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The explanations for why the Earth's core is hot I found on the internet included:

  • leftover energy from the Earth's formation
  • radioactivity of the elements inside the core
  • friction between the core and the more outer layers which spin more fast

However, I haven't found any indications that would point to the high pressure being a factor. So does the large pressure inside the Earth's core contribute to its high temperature?

EDIT: If it doesn't, I'm interested in why. If pressure is the kinetic energy of the molecules, I'd expect higher pressure to cause higher temperatures, similarly to the ideal gas law

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First off, I'll look at the explanations you have found.

  • leftover energy from the Earth's formation

This is typically split into two parts, the energy from the collisions that formed the Earth, and the energy from the differentiation of the proto-earth into a core, mantle and crust.

  • radioactivity of the elements inside the core

This is highly debated. Geophysicists and geochemists agree to disagree. Geophysicists want a rather high heat flux across the core-mantle boundary because their geodynamo models (which aren't quite perfect) demand it. Geochemists say otherwise. The problem is that the three elements (uranium, thorium, and potassium) that provide four long-lived isotopes are incompatible elements. Moreover, uranium and thorium can be ruled out as sources of core heating due to geoneutrino observations. The neutrinos emitted by potassium decay are not detectible by current technology. Perhaps potassium behaves very differently under very high pressure and temperature.

  • friction between the core and the more outer layers which spin more fast

I'm not sure where you found this. As a general rule, it's the other way around: the core spins faster than the mantle. The mantle and crust are subject to tidal torques from the Moon that is gradually slowing the planet's rotation rate. The vast majority of this slow down results from interactions between ocean tides and the Earth's crust. This in turn makes the mantle rotate ever more slowly, and that in turn makes the core rotate ever more slowly. That said, this is a small contribution.

You missed a key component, which is

  • the formation and growth of the Earth's inner core

A liquid freezing into a solid is an exothermic reaction (a reaction that releases heat). The ongoing formation of the Earth's solid inner core adds heat to the core.

However, I haven't found any indications that would point to the high pressure being a factor. So does the large pressure inside the Earth's core contribute to its high temperature?

No.

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    $\begingroup$ You did a lot of debunking of OP's bad assumptions but you addressed the core question with just a "No". I think it deserves more than that -- Did you look in to whether pressure affects radiant heat transfer? $\endgroup$
    – Spencer
    Commented Jan 18, 2023 at 17:07
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An analogy: does the high pressure at the bottom of the sea rises the water temperature? No, once you pass the thermocline sea water temperature is pretty much constant, no matter the depth. The oceans are at hydrostatic equilibrium, i.e. the vertical pressure gradient pushing the water upward is balanced by gravitational acceleration. The same goes for the whole planet; actually, being at hydrostatic equilibrium is part of the updated definition of a planet adopted by the IAU in 2006 (emphasis mine):

The IAU members gathered at the 2006 General Assembly agreed that a "planet" is defined as a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit.

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Maybe a little, in a way.

I was a bit surprised to find this because the pressure gradient in the mantle actually enhances mantle convection and thus helps remove heat from the Earth.

But in the core?

In 2003, Kanani Lee and Raymond Jeanloz of UC Berkeley, together with Gerd Steinle-Neumann of the University of Bayreuth, found that at high enough pressures, potassium can form an alloy with iron.

This means that during the core differentation process while the Earth was forming, this alloy could have sunk into the core. This would solve the mystery surrounding the relative lack of potassium in the Earth's crust.

Some of the potassium would be potassium-40, one of the longest-lived radioactive isotopes, with a half-life of 1.25 billion years. Although much reduced now, the decay of potassium-40 in the potassium-enriched core would have added heat to the core during the Earth's first couple of billion years.

https://newsarchive.berkeley.edu/news/media/releases/2003/12/10_heat.shtml.

https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2004GL019839

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