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Earth's core is hot because of the sustained nuclear reactions that happen there. It is constantly producing and dissipating heat, it is not a reserve, like oil.
Geothermal energy is renewable on the same sense that solar is renewable.
While, today, such a statement is taken as true, similar statements were made about oil and CO2 in the air in the past.
I and any future generations I might know personally will not have to worry about the cooling of the core of the earth. I'd even be willing to bet that moving the heat from the Earth core into the atmosphere would be a bigger issue.
But as soon as you start removing the heat, you start cooling the rock... So you can say that there is a "reserve" of heat in a certain "field". I would say, geothermal energy is renewable on the same sense that abiotic oil is renewable 8O).
Solar, on the other hand, does not have that behaviour. Behind each photon there is another one, and the flow is exactly the same if you take 0% or 100% of them.
BTW, minor nitpicking, Iceland is not in the European Union (nor was in the European Common Market).
Although there have been suggestions to the contrary, the uranium whose fission provides the thermal in geothermal is not in the core but rather distributed in the crust.
Yes, geothermal is renewable (until the U and other unstable isotopes are gone), but the unfortunate timescale (see low heat flux stated above) means that what one is doing is actually mining stored heat. Yes, there is a lot of it (and in certain places it is rather close to the surface), but the very reason that the heat is stored at depth (low thermal conductivity of the rock) also means that harvesting the heat at an economical rate is a challenge. And if you solve that problem (perhaps using e.g. horizontal drilling), then you will nevertheless deplete the heat--you are limited by the thermal conductivity of the rock. Eventually, you will need to drill again elsewhere.
Actually, experience in the Geysers field in California shows you need to drill again rather quickly, owing to low heat conductivity of rock. Over human timescales, geothermal is definitely depletable, but you can compensate by constantly developing adjacent areas. This continual drilling has to be allowed for in your cost estimates, of course.
There's one other thing which has been done that's a bit odd at the Geysers: they're pumping (treated) sewage into the geothermal field to compensate for steam depletion. It regularly causes small earthquakes as the water vaporizes in steam explosions underground.
More at http://arxiv.org/PS_cache/hep-ph/pdf/0501/0501111v2.pdf .
Also, the heat it produces, it produces 99.999+ percent by alpha decay, not fission.
--- G. R. L. Cowan, former hydrogen-energy fan
http://www.eagle.ca/~gcowan/Paper_for_11th_CHC.html :
oxygen expands around boron fire, car goes