Source of heat in the center of Earth

Question

If I read around most of comments and articles on the Internet give two main reasons for the heat found in the depths of our planet :

• Super high pressure at the center of it
• Radioactive decay

I need clarification on both points.

Pressure: while it's pretty clear why pressure and temperature are bound in gas (*) this becomes unclear when matter is in solid or liquid phase. Why pushing on a solid mass would cause its thermal agitation to raise? It looks to me like most of the people takes for granted such point without proper analysis which of course involves more physics than geo-science.

Radioactivity: if I put together radioactive matter it will produce heat by radioactive decay. That's fine. Nevertheless my assumption is that if I take 100kg of any matter here at Earth surface it should contain the same percentage of radioactive isotopes of 100kg of same matter taken from the center of Earth. If this is not the case, then I ask my self why we have higher percentage of radioactive isotopes in the center of Earth rather than in its surface? I've read somewhere that unstable isotopes are heavier and that explains why they accumulated at the center of Earth, just by gravity; but usually radioactive isotopes have just few neutrons more (or actually less!), and that make the element heavier than just 2 or 3 element next to them in the periodic table. For example Carbon-14 is lighter than Oxygen.

Can someone clarify if these two points are valid or not, and why?

(*): even if with volume and mass constant I would say you can augment pressure by increasing temperature and not the other way round as you can't augment pressure under the constraint of having mass and volume constant

Answer 1

depths of our planet

How deep? "Deep" is a relative thing. You can have 10 kilometres deep, or 5000 kilometres deep.

Super high pressure at the center of it

It's not the pressure per se that's causing the heat, it was the process of getting to the pressure when the Earth's formed. Compression creates heat. That's easy to know - just touch a bicycle air pump after filling up. There's also the issue of gravitational potential energy converting into heat once Earth was accreted. The the pressure and heat are together the result of Earth's formation. It's not that pressure itself makes the heat.

Radioactive decay

According to what we know, the three modern heat producing elements (thorium, uranium and potassium) are actually concentrated in the mantle, with an even greater concentration in the crust, which is just the top few kilometres. It's still deep for us humans, but extremely shallow when compared to the core. There is still some debate on this (see the two other answers), but my own personal opinion is that it's safe to say there's very little U Th and K in the core.

Also read my very relevant answer on the World Building website:

https://worldbuilding.stackexchange.com/a/123951/39999

Answer 2

Geophysicists and geochemists agree on some issues, but agree to disagree on others.

Where they agree is that much of the thermal energy in the Earth's core is primordial. A huge amount of heat resulting from the collisions of the myriad objects that collectively formed the Earth. Yet more heat resulted when the early Earth differentiated into an iron-heavy core and a silicon-heavy mantle and crust. The formation of a solid inner core is yet another source of heat upon which geophysicists and geochemists agree.

Where they agree to disagree is that geophysicists want a large heat flux across the core-mantle boundary so as to explain the existence of the Earth's magnetic field (and to differentiate the Earth from Venus and Mars, which don't have a persistent dipole magnetic field). There is no viable source for such a large heat flux in the eyes of geochemists. Radioactive decay has been conjectured as a source of this heat.

The problem with this conjecture is that the four long-lived isotopes appear to be chemically incompatible with sinking into the core. It's the other way around. They rise to the surface. Those four isotopes are isotopes of three elements, uranium, thorium, and potassium, each of which is chemically active and each of which is an incompatible element. This makes these elements more concentrated in the Earth's crust than in the mantle, and more concentrated in the mantle than in the core. The one exception might be potassium. Some studies show that potassium might change from a lithophile ("rock loving") incompatible element to a sidereophile ("iron loving") element at high temperature and pressure. Other studies don't show this. So once again, we're at the agree to disagree stage.

The agree to disagree stage is what makes science "science".

Answer 3

"Why pushing on a solid mass would cause its thermal agitation to raise?"

It doesn't.: Earth's interior heat ratio between pressure and atomic decay

"why we have higher percentage of radioactive isotopes in the center of Earth rather than in its surface?"

We don't know how exactly radioactive isotopes are distributed in the earth. Radiogenic heat in the core may be insignificant, also because the elements responsible for radiogenic heat are found rather in the Earth's bulk (mantle and eve more so crust) than in the core (Lithophile elements). The core is mainly kept hot by primordial heat, sotosay left over heat from the release of gravitational energy during accretion and differentiation, tidal heating may also have a small part in it. What is the total Earth's interior energy budget?

Mantle and crust store the most of earth's heat and host most of the radioactive isotopes that generate heat, specifically the crust. There's also this reasonable looking Wikipedia article.