Earth core

Suppose the Earth were destroyed and only the core remained. How long would it take to cool down to less than say, 273 Kelvin? Anyone knows how to calculate this?
Thanks

Now there's a wild question. Is this your homework, Larry? (Big Lebowski reference, nevermind).

So you want to know how long it would take the Earth's core to cool down to the freezing temp of water?

First of all, there's not a real good answer for the temp of the core, but there is some reasonable speculation.

Then' we'd need to consider what causes the core to be the temperature it is. And it may be due to radioactive potassium. So I'd think maybe you need to calculate its half life since the ambient temperature of space isn't going to cool down a radioactive element by itself.

Then again, I have absolutely no idea what I'm talking about. So good luck with that.

Hehe. No its not homework, just something that came across my mind. I figured that if stars are born and die, it is the same for planetary cores.


Another interesting question would be that: if intelligent life is common in the universe, how can they ever hope to survive when stars eventually die? Seems like they would just have to keep moving from planet to planet to avoid the destruction caused by a Red Giant, and the cold caused by dwarves.