To understand how convection sets up this
temperature difference between the ground and the upper atmosphere
that drives the Greenhouse Effect, we need to talk about
three or four separate pieces of physics.
It may seem kind of unrelated and off the wall to
you, but we'll put them all together when we get there.
The first is about pressure in a standing fluid.
If you stand here in the atmosphere, or if we were
to stand at the bottom of a swimming pool, we feel pressure.
And the pressure that we feel is due to the weight of the material over our heads, pushing down.
Standing at the bottom of a swimming pool
we've got this water over our heads, and the
gravitational from the water is what we feel
as pressure, and the same is true of the atmosphere.
But the difference between the water and the
air is that water is basically incompressible.
So it's basically all the same density,
all the way up to the top, whereas gasses
expand if they're not under pressure,
so, the gas is much thicker close to the ground
and then it gets thinner as you go up in the atmosphere.
What that means for pressure in an incompressible medium like water,
if you start at the surface of a swimming pool,
and you swim down, the pressure is going to increase linearly with the depth,
so the pressure will be equal to some pressure at the top plus a constant
times the depth, and so this describes a straight line.
That's because if you start at the top and you swim down a meter
you've got one meter's worth of water over your head.
And you do it all the way at the bottom of the pool, one more meter.
The water has the same density at the top as at the bottom
so the slope of this line is constant, meaning it's a straight line.
Whereas in a compressible medium like a column of air, the pressure
change, if you climb up a little ways in the atmosphere,
is more intense than if you're already at the top of a mountain and you go up a little bit higher,
because the air is so much thinner up at the top of a mountain. So if you climb up
say 100 meters at the top of the mountain, you don't leave behind as much air as if
you were at the ground or sea level,
and if you climb up 100 meters, you're leaving behind more air.
That means that the pressure isn't linear with altitude like
it is in water, but it gets more and more gradual
as you go up. It follows an exponential profile.
The pressure at some height is equal to the pressure at the ground times
e, which is a number raised to the power of
the height divided by a value of about eight kilometers.
One thing to note about this atmospheric
pressure profile, is it never actually really reaches zero.
Mathematically it gets closer, and closer, and closer but it's
as if the pressure of the earth's atmosphere extends out,
forever into the entire galaxy, which is kind of,
an idea that only a mathematician could love probably.
But it might give you the impression that the atmosphere is infinitely thick.
But this multiplier here in the exponent is an important number and
it sort of sets the height of the atmosphere in some way.
It's called a scale height.
So that number is about eight kilometers and it turns out that if you could make
the air all have the same density as air at the ground,
so that it was like incompressible water
then the atmosphere would run out at eight kilometers high.
Eight kilometers is kind of like how thick the atmosphere is,
even though mathematically it kind of is infinitely thick.
But, this tells you a scale height.
When you're actually at eight kilometers
the pressure is a factor of one over e
times this pressure, which is about 30% or something like that.
It sets the height scale of the atmosphere.
The next thing that we need to worry about, is what happens
to the heat when this gas expands as it rises up,
or when it gets compressed, when it comes down toward the Earth under higher pressure.
Because it affects the temperature of the gas, actually.
And you can think of this by imagining a piston that's
got a sleeve that's insulated here so that no heat can cross the walls.
And then you've got this plunger that you
can push in there to compress the gas.
So you push on this plunger and
you're actually doing work to do that. You're pushing the gas molecules together.
It turns out that where that energy goes from doing the
work is to make the temperature of those gas molecules higher.
So you may have encountered this if you've ever
gone to a dive shop to go scuba diving.
You take a scuba tank and you need to
get your tank filled up and so they could just,
pump air into it.
But when they do that it gets very hot
and the tank doesn't want to hold more than a certain amount of pressure.
Hot gas is exerting more pressure and so if you went to a cheap dive shop.
and they just put air in your tank and let it get hot,
you would then take the tank and go jump in
the cold water, and the pressure would go way down.
You'd only have a half a tank of air to breathe.
A good dive shop will put the scuba tank
into a big tub of water and cool it down as
you put the gas in, to prevent the heating
up of the gas from affecting how much gas you take.
Or you can feel it if you ever let the air out of a bicycle tire.
You can feel the expansion of the gas as it's
coming out of the tire, makes it get really cold.
You can feel it on your thumbnail when you do that.
The air when it was inside the tire was at
the same temperature as the air outside, but just because it
expands, the fact that it's expanding decreases the average kinetic energy
of the molecules of gas and so it makes it colder.
Convection is the process of
heating a fluid from below and
causing it to overturn, or warming
it or cooling it from above.
If you heat from below you make the fluid at the bottom expand
because it's warmer.
And when it expands, it's less dense, and it will tend to rise up.
Or if you cool it from above, it will contract, and that
makes it more dense, then it will tend to fall down.
This is a picture of a lava lamp.
You have to have the light bulb at the bottom to heat it from below.
If you had a light bulb at the top, it
wouldn't convect, it wouldn't be any fun,
it wouldn't work.
So this happens in the real world when sunlight hits the
ground, it warms the atmosphere from below and that causes the atmosphere
to convect, or the ocean can convect
upside down, if you cool it from the top, like around Antarctica.
Up in the North Atlantic, you make the water at the
top denser and so it sinks and you do this overturning thing.
It's easiest to understand convection
first in the incompressible case, because it's simpler.
We'll start from a case where let's say we've got a pan of water
on a stove and we're heating it from below so it's going to be convecting.
So let's start out and say that the water is
well mixed in the pan.
That means that it will all be the same temperature,
because there isn't any expansion of the
(liquid) that makes it change its temperature
liquid I mean, because liquids are not compressible.
So it's all the same temperature just like
if you put some sugar into your coffee and
then stir it, it would all have the same amount
of sugar all through the the column.
So then we heat it from below, if this is the
temperature, we make a little blob of hot water at the bottom, but
that's going to expand, and it's going to be less dense than the
water above it, and that's not the way it wants to be.
So it's going to rise up.
Now, in the lava lamp, they have two different
kinds of fluids that can't mix, it's like oil and water.
So the blob from the bottom gets hot and it rises, goes all the way to
the top and then it cools down and comes all the way to the bottom again.
But what tends to happen in the atmosphere is that when this blob of hot stuff rises.
It mixes with everything above it and so it tends to move the
temperature of the whole column to a higher value, instead of just this blob
going up to the top like it would in a lava lamp.
Now in a compressible column of fluid, of
gas, we start out with a well-mixed profile.
But now here's the tricky part.
A well mixed profile is not all the same temperature.
Because this gas up here is under lower pressure.
If you were to take this gas and pull
it down to the bottom of the column so that it was under higher pressure, that
would make it warm up because it's being compressed, and it would, if this
is a well-mixed profile, it would just
exactly follow this trajectory going down,
so a well-mixed profile of gas is not all
the same temperature because of this expansion effect.
And then the rest of it is pretty easy.
We heat it from below and mix it, and it goes to another well-mixed profile.
Which is parallel to the first, pretty much, but warmed up.
The whole thing is kind of just tilted over by this expansion effect of the gas.