Geology Reference
In-Depth Information
The remaining 30% comes from two sources: the core (7.6 TW) and internal heat
released as the mantle cools (the balance, 4.2 TW).
We can check this by looking at the rate of temperature decrease implied by the
4.2 TW released by cooling, using Eq. (9.3). Taking the mantle mass to be 4
×
10
24
kg and its specific heat to be 1000 J/kg
◦
C, the temperature declines at a rate
of 1.05
33
◦
C/Gyr. This corresponds well with the decline of 31
◦
C
over the final billion years of the model.
The silicate part of the Earth is estimated, from meteorite studies, to contain
about 20 ng/g of uranium [140]. (I give concentrations in this form, nanograms of
U per gram of rock, to avoid the ambiguity of the term 'parts per billion' commonly
used by geochemists, because the latter could be a ratio by weight, by volume or by
moles.) The ratios of thorium and potassium to uranium are commonly estimated to
be about Th/U
10
−
15
◦
C/s
×
=
10
4
g/g (Section 10.2). These quantities
will generate about 5 pW/kg of heat [141] (1 pW
=
3.8 g/g and K/U
=
1.3
×
10
−
12
watt). With
=
1picowatt
=
10
24
kg this implies a total heat production of 20 TW.
This is a little less than the radiogenic heating required by the thermal evolution
model, but the difference is probably within the uncertainties of the model and the
geochemical estimates.
However, there is a problem, because about half of the Earth's heat source
elements are estimated to have been sequestered into the continental crust [142].
The heat generated within the continental crust (and lithosphere) will conduct
directly to the surface and play no part in heating the mantle. Because the continental
crust is quite heterogeneous, estimates of its uranium content have varied through
the range 30-60% of Earth's budget [118]. Thus only 40-70% of the Earth's total
uranium is available to heat the mantle, so it would generate only 8-14 TW of
heat. With a total mantle heat loss of about 35 TW, this implies a Urey ratio of
only 0.23-0.4, much less than the 0.7-0.9 range required by the thermal evolution
models.
This is a major discrepancy that implies there is something important we don't
understand about the Earth. There are three possible resolutions of the puzzle.
First, the geochemical estimates could be wrong. Second, the present rate of heat
loss is unusually high, with the implication that the present rate of cooling is also
unusually high. Third, the rate of heat loss and the rate of cooling are not unusually
high, with the implication that the mantle was a lot hotter in the past than implied by
the thermal evolution calculations just presented. The third option would also imply
that there is something important missing from the physics of mantle convection
as so far presented.
The first option will be discussed in Chapter 10. For now we can note that
there are certainly uncertainties in both the values and the assumptions involved
×
a silicate mass of about 4
