EPS 102 Lecture 13 Thursday February 05
th
, 2009
•
Geotherms and Paleoclimate. Thermal diffusivity =kappa=10^6 m^2/s for rock. We can
use this to estimate how much of a meteorite would get heated up as it comes into the
atmosphere. The atmosphere is ~ 100km thick and an incoming object (The escape
velocity is 10km/s for earth) would come in at 10km/s. It would take 10 seconds for a
meteorite to get through the atmosphere. Multiply this by the thermal diffusivity to get 10
mm^2 and taking its square root gives us the skin depth for the heating of that meteorite
in 10 seconds which is close enough to 3 mm. Rock and metal are different because metal
transmits heat 10 x faster than rock. Kappa is 10^5 m^2/s for metal, and this is because
in metal , electrons move around which is why metals conduct electricity. Those
electrons can also transport heat energy. The most special mineral that is an exception to
this rule is diamond. Diamond is very unusual in not only being the hardest materials we
know, it also conducts heat extremely effectively, better than copper. This calculation
was for a stony meteorite. For an iron meteorite, we’ll get
about
the same number (only a
few extra millimeters of penetration of heat).
•
We do exactly the same calculation for plate cooling (ocean plates). We have 10^8 years
of age which is 3*10^15 seconds, and we plug it into to calculate the cooling front (as the
oceanic plate is created, it starts off warm and cools down progressively on its way to the
mantle it moves a few 10s of km).
What matters is the shape of the temperature
distribution or the shape of the concentration of material (when diffusivity is important).
The erosion of topography can be modeled like a diffusion process. The degree to which
topography gets eroded away has to do with the curvature of the topography. There is a
paper written: Steve Morris and Raymond Jeanloz about geotherms, heat flow, and
thermal diffusivity.
•
We want to look at temperature profiles near the earth because they are related to
dynamics. We will think about how a fluid moves , ex: think of a pan of water which is
sitting on the stove being heated gently from below. The water is just sitting there in
steady state; if you heat it slowly you would get a temperature distribution that is steady.
The heat flux out of the top (as J) by conduction is = thermal conductivity * temperature
gradient. This is for no convection. But what if you continue to heat the pan of water.
There is a buoyancy force that builds up because most materials expand as they heat so
hot air rises because it is less dense than the colder material. Specifically, this force =
mass * acceleration of gravity. Thermal expansion coefficient= percent change in density
with a given change in temperature. For materials like rocks, thermal expansion
coefficients are small at 10^5 kelvin. If you heat up a rock by 1000 degrees C, you will
get one percent change in density. That enters into the force balance we need to use to
describe how this fluid will become unstable to convection. The hotter regions want to
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 Spring '08
 Staff
 Thermodynamics, Heat, Heat Transfer, Heat Flow, Rayleigh number

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