4 ms·

Heat passes from the Earth's core through the mantle to the crust at 45 TW. That heat can be converted to usable energy (aka exergy) at 70% efficiency. So glo

Heat passes from the Earth's core through the mantle to the crust at 45 TW. That heat can be converted to usable energy (aka exergy) at 70% efficiency. So global geo-thermal energy production is limited to 32 TW. A given geo-thermal plant slowly cools the rock below it and produces less and less energy until it reaches equilibrium with the flow of heat energy into the rock it draws from. See page 20 of https://gcep.stanford.edu/pdfs/DyUMPHW1jsSmjoZfm2XEqg/1.3-Hermann.pdf https://gcep.stanford.edu/pdfs/DyUMPHW1jsSmjoZfm2XEqg/1.3-He... And https://gcep.stanford.edu/research/exergy/resourcechart.html https://gcep.stanford.edu/research/exergy/resourcechart.html Nuclear decay and fission produce 30 TW in the earth's core and 45 TW flow out to the crust, so the earth's core is gradually cooling. The core contains 1e31 J of energy and is currently cooling down at a rate of 15 TW = 1.5e13 W. A Joule is 1 Watt-second. Therefore the earth's core will take longer than 30 billion years (1e18 seconds) to cool down. See https://en.wikipedia.org/wiki/Geothermal_energy#Renewability_and_sustainability https://en.wikipedia.org/wiki/Geothermal_energy#Renewability... And https://en.wikipedia.org/wiki/Newton%27s_law_of_cooling https://en.wikipedia.org/wiki/Newton%27s_law_of_cooling

programmer_dude 9y ago
> The core contains 1e31 J of energy What does that mean? Does it mean the core temp will drop to zero degree kelvin when 1e31 J is removed from it? Can we realistically bring the core temp down to absolute zero? I think you need a temperature difference between a "source" (here earth's core) and a "sink" (here surface of the earth (radiation), atmosphere (convection)) to drive any engine. So geothermal energy stops being useful when this difference is zero or less?
- AnkhMorporkian 9y ago
  No, definitely not. It would reach the temperature of the other side of the heatsink, and since that's 30 billion years, the Earth will be long, long, LONG gone by then. Even if the sun doesn't engulf the earth, the lowest it could get would be the temperature of the CMB, which is about 3K. Granted, over a couple trillion years, that number would lower. Reaching absolute zero is pretty much one of the only few things that physicists consider impossible, along with exceeding light speed.
- deleted 9y ago
  [deleted]
QAPereo 9y ago
It’s worth noting that Earth will have been roasted to a cinder by the expanding layers of Sol’s atmosphere many billions of years before that, just for a sense of scale.

programmer_dude 9y ago

> The core contains 1e31 J of energy What does that mean? Does it mean the core temp will drop to zero degree kelvin when 1e31 J is removed from it? Can we realistically bring the core temp down to absolute zero? I think you need a temperature difference between a "source" (here earth's core) and a "sink" (here surface of the earth (radiation), atmosphere (convection)) to drive any engine. So geothermal energy stops being useful when this difference is zero or less?

AnkhMorporkian 9y ago
No, definitely not. It would reach the temperature of the other side of the heatsink, and since that's 30 billion years, the Earth will be long, long, LONG gone by then. Even if the sun doesn't engulf the earth, the lowest it could get would be the temperature of the CMB, which is about 3K. Granted, over a couple trillion years, that number would lower. Reaching absolute zero is pretty much one of the only few things that physicists consider impossible, along with exceeding light speed.
deleted 9y ago
[deleted]

QAPereo 9y ago

It’s worth noting that Earth will have been roasted to a cinder by the expanding layers of Sol’s atmosphere many billions of years before that, just for a sense of scale.