The
average rate at which heat flows out through the surface of the Earth
in North America is
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Solution: Click For PDF Version
This is a
problem of heat conduction. The rate of flow of heat across a slab
of width L,
cross-sectional area A,
when its two ends are maintained at temperatures
Data of the problem are average thermal conductivity of the rocks
rate of flow
of heat across one square meter surface of the rocks is
length across
which the heat is conducted through the rocks to the surface of the
Earth is
temperature
of the surface of the Earth
and let the
temperature at the depth of 33 km be
We therefore have
or
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,
and the average thermal conductivity of the near surface rocks is
.
Assuming a surface temperature of
,
we have to estimate the temperature at a depth
of 33 km ( near
the base of the crust). We
may ignore the heat generated by radioactive elements and can also
ignore the curvature of the Earth.
and
,
is given by
,
,
,
,
,
