small.

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Although, if you start putting a ton of particles into a

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certain volume, then at some point, especially if they're

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big molecules, it'll start to matter in terms of their size.

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But we're assuming for the purposes of our little mental

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exercise that the molecules have inconsequential volumes

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and they don't attract or repel each other.

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And in that situation, we can apply the ideal gas equation

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right here.

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Now, we've established the ideal gas equation.

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But you're like, well what's R, how do I deal with it, and

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how do I do math problems, and solve chemistry

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problems with it?

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And how do the units all work out?

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We'll do all of that in the next video where we'll solve a

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ton of equations, or a ton of exercises with

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the ideal gas equation.

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The important takeaway from this video is just to have the

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intuition as to why this actually does make sense.

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And frankly, once you have this intution, you should

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never forget it.

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You should be able to maybe even derive it on your own.