Is Earth's core cooling?

Chris - Well, it's a very good question. There are a number of answers to this. One of them is that the Earth is a fairly big planet, as planets go, and it had a bit of heat to start with. So the particles that coalesced to make the early Earth, when they came together and accreted, they actually had some energy so when they got together that energy was imparted into the Earth so it had some embodied energy to start with.

Then there's another effect to do with gravity. Because gravity works through an object's centre of mass, heavy things are pulled towards the middle and lighter things are therefore displaced above them. When the Earth first formed there would have been a mixture of the big stuff and the small stuff all mixed up. Over time, under the influence of gravity, the heavier things have settled towards the centre, and the lighter things towards the surface, and that would have generated some frictional effects and therefore you've turned some gravitational potential energy into heat.

Those two mechanisms are quite minor contributions to where the Earth's heat comes from, though they're not insignificant. By far the biggest player is what we call radiogenic heating. The Earth is effectively a giant nuclear reactor. There are particles in the Earth's core and throughout the mantle which are radioactive.

When things decay radioactively they produce heat. The vast majority of the Earth's energy is coming from the radioactive decay of these components, and they include things like thorium and also potassium.

Interestingly, there was always a big quandary: if potassium is a source of all this heat, why is there so little of it present in the mantle and outer surface of the Earth? It's a light element so we should find it in abundance at the surface. Well, it turns out that under very high pressures, potassium can form an interesting alloy with iron (a much heavier element). Of course, the iron is all in the core of the Earth, so what scientists think has happened is that the potassium has sunk with the iron down into the core of the Earth, and it's down there in the middle, decaying, producing a lot of the heat that we have warming up the Earth today.

Where is all that heat going and is the Earth cooling down? Not really, it's staying about the same temperature. Geological estimates are that the Earth loses heat at a rate of about 50 terawatts. That's about 50,000 1 gigawatt power stations worth of heat loss, i.e. if power stations pump out power at a rate of 1 gigawatt then you'd need about 50,000 of them - that's how fast the Earth is losing heat through the oceans, continental surfaces, volcanoes and so on, and that means that those processes inside the Earth that I've mentioned must be producing heat energy at a similar rate to balance things out because the Earth isn't cooling down that much.