Re: this planet
Posted by Uncle Al on Jul 20, 2002 at 11:25
(68.5.243.16)Re: this planet (oliver claypool)
1) Accretion energy, about 2.47x10^32 joules. How do you get rid of that, git?
2) Accumulated heat of radioactive decay. How do you get rid of that, git?
If you look at the energy necessary to heat the Earth to measured numbers, any frictional origin is not even ridiculous. For our readers who have IQs larger than their hat sizes...
Treat the Earth as a solid made of Mx6x10^27/A atoms of atomic weight A, with the specific heat per atom of a three-dimensional harmonic oscillator, 4x10^(-23) J/deg. The mean atomic weight is surely less that 50 and more than 20, for the Earth is mostly silicon, oxygen, magnesium and iron. If we assume A = 30, we cannot be off by as much as a factor of 2 either way. This gives us 860 J/deg for the mean specific heat per kilogram.
We know the interior of the Earth is hot — at least as hot as the glowing lava that erupts from it. A few thousand degrees seems a reasonable guess for a mean interior temperature. Try 3000 K, thus obtaining for the thermal energy 1.5x10^31 J.
We thus see that the heat of accretion alone is more than ten times the energy necessary to melt the entire Earth and heat it white hot. Add radioactive decay to that (almost all the argon in the atmosphere, 1% by volume, came from decay of K-40; then add uranium and thorium decay series). The interior of the Earth is NOT cold, and trivially proven so, even given 5 billion years of radiating heat into space.
--
Uncle Al
http://www.mazepath.com/uncleal/eotvos.htm
(Do something empirically naughty to physics)