Heat - The Solid Earth - page 274

very small quantities, parts per million for uranium and thorium and of the order
of 1% for potassium; in the mantle they are some two orders of magnitude less
abundant. Nevertheless, these radioactive elements are important in determining
the temperature and tectonic history of the Earth. Other radioactive isotopes, such
as aluminium-26 and plutonium-244, have been important in the earliest history
of the planet.
The radioactive isotopes producing most of the heat generation in the crust
are 238 U, 235 U, 232 Th and 40 K. The uranium in the crust can be considered to
be 238 U and 235 U, with present-day relative abundances of 99.28% and 0.72%,
respectively; but 40 Kispresent at a level of merely one in 10 4 of total potassium
(Chapter 6). The radioactive heat generation for these elements in the Earth is
therefore as follows: uranium, 9.8 10 − 5 Wkg − 1 ; thorium, 2.6 10 − 5 Wkg − 1 ;

× ×

10 − 9 Wkg − 1 .Table 7.1 gives the radioactive heat genera-
tion of some average rock types. It is clear from this table that, on average, the
contributions of uranium and thorium to heat production are larger than that of
potassium. On average, granite has a greater internal heat generation than do
mafic igneous rocks, and the heat generation of undepleted mantle is very low.
The heat generated by these radioactive isotopes when measured today can be
used to calculate the heat generated at earlier times. At time t ago, a radioactive
isotope with a decay constant

and potassium, 3.5 ×

would have been a factor e λ t more abundant than
it is today (Eq. (6.5)). Table 7.2 shows the changes in abundance of isotopes and
consequent higher heat generation in the past relative to the present.
Although the heat generation of the crust is some two orders of magnitude
greater than that of the mantle, the rate at which the Earth as a whole produces heat
is influenced by the mantle because the volume of the mantle is so much greater
than the total crustal volume. About one-fifth of radioactive heat is generated
in the crust. The mean abundances of potassium, thorium and uranium, for the
crust and mantle taken together, are in the ranges 150-260 ppm, 80-100 ppb
and 15-25 ppb, respectively. These abundances result in a total radioactive heat
production for the crust and mantle of (1.4-2.7)

λ

10 13 W, with a best-guess value

×

10 13 W. of 2.1 ×

7.3 Calculation of simple geotherms
7.3.1 Equilibrium geotherms
As can be seen from Eq. (7.18), the temperature in a column of rock is controlled
by several parameters, some internal and some external to the rock column. The
internal parameters are the conductivity, specific heat, density and radioactive
heat generation. External factors include heat flow into the column, the surface
temperature and the rate at which material is removed from or added to the top of
the column (erosion or deposition). Temperature-depth profiles within the Earth
are called geotherms .Ifweconsider a one-dimensional column with no erosion