Edit: how does the size of the earth matter? The molten core is the (nuclear?) energy source. If you have done the math please share your work.
See page 20 of https://gcep.stanford.edu/pdfs/DyUMPHW1jsSmjoZfm2XEqg/1.3-He...
And 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...
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?
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.
I was curious, though, so I did the math. My very rough calculations, which are a huge underestimate, say that it would take over 900,000 years at current total human energy use to change the Earth's internal temperature a single degree. https://gist.github.com/kkremitzki/b7d0aa6ee8ed75e0c2afd8c07...
That is: the lower the cost of a thing, the greater the induced demand, and hence, the greater to total use.
William Stanley Jevons, an engineer and economist, first observed this concerning coal, in the 1860s.
You'll find this expressed in Jevons' preface to the 2nd edition of his book:
A further class of opponents feel the growing power of coal, but repose upon the notion that economy in its use will rescue us. If coal become twice as dear as it is, but our engines are made to produce twice as much result with the same coal, the cost of steam-power will remain as before. These opponents, however, overlook two prime points of the subject. They forget that economy of fuel lead to a great increase of consumption, as shown in the chapter on the subject; and, secondly, they forget that other nations can use improved engines as well as ourselves, so that our comparative position will not be much improved.
https://archive.org/stream/coalquestioninqu00jevo#page/n37/m...
Or something. I mean it's such a phenomenal timescale that it's almost pointless to speculate.
I’m not sure what the math for the energy harvesting method described in this thread ends up being exactly like, but it seems that in order for it to have an effect you’d need to have something like every human consuming, on average, as much energy as all of humanity currently consumes. That starts stretching the imagination.
The entire Earth's crust makes up less than 1% of the Earth's volume. The Earth's mantle makes up about 84%.
”In 1919, David White, chief geologist of the United States Geological Survey, wrote of US petroleum: "... the peak of production will soon be passed, possibly within 3 years."”
The abstract of White’s paper (and its paywalled conten) are at http://papers.sae.org/190011/. It says:
”American oil companies must protect the future by acquiring great and widespread foreign oil concessions.”
Is that prescient or did it drive policy?
It also says:
”Oil in vast amounts can be artificially made from the great oil-shale deposits of the West, but the processes and prices necessary to commercial success remain to be determined, and the task of building up an oil-shale industry sufficient to meet a considerable part of the demand is enormous, requiring several years.”
TLDR: The earth's core contains enough energy that (if 100% extracted) could power modern-day civilisation for 100 billion years. If we increased global power production 10 times and extracted all that from the core it would not have an effect before the sun dies in approximately 5 billion years time.
There’s no equivalent to that for geothermal power. The energy you extract is the energy that’s lost, and that’s it.
The Earth's crust is less than 1% of the Earth's volume. The mantle is 84%.
Anyway, you did raise a good question, althoug focused on the core.
I have a similar concern with the immediate extraction. We know that there is plenty of water underground we can relie on for many years - critical for drought seasons, but underground overuse (or called ungerground depletion) can lead to a number of environmental problems such as land subsidence.
The extraction must be done at a reasonable depth below the surface, but what is the rate of the heat influx reaching this depth? Would we deplete this energy before wr can replenish? Is this even a concern?
Furthermote, if you look at Wikipedia, there are a number of environment concerns. Although pollution is far less than what is generated by burning fossil fuel, nonetheless, careful design and location are required.
Because we are but a mote of dust in a tiny span of time. The earth has such a tremendous amount of volume that it's impossible for us to change it any significant amount. Look at global warming, We've been dumping gigatons of CO2 into the atmosphere every year for the last century. Even with all of the immensity of human activity we've changed the temperature of the atmosphere by less than a degree. Even that tiny temperature change from global warming is pretty much entirely from the release of CO2 and other greenhouse gasses and not the release of energy. The atmosphere is also just a tiny thin wisp of a shell around the planet. The amount of thermal energy we could ever hope to extract from the planet is too small to be considered a rounding error.