What if Earth's core suddenly was heated to 1 000 000 kelvins?

[raxo2222]

Lets say most central part - 100 km - of Earth core was heated up by magic.

What happens to rest of Earth?

Do Earth's surface eventually melt?

Do 15 - Richter magnitude earthquakes happen everywhere?

 

 

I miss XKCD's whatif... shame they stopped coming regularly...

[peadar1987]

The iron that makes up the core vaporises, and blows the earth into smithereens. I don't know the specific heat capacity of gaseous iron, but the gravitational binding energy of the earth is about 2*10³²J, so if it's above 100 J/kgK, and it almost certainly is, it will blow it to pieces so completely that it won't recoalesce. Most of it will probably be blown completely out of the solar system.

As for us on the surface, the shock wave would propagate at the speed of sound, which, in the mantle, is about 5-8km/s. The mantle is about 2900km thick, so you'd have a good 6-10 minutes to say goodbye to everyone before you were obliterated into a rapidly-expanding cloud of plasma

[cubinator]

5 hours ago, raxo2222 said:

I miss XKCD's whatif... shame they stopped coming regularly...

I think they come as often as people ask for them...use the "Submit a question" button at the bottom of the page to...well, submit a question.

[cantab]

So only the innermost 100 km radius. The density (pre-heating) is about 13000 kg/m³ and it's basically solid iron with a specific heat capacity of about 0.4 kJ/kgK . Heating it to a million Kelvin pops out at around 10²⁸ Joules of energy. That's a lot - it's equivalent to several thousand years of solar energy received - but nowhere near enough to blow the Earth apart.

So what will happen to it? Well we can discount heat conducting outwards, that process is very slow even with a million K on one side. And though the temperatures are hot, I don't think they're hot enough for significant iron fusion to occur. So the most prominent effect is probably the shock/pressure wave expanding outwards.

If we treat it as an earthquake, then the upper limit is about magnitude 13, which is a million times more powerful than any normal earthquake in history. But then it's also a thousand times deeper than most earthquakes. I'm inclined to think the effects would balance out, and the surface shaking would be strong but not vastly stronger than what normal quakes can cause. However, it would be strong shaking everywhere.

The effects on human civilization could be devastating, but the effects on natural ecosystems would probably be not so much.

[StupidAndy]

try using US2

ill boot it up and send you pictures if i can

• find out how to take them
• find out how to post them, i tried to make a KSP meme thing for the forum game, but it didn't have a HTML thingy

ill send you pics if i can figure out how to do that

EDIT: i dont need to boot it up, after about 5000*K it either turns to a burning gas giant, or just a blur of blue light

EDIT 2: they have a sim for it, it just turns to gaseous everything

Edited November 25, 2016 by StupidAndy

[YNM]

AFAIK Universe Sandbox only model whole/surface temp, it never models heat transfer.

I suppose one would need to solve the energy transport equation to see what kind of heat transfer is sufficient. Will it be conduction (or rather, radiation), or convection, or some explosion...

https://en.m.wikipedia.org/wiki/Stellar_structure

*yes I know this says stellar but it can be used for almost everything.

[kerbiloid]

Given: inner 100 km of the Earth warmed up to 1 000 000 K.

Mostly iron (56Fe), with density (wiki) ~14 000 kg/m3.

1 MK means total ionization. But no fusion reactions are possible with Fe unless it's a supernova.
So we have a mix of two gases: Fe ions (nuclei) (molar mass ~ 56*10^-3 kg/mol) and electrons.

Electron mass = 9.11·10⁻³¹ kg, so molar mass = 9.11·10⁻³¹ * 6.022*10²³ ~= 5.5*10^-7 kg/mol
We have 26 electrons per 1 Fe ion, so 26 mols of electrons per 1 mol of Fe.
Density = 26 * 9.1*10^-31 / 56*10^-3 * 14000 = 6*10^-24 kg/m3

At a first approximation we can presume that both are monoatomic ideal gases.

Volume = (4/3) * pi * R³ = 4.2*10¹⁵ m3.
Total mass of Fe = 4.2*10¹⁵ * 14000 = 5.9*10¹⁹ kg.
Total mass of electrons = 4.2*10¹⁵ * 6*10^-24 = 2.52*10^-8 kg.

pV = (3/2)mass * R * T/molar_mass

pVFe ~= (3/2) * 5.9*10¹⁹ * 8.31441 * 1*10⁶ / 56*10^-3 ~= 1.3*10²⁸ J.

pVe ~= (3/2) * 2.52*10^-8 * 8.31441 * 1*10⁶ / 5.5*10^-7 ~= 1*10⁶ J.

So, we can estimate total mechanical energy that can be converted into job: 1.3*10²⁸ J.

The Earth total mass is 6*1024 kg, so this will release 1.3*10²⁸/(6*10²⁴) ~= 2 kJ/kg what corresponds to kinetic energy of ~60 m/s.
Earth as planet will stay at place, but its surface will lift and fall for hundred meters up and down.

A rough formula for the earthquake energy (from wiki):
magnitude = (2/3) (lg E - 4.8) = (2/3) * (lg(1.3*10²⁸) - 4.8) = 15.5

Of course, the magnetosphere will be disturbed (as the liquid core would be put in chaos), which would cause magnetic storms and weaken the protection shield.

_{Now you can see that you really need this certificate of insurance including such cases as the Earth inner core boil-up.
If you will find a cheaper one, we pay the difference.}

 

[p1t1o]

9 hours ago, cantab said:

I don't think they're hot enough for significant iron fusion to occur.

Hot enough, but definitely not a high enough pressure, besides, if iron fusion did occur, it would *cool* the explosion, not contribute to it.

9 hours ago, cantab said:

So only the innermost 100 km radius. The density (pre-heating) is about 13000 kg/m³ and it's basically solid iron with a specific heat capacity of about 0.4 kJ/kgK . Heating it to a million Kelvin pops out at around 10²⁸ Joules of energy. That's a lot - it's equivalent to several thousand years of solar energy received - but nowhere near enough to blow the Earth apart.

Its not enough to blow it apart so that it doesnt re-coalesce back into a planet (*complete* destruction is defined as putting all of earths mass into an escape trajectory), but it will almost certainly convert it into a random mish-mash of rubble, after expanding some and re-contracting.

[peadar1987]

17 hours ago, peadar1987 said:

The iron that makes up the core vaporises, and blows the earth into smithereens. I don't know the specific heat capacity of gaseous iron, but the gravitational binding energy of the earth is about 2*10³²J, so if it's above 100 J/kgK, and it almost certainly is, it will blow it to pieces so completely that it won't recoalesce. Most of it will probably be blown completely out of the solar system.

As for us on the surface, the shock wave would propagate at the speed of sound, which, in the mantle, is about 5-8km/s. The mantle is about 2900km thick, so you'd have a good 6-10 minutes to say goodbye to everyone before you were obliterated into a rapidly-expanding cloud of plasma

Edit: My mistake, I thought we were talking about the whole core, not just the innermost 100km