I wonder, if we draw enough heat out... would the core cool enough to shrink? And if so, would the crust collapse to the new size?
Pure speculation of course, but did the first guy burning coal know the outcome?
Anyhow, I love geothermal, think you're right, but just got tweaked on the word "infinite".
Q = m c ΔT
m = mass of the crust (roughly 10^22 kg)
C = specific heat of crust (roughly 1000 J/kg·K)
ΔT = 1 K
Q = 10^25 joules would be needed to lower the earths crust by 1 degree K
About 10,000 years worth of today’s human energy consumption
We know how weather works quite well, but knowing if it will rain in a week is an entirely different beast.
My memory is that the calculation found that if humanity switched to geothermal for all its energy needs, then in only about 1000 years, the core cools enough for the magnetic field to stop, but I am not sure.
(We should definitely deploy geothermal in the Yellowstone caldera though long enough to cool it down enough so that it will not erupt again.)
Humanity could max out geothermal for a million years and never make a dent.
Even at million+ year timescales, I can’t see any way the temperature of the upper crust could matter to the core at all - even if the crust was at absolute zero.
Dirt insulates relatively well, and the amount of thermal mass present is mindboggling.
Kind of joking: unless there are nonlinear effects near 300K? Fig 4 [1] seems to suggest that the thermal diffusivity of the mantle grows very fast as temperature declines past 300K... but the data stop at 200K.
Reason for initial comment: we could probably set up a spherical heat equation to guess how crust cooling would change heat conduction at the outer core. But I have absolutely no idea how to reason about changes in heat conduction affecting the convection dynamics that generate the field. I was silently hoping for one of the domain experts lurking this forum to see it and share wisdom. (But overall it was a silly question, I know).
[1] https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/200...
(1GW of solar PV is deployed every 15 hours globally as of this comment)
It'd take multiple orders of magnitude more impact from humanity for us to actually affect the core, no?
Pro-geothermal position: https://www.caltech.edu/about/news/producing-clean-energy-ca...
Anti-geothermal position: https://news.stanford.edu/stories/2019/05/lessons-south-kore...
My conclusion: Geothermal makes research into plate tectonics and earthquake mitigation considerably more valuable, so we can figure out how to do it in a way that reduces earthquakes rather than creating them.