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[MUSIC]

Â So to understand how convection sets up this temperature difference between

Â the ground and the upper atmosphere that drives the greenhouse effect,

Â we need to talk about actually three or four separate pieces of physics.

Â That may seem kind of unrelated and

Â off the wall to you, but we'll put them all together when we get there.

Â So the first is about pressure in a standing fluid.

Â So as we stand here in the atmosphere or

Â if we were to stand at the bottom of swimming pool, we feel pressure.

Â And the pressure that we feel is due to the weight of the material over our heads,

Â sort of pushing down.

Â So standing at the bottom of the swimming pool we've got this water over our head

Â and that, the gravitational attraction of the water is what we feel as pressure,

Â and the same is true of the atmosphere, but the difference between the water In

Â the air is that water is basically incompressible.

Â So it's basically all the same density all the way up to the top whereas

Â gasses expand if they're not under pressure.

Â And so, the gas is much thicker close to the ground, and

Â then it gets thinner as you go up in the atmosphere.

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So what that means for pressure in a incompressible medium like water,

Â if you start at the surface of a swimming pool and you swim down,

Â the pressure is going to increase linearly with the depth.

Â So the pressure would be equal to some pressure at the top plus a constant

Â times the the depth, and so this describes the straight line.

Â And that's because if you start at the top and

Â you swim down a meter you've got one meters worth of water over your head, and

Â you do it at all the way at the bottom of the pool, one more meter.

Â The water has the same density at the top as at the bottom, so

Â the slope of this line is constant, meaning it's a straight line.

Â Whereas, in a compressible medium like a column of air,

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the pressure change if you climb up a little ways in the atmosphere

Â is more intense than if you're already at the top of a mountain and you go up

Â a little bit higher, because the air is so much thinner up at the top of a mountain.

Â So if you climb up say, 100 meters at the top of a mountain,

Â you don't leave behind as much air as if you were at the ground or sea level and

Â you climb up 100 meters, you're leaving behind more air.

Â And so, that means that the pressure isn't linear with altitude like it is in water,

Â but it sort of gets more and more gradual as you go up.

Â It follows an exponential profile.

Â So the pressure at some height is equal to the pressure

Â at the ground times e which is a number raised to the power

Â of the height divided by a value of about eight kilometers.

Â So one thing to note about this atmospheric pressure profile,

Â is it never actually really reaches zero.

Â Mathematically, it gets closer and closer and closer, but it's as if the pressure

Â of the Earth's atmosphere extends out forever into the entire galaxy.

Â We just kind of, an idea that only a mathematician could love, probably.

Â But, it might give you the impression that the atmosphere is infinitely thick.

Â But actually, this multiplier here in the exponent is an important number, and it

Â sort of sets the height of the atmosphere in some way is called the scale height.

Â So that number is about eight kilometers.

Â And it turns out that if you could make

Â the air all have the same density has air at the ground.

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water that the atmosphere would run out at eight kilometers high.

Â So eight kilometers is kind of like how thick the atmosphere is in some sense,

Â even though mathematically it is infinitely thick.

Â But, this tells you a scale height, so

Â when you're actually at 8 kilometers the pressure is a factor of

Â 1 over e times this pressure which is about 30% or something like that.

Â It sort of sets the height scale of the atmosphere.

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So the next thing that we need to worry about is what happens

Â to the heat when this gas expands as it rises up, or

Â when it gets compressed when it comes down toward the earth under higher pressure,

Â because it affects the temperature of the gas actually.

Â And you can think of this by imagining

Â a piston that's got a sleeve that's insulated here, so

Â that no heat can cross the walls, and then you've got this

Â plunger thing that you can sort of push in there to compress the gas.

Â So you push on this plunger and

Â you're actually doing work to do that, you're pushing the gas molecules together.

Â It turns out that where that energy goes from doing the work,

Â is to make the temperature of those gas molecules higher.

Â So you may have encountered this if you've ever gone to a dive shop

Â to go scuba diving.

Â You take a scuba tank and you need to get your tank filled up.

Â And so, they could just pump air into it.

Â But when they do that, it gets very hot, and

Â the tank doesn't wanna hold more than a certain amount of pressure.

Â So hot gas is exerting more pressure, and so if you went to a cheap dive shop, and

Â they just put air in your tank, and let it get hot, you would then take the tank and

Â go jump in the cold water, and the pressure would go way down.

Â You'd only have like half a tank of air to breathe.

Â So a good dive shop will put the scuba tank into a big tub of water, and

Â cool it down as you put the gas in to prevent

Â the heating up of the gas from effecting how much gas you take.

Â Or you can feel it if you've ever let the air out of a bicycle tire.

Â You can feel the expansion of the gas as it's coming out of the tire

Â makes it get really cold.

Â You can feel it on your thumbnail when you do that.

Â The air when it was inside the tire,

Â was at the same temperature as the air outside.

Â But just because it expands, the fact of its expanding decreases

Â the average kinetic energy of the molecules of gas, so it makes it colder.

Â [NOISE] Convection is the process of

Â heating a fluid from below and

Â causing it to overturn, or

Â cooling it from above.

Â If you heat from below, you make the fluid at the bottom expand, because it's warmer.

Â And when it expands, it's less dense and it will tend to rise up.

Â Or if you cool if from above, it will contract, and that makes it more dense and

Â it will tend to fall down.

Â So if you were to, this is a picture of a lava lamp.

Â You've got to have the lightbulb at the bottom to heat it from below.

Â If you had a lightbulb at the top it wouldn't convect,

Â it wouldn't be any fun, it wouldn't work.

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So this happens in the real world when sunlight hits the ground.

Â It warms the atmosphere from below and that causes the atmosphere to convect.

Â Or the ocean can convect in a sort of upside down way,

Â if you cool it from the top, like around Antarctica or

Â up in the North Atlantic, you make the water at the top denser,

Â and so it sinks and you do this over turning thing.

Â [SOUND] So it's easiest to understand convection

Â first in the incompressible case, because its just sort of simpler.

Â We'll start from a case where, let's say, we've got a pan of water on the stove and

Â we're heating it from below, so it's gonna be convecting.

Â So let's start out and say that the water is well-mixed in the pan, and

Â so that means that it will all be the same temperature.

Â Because there isn't any expansion of the gas that makes it

Â change its temperature or anything, because gases, of the liquid, I mean.

Â Because liquids are not compressible.

Â So it's all the same temperature.

Â Just like if you put some sugar into your coffee and stir it,

Â it would all have the same amount of sugar all through the column.

Â So then, we heat it from below.

Â So if this is the temperature we make a little blob of hot water at the bottom,

Â but that's gonna expand and it's gonna be less dense than the water above it,

Â and that's not the way it wants to be, so it's gonna rise up.

Â Now, in the lava lamp, they have two different kinds of fluid that can't mix.

Â It's like oil and water.

Â So the blob from the bottom gets hot and it rises.

Â It goes all the way to the top,

Â and then it cools down and comes all the way to the bottom again.

Â But what tends to happen in the atmosphere is that when this blob of hot stuff rises,

Â it kind of mixes with everything above it, and so

Â it tends to move the whole temperature of the whole column to a higher

Â value, instead of just this blob going up to the top like it would in a lava lamp.

Â