Why hasn't the earth cooled down by now?

[exchemist]

9 hours ago, sethoflagos said:

 

A bit after the lord mayor's show,. However ...

While thermal expansion must play some part in mantle convection, it seems that the primary driver is phase change (ref: https://authors.library.caltech.edu/25038/145/Chapter 5. The eclogite engine.pdf). This implies that most of the transported energy is locked up in the enthalpies of various sequences of crystal structural readjustments with depth (eg the olivine-wadsleyite-ringwoodite-perovskite sequence) rather than as thermal energy. 

Hence there is within the mantle a huge reservoir of energy bound up in high pressure mineral polymorphs, that may be released as heat at specific lower pressure locations (mid-ocean ridges. volcanic island arcs etc) moreorless independently of the overall thermal gradient. This localised heat release drives the processes of crustal magmatic fractionation, adding low density granitic material to the continents, and consequently increasing the density of the returning subduction slab.

The excess of gravitational potential energy of this continental scale mass of dense material over and above the surrounding asthenosphere represents a second huge reserve of energy that is partially returned as heat back to the base of the mantle, but is mainly consumed in restoring the high pressure polymorphs of its constituent mineralogy.

Overall, the process of continent building via magmatic convection and fractionation might be approximated as raising 3 billion km3 of granite (SG ~2.5) through 1,000 km of mantle (SG ~ 4) which looks like 4.5 x 10^28 Joules over a period of 4.5 billion years resulting in a heat output of 0.3 TW purely on isostatic considerations.

Contrast this with the estimated total crustal heat flow of 47+/-2 TW (based on 38,000 measurements).

If we were to consider the approach toward gravitational equilibrium of all structures within the earth (not just the surface ones), then the process of planetary differentiation (ref: https://en.wikipedia.org/wiki/Planetary_differentiation) would seem to amount to an appreciable percentage of the total. And that's based only on the isostatic aspect. We are as yet nowhere near full planetary chemical equilibrium either, and that must also factor into the balance sheet.  

I've seen figures of ~20 TW given for the heat produced by radioactive decay, and can only add the comment that it seems credible.

More critically some authors have ascribed the balance to 'primordial heat'. I don't quite know what they mean by that. Or rather, I do. It's the heat generated during the initial accretionary growth of the planet, the sum total of initial gravitational potential energy of all its constituent parts and released as heat on impact. But isn't this just the initial phase of planetary differentiation? The phase where space was gravitationally displaced by matter? And has it been sat around doing nothing since? I think not. Rather its being doing what heat does - driving convection currents and fuelling endothermic reactions for the last 4.5 billion years. 

Seen in this light, I'm tending to lean towards there being an approximate balance between radiogenic heating and the nett release of gravitational and chemical potential energy arising from planetary differentiation.   

 

Yes, undoubtedly it seems likely that phase changes play a big role, both due to latent heat effects and changes in specific volume/density.