731
checkmate, big geology!!
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Maybe not geothermal per se, but something would be possible, with unlimited budget and resources.
Though the problem is just how MUCH energy volcanos have. Heat content is A LOT of energy. The vast (on a human scale) magma chambers contain an insane amount of energy. Rock has a heat capacity less than water by weight, but rocks weigh a lot more than water and can get a lot hotter.
So, it'd have to take away a TON of heat, likely more than humans use in a year for a single small eruption, but I'm too lazy to do the math right now...
Also, many eruptions are fueled by pressure from dissolved gasses in the magma. That pressure will stay present until the magma cools enough to resist it itself, which could require dropping an entire underground lake of lava by hundreds of degrees.
Then there are undoubtedly some eruptions that are driven by tectonics, meteor impacts, and other physical pressures that might not be manageable via heat control at all.
Rad. That's probably a level of energy harvesting between fusion and Dyson sphere.