9: Geothermal Power

The Earth’s interior is hot – incredibly hot! According to estimates made by learned scientists, the temperature at the Earth’s center is roughly the same as at the Sun’s surface, nearly 6000^◦. And because the Earth’s surface, as you know, is much cooler, heat continuously drifts from the Earth’s interior to the surface and out. The total flux of the thermal energy emerging from the Earth’s interior is about 45 TW – more that twice as much as the total global consumption of power by all humanity.

What is the source of that energy coming out “from down under”? Well, in part it’s the primordial energy. As the science of cosmology teaches us, the Solar System formed about 5 billion years ago, from a spinning cloud of dust, called the “solar nebula”. Over 90% of the nebula’s mass formed the Sun, and the remainder coalesced into smaller objects, one of which was our Earth. The coalescence happened primarily due to gravity – in other words, the gravity performed a colossal work for merging all those dust particles together – and, as we knot from the First Law of Thermodynamics, all that work ended up as thermal energy. So, the Earth at the beginning of its existence was red-hot – then, it stated radiating out its thermal energy. But for a sphere that big loosing energy is not a uniform process: first the areas close to the surface area cool down. It creates a temperature gradient that enables the heat residing closet to the center to start flowing out. But this is not the whole story, because more thermal continues to be generated within the entire Earth’s volume: it’s coming from the decay of long-lived radioactive isotopes such as Uranium 238, Thorium 232, and Potassium 40 (with half-life times, respectively, of 4.5, 14.1, and 1.25 billion years). It’s not exactly known how much of the energy presently emerging from the Earth’s interior is of primordial origin, and how much is due to radioactive decay of minerals – in some sources one can find a 50-50 proportion, in some other 20% primordial, 80% from radioactive decay. But, in fact, it’s not so important for us – we know that the total power is about 45 TW, and this is all we need to know.

45 TW is an impressive number – but keep in mind that the surface area of Earth is also pretty big, about 126 billion acres, or 0.126 Tera-acre – so the average flux of heat emerging from “the netherworld” is only about 360 W/acre, or 0.088 W/m². For comparison, the heat flux emerging from the body of an adult human at ambient temperature of 20^◦ is of the order of 20 W/m². And we know that the heat our body produces is enough for keeping us warm in a sleeping bag at nighttime at a backpack hiking trip – and that’s all. So, 0.088 W/m² can hardly be thought of as an impressive figure...

Suppose that we have a “magic technology” enabling us to collect 100% of the geothermal heat emerging from the ground, and to convert it all to electric power. It only requires covering the ground with a thermally insulating “blanket”. Suppose that using this magic technology we want to produce free electric power for all people and all institutions in Benton County. The population is 90,000 people. The average electric power generation per capita in Oregon is 1.9 kW, so the power we need is 90,000 1.9 kW = 171 MW. And the geothermal power flux is 0.088 MW per square kilometer. So, we need to cover 171/0.088 = 1943 square kilometers. But the whole land area of Benton County 1759 square kilometers! We cover all Benton County with our magic “Geothermal Power Capturing Blanket”, no leaving a single square inch for people, homes, animals, farmland, forests, OSU campus... And what?! Even then we are not able to generate enough electricity!