Kelvin, Darwin and cooling coffee

Viewed from the perspective of 21st Century science, two of the greatest achievements of nineteenth century science are, arguably, Darwin’s ‘theory of natural selection’ and ‘thermodynamics’.  Darwin’s theory established how life on earth evolved through the centuries.  Thermodynamics dealt with the energy, temperature and pressure of systems such as the steam engine.  Both are indispensable to our current understanding of the world. At one point in the nineteenth century though, these two theories appeared to disagree with each other; one of them had to be wrong.

pigeon, sun, sunbathing, age of the earth

Perhaps they are blissfully unaware of it, but the pigeons in the photograph above illustrate the root of the problem between natural selection (represented by Darwin) and thermodynamics (represented by Kelvin).  The pigeons are enjoying the last of the summer sun, soaking up the energy radiated from the Sun in an effort to stay warm.  This is the problem.  It is clear that the Sun is the source of most of the energy on the earth.  The clouds and wind system are driven by the heat from the Sun (more in the Daily Grind on 17 September 2014), crops grow and pigeons warm themselves all from energy received from the Sun.  As the polymath John Herschel wrote in 1833 “The great mystery [of the Sun’s heat]… is to conceive how so enormous a conflagration (if such it be) can be kept up”.

Sun, heat, coffee and Sun
The Sun is our nearest star and source of heat, but what heats the Sun? Image © NSO/AURA/NSF

This is where the coffee comes in.  To make the coffee, we boil the water, let the coffee brew a while and then wait while it cools until we can drink it.  If we do not use a heater or candle flame or other means of keeping the coffee hot, it will get cold.  Thermodynamics tells us how quickly it gets cold by relating how much energy is given off by the cup to the time it takes to lose this energy.

The question that Kelvin was considering was, what heats the Sun?  Our current idea, that the heat from the Sun is caused by the nuclear fusion of hydrogen into helium, was unavailable to Kelvin as nuclear fusion had not then been imagined.  This would eventually lead to a reconciliation between evolution and thermodynamics but at the time of Kelvin, a more classical model was needed.

There were three immediately apparent possibilities for what caused the heat of the Sun. Firstly, the Sun was a heated body slowly getting cold; the situation for our coffee cup. Secondly, it could be heated by its chemistry causing ‘a great fire’.  Lastly, the heat of the Sun could have been caused by the loss of gravitational potential energy elsewhere such as the impact of meteors on the Sun’s surface.  The concept that the Sun’s heat had to be caused by a mechanism which was eventually going to ‘run out’  (meaning that the Sun would eventually ‘die’) was a thermodynamical concept. Thermodynamics was woven through Kelvin’s attempts to understand how the universe worked.

The original theory of meteors and comets crashing into the Sun thereby heating it, had to be abandoned. Image courtesy of Lowell Observatory/NOAO/AURA/NSF
A theory whereby meteors and comets crashed into the Sun and thereby heated it, had to be abandoned. Image courtesy of Lowell Observatory/NOAO/AURA/NSF

The coffee cup model for the Sun could be fairly quickly ruled out.  Estimates of the rate of energy loss from the Sun led Kelvin to say in 1854 “If we consider, however, the whole emission at the present actual rate, we find even if the Sun’s thermal capacity were as great as that of an equal mass of water, that his mean temperature would be lowered by about 3C in two years…” (italics mine).  By specifically equating the Sun to a mass of water (he could have equivalently used coffee), Kelvin found that the rate of cooling was too great, it would have been discernible. Similarly the idea of the Sun’s heat as arising from a great conflagration could be ruled unlikely. Kelvin estimated that if the Sun were powered by coal, 1500 lb (680 kg) of coal per hour per square foot (0.1 square metres) of the Sun’s surface would be needed.  He noted, where would the supply of air come from to burn such a fuel source?  No, the conflagration model would have extinguished all light from the Sun in “a few minutes”.

The gravitational model however had merits.  Even if the original model of meteors crashing into the Sun’s surface had to be abandoned, a later model suggested by Helmholtz where the Sun’s own contraction caused its heating gave numbers that were reasonable.  The estimated temperature, the size of the Sun and the energy received at the earth, could all be explained with sensible values of constants (e.g. the heat capacity of the Sun) in the model.  Viewed alone, the theory appeared consistent.

The Weald of Kent in watercolour by Henry Edridge. Darwin calculated it to be 300m years old. Image © Trustees of the British Museum
The Weald of Kent in watercolour by Henry Edridge. Darwin estimated that the Weald of Kent was 300m years old. Image © Trustees of the British Museum

Why did this lead Kelvin into disagreement with Darwin?  For natural selection to be feasible, Darwin needed time, geological time.  For Darwin himself, this was not a problem, he estimated the age of the Weald of Kent based on coastal erosion as 300 million years.  Long enough for evolution to have occurred. Viewed alone, the theory appeared consistent.

The problem was that if the Sun was indeed powered by gravitational collapse, Kelvin calculated that it was most probable that “the Sun has not illuminated the earth for 100 000 000 years and most certain that he has not done so for 500 000 000 years”. The solar system, based on estimates using the latest physics of the time, simply could not be old enough for evolution to have occurred.  Viewed together, the theories appeared inconsistent. The theory of natural selection was not just opposed by some religious, it was opposed by some of the most prominent physicists of the time and the opposition was based on the latest physics.

Kelvin and Darwin were both investigating their own fields to the best of their ability in order to find out how the universe worked.  They both recognised that, for both of their respective theories to be true (or even possibly true), they needed to be coherent with each other.  This is an important philosophical point about the nature of scientific theory and practise.  Of course, the two theories were reconciled when it was recognised that the Sun was powered by nuclear fusion rather than gravitational collapse and that the earth was around 4500 million years old. Does that mean that both theories (or at least one of them) are true?  What is truth?


Quotes taken from “Energy and Empire a biographical study of Lord Kelvin, C. Smith and M Norton Wise, Cambridge University Press, 1989”