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If the pressure of the Earth is keeping the inner core solid, keeping it rigid to take up the least space, and temperature is dependent on how much the atoms are moving, why isn’t the inner core cold? If the pressure is so high that it’s forcing the inner core to be solid then the atoms can’t move around and thus they can’t have temperature.

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    $\begingroup$ My understanding from reading the title, and the apparent understanding of several of the people answering, is that you're asking where the heat of the core came from, but reading your question, you seem to be asking why the pressure doesn't cause a loss of temperature. Perhaps you should edit the title and question to clarify. $\endgroup$ – Acccumulation Feb 14 at 4:20
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Your argument would require that all solids must be cold, because all solids have constituent atoms that are constrained to remain in their solid lattice positions. But clearly not all solids are cold, so there is something wrong with your argument. That thing is that atoms or molecules constrained within a solid structure can still vibrate and oscillate around their equilibrium positions. So they do have an internal energy and this is where the heat is stored.

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    $\begingroup$ Yep. That said, compressing it does still have an important effect: it permits the core to remain solid, even despite the temperature being around 5700 K, when iron would melt under normal conditions (100 kPa outside pressure, vs. the approx. $3 \times 10^8$ kPa at the Earth's core) at only 1811 K - indeed, vaporize at 3134 K. You might say that, in a sense, it lets the iron act "colder" despite not actually making it colder because, while the atoms are still vibrating very fast, they are prevented from getting away from each other by the compressing forces. $\endgroup$ – The_Sympathizer Feb 12 at 4:48
  • $\begingroup$ @The_Sympathizer Maybe that's how the Death Star blew up planets - it only had to vaporize a large hole into the planet's mantle, and the escaping pressurized material from the core & mantle did the rest. $\endgroup$ – RobertF Feb 13 at 17:14
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    $\begingroup$ @RobertF, The enormous pressure deep within the Earth is due to the weight of everything above. In other words, the Earth is held together by gravity. If you made a big hole through Earth's surface all the way down to the mantle, there might be a brief (geologically speaking) interval of time during which some stuff from the surface and some stuff from deeper down would trade places (i.e., you might create a supervolcano), but it all still would hold together in a roughly spherical shape because of its gravity. $\endgroup$ – Solomon Slow Feb 13 at 18:24
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Your association of temperature with "how much the atoms are moving" is fine as rough description, but it can't really be used as-is as an an accurate, quantitative definition of temperature. Even if a solid is under high pressure, it can also be at high temperature. It's true that the amplitude of the atomic vibrations of the high-pressure, high-temperature solid may not be as large as the atomic vibrations of the same solid material at zero pressure and at the same high temperature, but there is no suppression of the absolute temperature because of high pressures.

Having said that, there is a special sense in which one may be able to say that the solid at some high pressure and temperature is at a "lower effective temperature" than the same solid at zero pressure and the same temperature due to the smaller atomic vibrations of the high pressure solid. There is a term called the "homologous temperature" of a material, which is the temperature of the material (in Kelvin) divided by it's melting temperature (in Kelvin), or in other words the material's temperature relative to its melting temperature. According to the Lindemann melting criterion, many crystalline solids melt when the average amplitude of their thermal vibrations reaches a certain fraction (typically 0.15 to 0.3) of their interatomic spacing. So by applying high pressures to a solid at a fixed temperature one can indeed often reduce the homologous temperature of a solid (but not its absolute temperature) due to the suppression of its atomic vibrations and the raising of its melting temperature. In fact, note that the temperature of the Earth's iron solid inner core is estimated to be around 5430 ˚C which means that the melting temperature of iron has been pushed to temperatures above 5430 ˚C due to high pressure. In contrast, the zero pressure melting temperature of iron is much lower at 1538 ˚C.

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The core is hot because of radioactive decay. If the pressure applied to a liquid like molten iron is great enough, it will get squeezed into a solid, even though it is tremendously hot. This is why the center of the earth's iron core is a solid. If that tremendous pressure were released, the iron would immediately melt to a liquid (and probably explode into iron vapor right afterwards).

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    $\begingroup$ @F16Falcon - do you mean on the surface? I don't think that's quite right; see this. $\endgroup$ – Filip Milovanović Feb 11 at 7:27
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    $\begingroup$ @F16Falcon if it were so, we wouldn't observe polar ice caps and very hot equatorial regions, as wouldn't we have any seasons. $\endgroup$ – Ruslan Feb 11 at 8:25
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    $\begingroup$ Aren't core mostly hot because when Earth was formed all that kinetic energy of dust and asteroids was converted into temperature? And cooling down takes a lot of time because of good insulation? Radioactive decay is only a small part of it if I remeber correctly. $\endgroup$ – user11153 Feb 11 at 9:22
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    $\begingroup$ That the Earth's core is hot because of radioactive decay is a widely repeated misconception. The four long-lived (but not too long-lived) isotopes are isotopes of three elements, potassium, thorium, and uranium, all of which are highly incompatible with being in the Earth's core. See, for example, In the earth's crust, why is there far more uranium than gold? $\endgroup$ – David Hammen Feb 11 at 12:49
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    $\begingroup$ @DavidHammen wrote "That the Earth's core is hot because of radioactive decay is a widely repeated misconception." - Woa! Wait a minute here. I've seen this fact stated in the scientific literature and in fact I recently had a short discussion with a professor of geology at an Ivy League university who referred to potassium-40 as an important isotope responsible for generating heat in the Earth's interior. I think that you need to provide some links to peer-reviewed scientific literature backing up your claim that the Earth's core and interior are not hot largely because of radioactive decay. $\endgroup$ – user93237 Feb 11 at 14:45
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I'll answer by analogy with a spring:

  • Temperature <=> Energy in vibration of spring
  • Pressure <=> Compression of spring
  • Phase state (solid or liquid) <=> Movement of the spring

Temperature is basically the energy of the moving particles.

If you take our analogous spring and have no weight on it (no pressure) it can bounce around with great movement as a liquid would. By virtue of the momentum of how fast the spring can travel in this state, it has high "temperature".

If you put a heavy weight on it (and thus apply pressure), the force from the spring becomes very high (with the same amount of energy), but obviously the distance it covers is a lot less. The energy in the spring is the same (equivalent to being the same temperature but in a solid state).

End analogy, the spring can have the same amount of energy in it's vibration, but one case can be constrained by weight (high force, low movement) and is free (low force, high movement).

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For two main reasons:

  • The formation of the earth was approximately an adiabatic process, and adiabatic compression increases temperature. The energy that wasn't stored in chemical bonds or radiated away didn't just disappear. It's still there, in the form of atomic-scale motion. Instead of having Brownian motion like gas molecules, the atoms in the earth's core are wiggling around within a tiny space. But it's still motion.

  • Radioactive decay releases energetic particles that bounce off of the other atoms, adding to the total amount of bouncing.

Think about what happens when a billion perfectly elastic balls zipping in every direction through space are all pulled in toward their shared center of mass. They'll start bouncing off of each other; the closer they are together, the more frequently they bounce. At the center, they're so close together that they can't move past each other, but they're still bouncing extremely rapidly within their "pockets". Meanwhile, some of the balls are shooting out little bullets that then bounce around between the balls.

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Temperature is more like the vibration of an atom. That has nothing to do with how much it can move around in a liquid.

The gravitational pressure makes the core hot in the first place. The atoms are pushed so close to each other that they rub on each other.

EDIT: Ok as commenters have pointed out 50% of the earth cores heat is left over from the gravitational forces during earths formation and the other half due to radioactive decay.

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    $\begingroup$ It's not gravitational pressure that makes the earth hot. Things under pressure can still be cold. The Earth's interior is hot mainly due to radioactivity. $\endgroup$ – dA-Ve Feb 11 at 2:19
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    $\begingroup$ This suggests that it's about 50/50. Also the radioactive decay would probably be lower if the stuff were further apart. en.wikipedia.org/wiki/Earth%27s_internal_heat_budget $\endgroup$ – Paul McCarthy Feb 11 at 11:58
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    $\begingroup$ The Earth's core is hot because of the input of gravitational and latent energy inputs when it was formed, combined with subsequent impacts, radioactive decay, insulation, and possibly even fusion. The current pressure does not provide any energy to the equation except for possibly allowing for fusion reactions (although it does help to turn kinetic energy in to thermal energy through increased friction). Source $\endgroup$ – johnDanger Feb 11 at 17:08
  • $\begingroup$ There's still a lot of space between atoms, even at the Earth's core. A sphere that is one meter across (100 cm across) at the Earth's surface would be compressed to a sphere 84.4 cm across at the very center of the Earth. A whole lot more compression is possible. The theoretical maximum for a pure iron "planet" is an object whose mass is a bit over one solar mass. With the extreme pressure that results from that much mass, my one meter sphere would get compressed to less than a couple of millimeters across. $\endgroup$ – David Hammen Feb 11 at 17:17
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Even assuming a model where temperature is only average kinetic energy of atoms and molecules, lowering the amplitude of average displacement doesn't imply decreasing temperature.

If we have $N$ gas molecules in a box at a given temperature, and replace it by $M$ smaller boxes, equaly dividing the particles, there is no reason to think the temperature will change. But their amplitude of displacement decreased.

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