LEEVENSPARK

The Earth started its existence as a red-hot rock, and has been cooling ever since. It’s still quite toasty in the core, and will remain so for billions of years, yet. Cooling implies a flow of heat, and where heat flows, the possibility exists of capturing useful energy. Geysers and volcanoes are obvious manifestations of geothermal energy, but what role can it play toward satisfying our current global demand? Following the recent theme of Do the Math, we will put geothermal in one of three boxes labeled abundant, potent, or niche (puny). Have any guesses? The Physics of Heat Thermal energy is surprisingly hefty. Consider that putting a room-temperature rock into boiling water transfers to it an equivalent amount of energy as would hurling it to a super-sonic speed! We characterize the amount of heat an object can hold by its  specific heat capacity , in Joules per kilogram per degree Celsius (or Kelvin, since one degree of change is the same in either system). Tying some energy conc

With the exception of tidal energy, our focus thus far has been on land-based energy sources. Meanwhile, the ocean absorbs a prodigious fraction of the Sun’s incident energy, creating thermal gradients, currents, and waves whipped up by winds. Let’s put some scales on the energetics of these sources and see if we may turn to them for help. We’ve got our three boxes ready: abundant, potent, and niche (puny). Time to do some sorting! Thermal Gradients Wherever there is a thermal gradient, our eyes light up because we can create a  heat flow across the gradient and capture some fraction of the energy flow to do useful work. This is called a  heat engine , the efficiency of which is capped by the theoretical maximum ( T h  −  T c )/ T h , where “h” and “c” subscripts refer to absolute temperatures of the hot and cold reservoirs, respectively. In the ocean, we are rather limited in how much gradient is available. The surface does not tend to exceed 30°C (303 K), while the depths cannot get