yes but I was correcting your answer, not addressing the OP which has been answered already
i don’t quite understand the difficulty in seeing that the insulating properties of 8 or 10 miles of crust will support a large temperature difference between bottom and top. After al, only about 2" of material supports a 55 C difference in temperature between room temperature and freezer temperature.
Or the 200 C difference between room temperature and oven temperature…
Because it just is, ya dig?
Groovy.
Well…first of all you aren’t using rock for insulation, and secondly what also supports that difference is the flow of heat that is being lost from the outside of an oven, for example. At the surface of the earth, this heat loss is only about 90milliwats or so per meter squared; doesn’t seem like much considering how hot it is inside the earth. Insulators retard heat flux but they don’t prevent it.
I think part of the answer is that rock is a better insulator–i.e. its thermal transfer is better than **Chief Pedant’s ** intuition (this is not a very high standard…) but I also suspect part of the answer is that the efficiency of heat transfer near the outside of the crust is substantially diminished by the inhomogeneity of its composition. It’s not (particularly near the surface) an unbroken layer of solid rock. There are multiple boundaries of various materials which contribute to the diminution of the heat transfer making the very outer shell a much better insulator.
Get past the first couple miles or so and it starts to feel a bit like an oven. But what comes between that depth and the surface is not just a homogenous layer of rock. Anyway, thanks all. I’m giving up my idea about patenting insulated shoes and preying on the (even weaker-) minded.
But if you assume an average thermal conductivity of 2 W/m/K and 10-km thickness, that 90 mW/m[sup]2[/sup] heat flow translates to a 450 C temperature difference. If it’s 20 km thick, it’s 900 C. It says here the top of the mantle ranges from 500 to 900 C, and here the thickness of the crust is listed as 5-10 km for the ocean and 10-30 km for land, so it more or less checks out. But you may be right, I think the remaining discrepancy may be due to layers of material with somewhat lower thermal conductivity (e.g. soil).