Learn about the science behind the current exploration of the solar system in this free class. Use principles from physics, chemistry, biology, and geology to understand the latest from Mars, comprehend the outer solar system, ponder planets outside our solar system, and search for habitability in our neighborhood and beyond. This course is generally taught at an advanced level assuming a prior knowledge of undergraduate math and physics, but the majority of the concepts and lectures can be understood without these prerequisites. The quizzes and final exam are designed to make you think critically about the material you have learned rather than to simply make you memorize facts. The class is expected to be challenging but rewarding.
Lecture 2.06: Heat transport
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Del curso dictado por Caltech
The Science of the Solar System
310 calificaciones
De la lección
Unit 2: The insides of giant planets (week 1)
Conoce a los instructores
Mike BrownProfessor
Planetary Astronomy
OK we do have one last task before we can
finally try to put together a story about the inside of Jupiter,
and that last task is because Jupiter is not a cold dead planet.
In fact, like the Earth,
Jupiter has a lot of heat in the interior leftover from its formation.
How do we know that the earth has heat in its interior?
Well actually some of the easiest ways are to go down into a mine.
I've been down inside of a cave before and that feels cool because you're
insulated from the hot daytimes and you're more like an average annual temperature.
If you go down inside of a mine, a kilometer-deep mine,
you quickly realize that it's getting hotter and hotter as you go down.
This is because there's heat on the inside of the earth that is
being conducted through the rocks to escape out to space.
In fact, you could argue that removal of heat is
the single most important task that the planet has.
Somebody asked me once on an Earth Day did I worry about the earth as a planet.
And I said well, no,
I think the earth as a planet is doing fine because all it cares
about is removing heat and it removes heat very efficiently through conduction,
through plate tectonics, through volcanoes.
The environment on that little thin layer on top of the earth,
I might worry about that, but the Earth is a planet.
It's a perfectly happy planet.
Jupiter has got the same issues;
it wants to remove the heat that it has leftover from that time of formation.
We'll talk a lot more about formation in a little bit so I'm not
talking about it as much about where that he came from.
But there's heat on the inside, it needs to get out.
How do you get rid of heat from a planet?
There are three ways you can transfer heat in a planet.
One, is by the one that I talked about for the earth: conduction,
and conduction is what would occur if I heated up the side of
this pen and I felt this side and felt the heat coming through,
conducting through the pen itself.
It's really, you can think of it as just electrons bumping
around and transferring to electrons bumping around and finally getting to here;
that is conduction of heat.
There's also radiation.
We talked a little bit about radiation and thermal emission when we talked about Mars.
That would be if there were a big bonfire and I couldn't
get up close to it because the radiating heat from it was so hot.
That's your feeling that radiation of the heat.
And finally, there's convection.
Convection simply means motion.
Easiest way to convect heat if I heated up this pen and I threw it at you,
that would be convecting heat towards you.
We usually think of convection in terms of heating up air
or heating up water and heating and thinking like
a boiling pot of water and you have hot water on
the bottom that's going up in cold water at the surface that's going down.
That's the process of convection that is cooling
the water by moving the hot stuff to the top taking cool stuff down.
What happens inside of Jupiter?
Well, radiation, although there are places where radiation might
be important in general inside the body of a planet,
radiation doesn't matter on the outside on the surface of the earth.
Of course, those photons that heat radiates to
space except in those places where it gets reabsorbed by the Earth's atmosphere.
But in general, radiation comes from the surface of the earth.
On Jupiter, and the same on the sun,
we call that place where the radiation comes from the photosphere.
And in general, that's up near
the very top of the surface so we're going to generally ignore that.
So, on Jupiter, it's conduction or convection that's going to do the big job.
We know that there's heat coming from Jupiter because we can actually
measure this emission coming from the photosphere and
we find that there's more emission from
the photosphere than can be explained simply by heating of sunlight,
something like 1.5 times more energy than there should be.
And where does that energy come from?
Well, it has to be from the cooling of this internal part.
The way that we have energy being
transmitted through this photosphere is that it's hotter on the inside,
hotter even further down and even hotter in the middle and that temperature
high temperatures cause heat to flow through the planet up to the surface.
All right, let's think about conduction.
Conduction is a pretty slow process.
Again if I heat this pen and I wait for it to get hot over here,
it can take a long time in something like
a pen because there's not much conductivity in the pen.
If I had instead, a metal bar right here,
I could heat up here and eventually it would get pretty hot.
Metal is very conductive; plastic,
not very conductive, wood;
plastic would probably just melt.
But if you have high conductivity,
you have a lot of heat flow.
If you have low conductivity,
you have low heat flow and if you think about what that
implies for temperatures on the inside,
it's a little bit counter-intuitive although it makes sense.
If you have a really high conductivity and you want to
have a certain amount of heat flowing out the surface here,
you need a temperature gradient;
this is the distance inside the surface inside the planet.
This is the temperature,
hotter temperatures are over here,
and you need to have it hot on the inside,
cool on the inside and if you have high conductivity it might look something like this.
It doesn't take much of a temperature difference to cause heat to flow through here.
Let's try a different case with low conductivity; there,
you need a huge temperature gradient to have heat flowing out the top.
Again, imagine if I had a stick of wood and I wanted to say how
can I transfer a lot of heat into my fingers from a stick of wood.
Well, you better not heat it up just a little bit on the side,
you better heat one side up a lot if I'm going to
ever feel it over here; that's low conductivity.
It's high conductivity if it's metal;
I only have to heat it up a little bit to feel the heat over here.
That's the difference between these two.
Jupiter, interestingly, is pretty low conductivity.
If we assume it's made out of hydrogen,
in fact, molecular hydrogen,
to get the heat flowing out the surface of Jupiter requires something like
an internal temperature of two million degrees Kelvin.
That's a ridiculous number.
There's no way to heat it up to that temperature again.
We'll talk about how you heated up to certain temperatures when we talk
more about formation a little bit but trust me on this one.
Two million degrees? No way.
You can hope that maybe something happens to hydrogen to
make it more conductive and you'd be right;
as we'll talk about it just a minute,
hydrogen turns into metallic hydrogen and,
just like a metal rod,
it's much more conductive,
in fact, it's something like 100 times more conductive.
And in this case, the internal temperature only needs be
something like 20,000 degrees Kelvin.
This is less ridiculous.
It's possible to imagine that there's something like
20,000 degree internal temperature inside Jupiter.
And yet this still doesn't happen. Let's explore why.
If we did start out this way with a 20,000 degree interior
and nice conduction slowly taking the heat out through here,
we still would have to consider the other effect which is convection.
Convection would mean taking hot pieces down
here and simply moving them up or moving them down.
Now, you need some mechanism to move them up or down so it doesn't happen
generally unless there's some reason that they do it. What's the reason they do it?
Well, if you remember from our ideal gas law PV = nRT,
one of the things that happens at an ideal gas and even in non-ideal gases,
as the pressure decreases, the temperature decreases.
If I take a parcel from down here,
a 20,000 degree chunk of gas,
and I move it upward just a little bit,
it goes down in temperature.
It's critical though how much it goes down in temperature.
If it goes down temperature a little bit like this, then what happens?
Well, it finds itself surrounded by a bunch of stuff that's cooler.
Stuff that's cooler, it's going to be higher density,
suddenly it's going to be buoyant.
You're going to have a low density hot blob sitting right
here surrounded by higher density hotter blobs.
What is this low density hot blob going to do?
Hot air. Hot air rises.
It's going to keep rising. It's going to go up like this,
cooling the entire time until it gets to the surface.
Likewise, imagine a blob that's right here that for
some reason moves downward a little bit,
it heats up a little bit from moving downward but
doesn't heat up as much as the stuff around it.
So suddenly you have something colder than all the material around it.
So what's going to happen? It's going to sink. Cold air sinks.
You're going to suddenly have hot air and cold air moving.
You're going to have the process of convection moving these things
around and you will continue to have hot air rising,
cold air descending until
the entire temperature profile is
equal to this curve that I've drawn here which is called the adiabat.
The adiabat is simply the temperature that a parcel changes as it
moves up and down in pressure just due to something like the ideal gas law.
So even if you had started out as 20,000 degree with
this huge change in temperature very quickly over time,
the internal heat would be removed
very quickly through this convection and you would end up with
a much cooler interior and a curve that looked something like this.
So in general, we're going to assume that the interior of Jupiter is
mostly along an adiabat;
sometimes I'll call that adiabatic.
It is possible that there are places in Jupiter where the temperature drops along at
adiabat and then for some reason the temperature drops even
more slowly and then maybe again along an adiabat.
You're allowed to drop more slowly than adiabat because
here if I have a little parcel of material move upwards,
it suddenly finds itself cold and goes back down again.
This is stable, this was unstable,
and the adiabat is the equilibrium state between the two.
All of this matters because we need to know what the temperature is on the inside.
We need to know what the temperature is on the inside both because
it's part of the equation of hydrostatic equilibrium but also
because the temperature tells us what's
actually going on with the hydrogen that we're assuming makes up
Jupiter and that's because the last piece of the puzzle
that we need is something called a phase diagram.
If you remember, I showed you a phase diagram
for water when we were talking about water on Mars;
this is a phase diagram for hydrogen and here's what you have,
you have pressure on this side,
this is the logarithm of pressure so this is 100, this is 10,000.
This is a million, 10 million bars.
Bar is a nonstandard unit of pressure that everybody uses because
one bar is about one earth atmosphere.
If you really wanted to use the right units in the metric unit MKS unit of pressure is
Pascals and it takes 10^5 Pascals is one bar,
but people who do high pressure stuff like to talk about bars and
megabars and up here 10^9 would be gigabars,
and of course over here we have temperature,
1,000 degrees Kelvin and something close to 100 degrees
Kelvin which is what the temperature is close at the surface of Jupiter.
And what you see on this phase diagram is
what happens to hydrogen at all these different temperatures.
On the earth at a couple hundred degrees Kelvin and 10^0 equals one bar.
What is hydrogen? It's a molecule, H2 molecule.
This region in through here,
if you look very carefully,
is the region where hydrogen prefers to be a molecule.
If you cool it,
you can make liquid hydrogen.
We don't talk much about liquid hydrogen,
we talk about liquid nitrogen,
liquid helium but, at low pressure,
you can have liquid hydrogen.
If you heat it, you no longer have a molecule,
you have a simple hydrogen atom all by itself.
You heat it even more, you ionize that atom and
really you just have a proton and an electron sitting around.
But here's what's interesting that happens.
As you increase the pressure,
well at low temperature as you increase the pressure,
you eventually solidify the hydrogen.
This is interesting though irrelevant;
there's nothing around with temperatures low enough and
pressures high enough to have solid hydrogen,
but here's where the interesting stuff happens.
If you have high temperatures and high pressures,
you cross this line and it's
a dashed line partially because no one quite knows exactly where it goes,
but it goes and moves from molecular hydrogen to this metallic hydrogen.
What is metallic hydrogen?
Well a metal generally is something where you have a crystal lattice of material and
electrons are free to move around on the surface instead
of being bounded to any one molecule or atom.
They just move around on the entire surface.
This is why metals conduct heat like we were just talking about;
the electrons rattle around and this happens to hydrogen.
It's not the same as being ionized where you're just disassociated,
but you are actually a liquid, metallic substance.
This is why we said the interior of Jupiter might have high conductivity and this is why,
as we'll talk about later,
Jupiter has quite a vigorous magnetic field.
OK, With the phase diagram and some idea about
the temperature structure inside Jupiter at
adiabat or perhaps something lower than adiabatic,
we can look at what the phase of the hydrogen
is throughout Jupiter and we get a curve that looks like this.
Regular H2, it's increasing in temperature.
This is the adiabat that it's moving along;
notice a nice straight line in this log-log plot.
Less is known as it gets deeper and as you can see there's a thicker line through here;
that's the uncertainty because nobody quite knows until
this transition as you go down to the center of Jupiter down at
about a megabar transition to the metallic hydrogen and
then the temperature continues to shoot up until you get to something like right here.
So we have an idea already that the structure of Jupiter should be
a molecular hydrogen exterior until
eventually a transition to metallic hydrogen on the inside.
We need to know that because these all have different equations of state and now
we can try to put it all together and do
full up models of what's on the inside of Jupiter.
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