There’s a little bit of buzz burbling around over Al Gore’s scientific goof during a Conan O’Brien interview. Discussing geothermal energy, he said the following:
It definitely is, and it’s a relatively new one. People think about geothermal energy — when they think about it at all — in terms of the hot water bubbling up in some places, but two kilometers or so down in most places there are these incredibly hot rocks, ’cause the interior of the earth is extremely hot, several million degrees, and the crust of the earth is hot …
Of course the interior of the earth is extremely hot, but not that hot. It’s several thousand degrees rather than several million. If the earth were several million degrees it would be a rapidly diffusing cloud of metallic vapor. Even the center of the sun is only perhaps 13 million degrees C.
But I’ll let him slide; pretty much everyone blanks out from time to time. And it gives us a chance to do a little thinking about just how much thermal energy is in the earth.
First of all, just because something is hot doesn’t mean you can squeeze energy out of it. You can only squeeze energy out of temperature gradients – you need something hot and something cold. This is why we can’t just set up a temperature-to-energy machine in the desert and have free energy. In your car, for instance, you need both the heat of the burning gasoline and the much cooler ambient temperature from the outside air via your radiator to turn the hot gasoline vapors into forward progress. Power plants frequently have large cooling towers for that very reason. It’s not the energy of the hot substance, it’s the process of moving that heat to a cooler place that creates useful work. Think of it in the same way as water flowing downhill can turn a paddlewheel – it won’t work unless the water starts off high and ends up low.
But that’s not a problem here. The interior of the earth is hot and the exterior is much colder. The difference in temperature is such that the efficiency of heat-to-work conversion could be near 100% in theory, though in practice it would be much lower. And we’re not likely to run out of geothermal heat any time soon. As a slightly wild Fermi calculation, assume that the earth is uniformly iron at 3000 C. The specific heat of liquid iron is about 611 J/kg K, so cooling the earth to room temperature this yields about 1.8 million joules of energy per kilogram. Multiply by the mass of the earth, and the total energy content might be in the neighborhood of 10^31 joules. The total energy consumption of the world’s human population is in the vicinity of 5e20 joules per year.
Divide out, the earth’s geothermal energy could support that consumption rate for about 21 billion years. We’re not likely to use it up.
So why isn’t it in widespread use? After all, every nation has domestic access to it – all you have to do is drill straight down. The main problem is that the temperature really doesn’t start getting ramped up until dozens of miles down. Drilling a hole that deep and pumping water (or whatever) down and up is technically unfeasible. Geothermal is at its best at those places which are close to geological activity that brings the heat closer to the surface. Volcanic and other geologically active locations often do very well with geothermal power. Iceland in particular produces vast quantities of usable energy from the internal heat of the earth. Most other places are much farther from the hot regions of the earth’s interior and geothermal is correspondingly much more difficult to get.
Sadly Al Gore’s hopes for geothermal as a major clean energy technology are probably futile until deep drilling develops into a much more mature form. It would be nice if that happened; the energy to be tapped is pretty close to inexhaustible.