PX266 Geophysics (2010/11)
Lecture 17 Handout – Heat Flow and Earth’s Interior Dynamics
Dr. Gavin Bell
Formation and early heating of the Earth
The Earth’s interior is hot (nearly 6000 K at thecentre). Part of this heat energy was derived
from the formation process of the Earth, during which the proto-Earth was bombarded by
planetesimals and other early Solar System material. Their kinetic energy was converted to
heat energy during this accretion process. Self-compression of the proto-Earth under its own
gravitational attraction releases further gravitational potential energy, again converted to heat.
Radioactive heating is also crucial. The energy of fission products (e.g. beta particles)
produces the fission heating effects. For example, 40-K to 40-Ca or 40Ar produces about
2.8×10-5 W kg-1, while for 208-U to 206-Pb it is about 9.4×10-5 W kg-1. Radioactive heating
therefore appears rather puny (fascinating facts #344: one cubic centimetre of granite would
take half a billion years to boil the water for a cup of tea), but over the large volume of the
Earth’s interior and over geological time it is hugely important.
Kelvin’s estimate of the age of the Earth and radioactive heating
William Thomson (Lord Kelvin) estimated the age of the Earth by guessing its initial heat
energy, assuming it was molten, and then calculating the heat flow through the surface. His
argument was mathematically sophisticated (using Fourier’s brand new heat flow equations)
and he refined his calculations over the years, always in the direction of a younger Earth. But
he was unaware of radioactive heating, and his final value of 24 million years, given with no
error bars, is woefully small. Many geologists, faced with enormously thick sedimentary
strata, and biologists, armed with fossil evidence in the framework of Darwin’s ideas,
vehemently disagreed with Kelvin’s estimate.
Figure 2 – an X-ray of Lord Kelvin’s
hand, from the book ‘Light, Visible and
Invisible’, 1923. Kelvin was not in a
position to include radioactive heating in
his calculations.
Huxley:
Mathematics may be compared to a mill of exquisite workmanship, which
grinds you stuff of any degree of fineness; but, nevertheless, what you get out
depends upon what you put in; and as the grandest mill in the world will not
extract wheat-flour from peascod, so pages of formulae will not get a definite
result out of loose data. [ = garbage in, garbage out]
Boswell:
That fellow seems to possess but one idea, and it is wrong.
Farnsworth: Baldercrap!
