The Age of the Earth--An Age-Old Question [Excerpt]

Lord Kelvin applied thermodynamics to the problem of Earth?s age. Although his estimates are now known to be incorrect by several orders of magnitude, they shook up the established theories of 19th-century geologists

By Paul S. Braterman

From Stars To Stalagmites: How Everything Connects Image: Paul S. Braterman

Editor's Note: This excerpt is from the first chapter of From Stars to Stalagmites: How Everything Connects, by Paul S. Braterman. Earlier in the chapter the author discusses the ideas among geologists in the 19th century that physical processes such as erosion had always occurred at the same rates and that the features of Earth were static, leading them to conclude that the planet had had no beginning nor would it have an end. Here he writes about how the ideas of physicist William Thomson would end up turning those theories on their heads, paving the way for our current understanding of Earth's early history and age.

Other developments, however, were to undermine this view. I have already mentioned steam engines and railways. Science in the mid 19th century was much occupied with matters concerning work and energy, and the efficiency of heat engines. This period saw the development of a new subject, thermodynamics, dedicated to such matters. One of the most fundamental results of thermodynamics (the First Law) is that energy is conserved. Another (the Second Law) is, that since energy tends to spread out and degrade irreversibly over time, there could be no such thing as a perpetual motion machine. Any real process, and certainly such a process as the uplift and erosion of the Earth, is operating against friction, with overall irreversible degradation of energy into heat, and this is something that cannot continue on its own indefinitely. Yet the Earth, as seen by Hutton and Lyell, appeared to be just one such machine, running through cycles of uplift and erosion with no visible source of energy to drive the process. Conflict between the thermodynamicists and the geologists was inevitable.

William Thomson, Lord Kelvin, in whose honour the absolute temperature scale is now named, was among the most distinguished scientists of the late 19th century. His work straddled the boundary between pure and applied research. Among other things, he played a major role in establishing the relationships between heat, work, and electricity, worked out the theory for how much information (as we would now say) could be carried by the first submarine cable, and improved the form of the compass and the methods of navigation. He was appointed Professor of Natural Philosophy (i.e. Physics) at Glasgow University when he was 22, and held that Chair for more than 50 years.

Kelvin was interested in the age of the Earth, considered as a problem in physics, from a very early stage. It was the subject of a prize undergraduate essay, and also of his inaugural lecture at Glasgow, now unfortunately lost. He was also a sharp critic of the science of geology as it was developing. He argued (correctly) that extreme uniformitarianism was not compatible with the laws of physics. Things must have been very different at some time in the past, and would be different again in the future. The Earth was losing heat and must have once been a molten ball. The Sun was emitting energy, could not have been there forever, and must eventually run out of energy, plunging the Earth into utter cold and darkness.

In a lengthy series of publications, Kelvin attempted to quantify these general objections. He developed a way of estimating the age of the Earth?s solid crust from cooling arguments. It is hot down a mine, and the deeper you go, the hotter. If you could go down deep enough, you would, at a depth of some miles, reach the Earth?s mantle, where the rock is actually molten. So if we have cooler rocks on top and hotter rocks lower down, heat must be flowing up through the rocks from the centre outwards. Knowing how fast the temperature increases as we go down, and how effectively the rocks of the crust conduct heat, Kelvin calculated how fast the Earth was losing heat. Where was this heat coming from? Kelvin thought he had the answer. He assumed (correctly) that the Earth was originally molten, and that heat must have dissipated as the Earth?s rocks solidified from an originally molten state (the opposite kind of process to ice absorbing heat as it melts). From an estimate of the thickness of the solid rock layer (the crust), and from measurements of how much heat it takes to melt a given amount of rock, he was able to estimate how much heat has been given out by this process of solidification. Then, by running the model backwards through time, he calculated that the thickness of the Earth?s solid crust corresponded to 100 million years. At this date before the present, all the rocks now on the surface would have been molten, and this, according to his argument, is therefore an absolute upper limit on the age of the solid crust of the Earth.

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