The Age of the Sun: Kelvin vs. Darwin - RHIG

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The Age of the Sun: Kelvin vs. Darwin
S. Gavin, J. Conn, and S. P. Karrer
Physics Department, Wayne State University, Detroit, MI, 48201
[email protected]
In the years before Einstein, it was stately Lord Kelvin who personified the Great Scientist. Born
William Thomson, the Lord Kelvin was indeed one of the great theoretical physicists of the 1800s. His
work in thermodynamics led to the notion of absolute zero and the temperature scale named in his
honor.
But to Charles Darwin and his new theory of evolution, Kelvin’s theories of the age of the Sun and the
Earth were a terribly sticky wicket! This case study focuses on the conflict between Kelvin and Darwin.
In part because of this conflict, Kelvin is now remembered as the iconic curmudgeon, opposing
innovation in defense of the scientific establishment. But is this fair?
Our presentation follows chapter 24 of the book Degrees Kelvin by David Lindley [1]. We refer to
Thomson as “Kelvin,” although he did not have the title at the time of this controversy. Contemporary
information on the Sun can be found here [2]. Kelvin’s key paper is also available online [3]. An article
by Badash covers the related debate over the age of the Earth in the 19th and 20th centuries. We
assume
[1] Degrees Kelvin by David Lindley, (Joseph Henry Press, 2004), pp 164-214.
[2] http://www.astronomynotes.com/starsun/s1.htm
[3] On the Age of the Sun’s Heat, by Sir William Thomson (Lord Kelvin), Macmillan's Magazine, vol. 5 (March 5,
1862), pp. 288-293; reprint in Popular Lectures and Addresses, vol. 1, 2nd edition, pp. 356-375;
http://zapatopi.net/kelvin/papers/on_the_age_of_the_suns_heat.html#fn2b
[4] The Age of the Earth Debate, by Lawrence Badash, Scientific American, August 1989, p. 90.
William Thomson was born in 1824 in Ireland and attended Cambridge
at the age of sixteen. As an undergraduate he published roughly a
dozen papers in mathematical journals, earning a reputation as a boy
wonder. His work as one of the first mathematical physicists en par
with the giants of the day: Gauss, Stokes, and Fourier. In 1848 he
published the paper later credited with establishing an absolute
temperature scale.
Kelvin achieved popular fame as an inventor and guiding light of the
industrial revolution. His work in thermodynamics contributed to the
invention of the steam engine. He also took part in the laying of the
first trans-Atlantic telegraph cable. Innovations related to the cable and
other projects made him a wealthy man. This material wealth plus his
scientific prestige allowed him to ascend to the ranks of nobility,
receiving the title of the 1st Baron Kelvin, named for the river Kelvin
near his university in Scotland.
William Thomson, Lord Kelvin.
Copyright 2008 Wayne State University. For educational use only. For permission to use: [email protected]
A Burning Question
Despite his technological achievements, Kelvin’s curmudgeonly reputation arose in a debate over
something very basic: the Sun. Today we understand that stars live for billions of years, driven by the
immense power of nuclear fusion. We have a very good idea of the Sun’s mass (about 2 1030 kg),
diameter (1,400,000 km), and distance (150 million km). It is composed mostly of hydrogen (70%) and
helium (28%).
But almost none of this was known in Kelvin’s time. Radioactivity was a curiosity, and the concept of
fusion was a century away. Indeed, Kelvin was puzzled by the Sun. His work in thermodynamics had
convinced him that perpetual motion was impossible. He therefore believed that the Sun could not be
eternal. He therefore wanted to determine its life span. He knew of three possibilities:
1. The Sun was burning some internal fuel, which would eventually run out.
2. The Sun was continuously supplied with energy from an external source.
3. The Sun was hottest when it formed, and is slowly cooling off over time.
He dismissed the first (correct) possibility, because he knew of no fuel that could do the job.
Kelvin’s one key piece of information was the energy radiated by the Sun per unit time. The Sun
radiates an incredible amount of power, which modern estimates place at 4 1026 watts (by
comparison a large power plant can generate energy at a rate of 5000 MW = 5 109 watts).
Kelvin dismissed the possibility that the Sun might be burning, because the fuels he knew could only
maintain such a tremendous power output for a few thousand years. To see why he felt this way, we
estimate the age of the Sun as follows. The chemical reaction that produces the most energy per unit
mass is 2H + O → H2O. Burning hydrogen can provide up to 143 MJ/kg (1 MJ = one million Joules)
per kilogram of fuel; less if the mass of the oxygen is taken into account. If the Sun were made entirely
out of hydrogen (never mind where the oxygen comes from), then it could release a maximum energy
E = (143 106 J/kg) (2 1030 kg) = 3 1038 J. The power radiated by the Sun, P, is roughly equal to
the total energy divided by the total lifetime. The Sun’s lifetime is therefore t = E/P = (3 1038 J)/(4
1026 J/s) = 7.5 1011 s. The Sun would last for only about 20,000 years at most.
Q1. Kelvin didn’t think of hydrogen as a fuel. How would the estimate change if he used coal instead?
Assume that burning coal releases 32.5 MJ/kg.
Q2. How can we estimate the Sun’s energy output knowing only measurements on Earth?
Q3. The modern estimate of the Sun’s power output of 4 1026 watts includes more than just visible
light. Kelvin included only visible light. How would this have changed his estimate?
Turning to the second possibility, Kelvin tried to imagine whether an external power source was
possible. He suggested that meteors and asteroids might fall into the Sun at a regular rate, releasing
large amounts of energy as they struck the Sun. Some of that energy would turn into heat, which in
turn would radiate into space. Some of that radiation would warm our planet. The conversion from
mechanical to thermal energy was a “hot topic” at this time, thanks to Joule's experiment on the
mechanical value of heat. In this experiment, a falling weight was used to turn a paddle-wheel
immersed in liquid. The temperature of the liquid was shown to rise due to the motion of the wheel.
Kelvin’s “meteor theory” had serious problems. To produce energy at the known rate, an enormous
amount of mass had to fall on the Sun over the course of a year. Kelvin estimated that 1/47 of the
Copyright 2008 Wayne State University. For educational use only. For permission to use: [email protected]
Earth’s mass per year would have to fall on the Sun to keep it steadily burning [3]. The added mass
moving from outside to inside the orbits of planets would alter those orbits. A variation of the orbit of
Mercury was detected, but not nearly of the amount predicted by the meteor theory. Meteors might
explain some of the Sun’s output, but not all.
Only the third possibility remained, so Kelvin began to think about the origin of the Sun [3]. He
suggested that the Sun might have formed from a giant gas cloud. Gravity would eventually cause the
cloud to collapse into a ball, since each molecule attracts all the other molecules. As with any falling
mass, the potential energy of molecules in the cloud would turn into kinetic energy as they fall. Kelvin
reasoned that this energy would turn into heat, as in the meteor theory. While each molecule would
not add very much heat, there were a lot of molecules! Kelvin was the first to suggest that the stars
form in this manner. Though we now know this is not how they generate all their energy, this is how
we think stars initially ignite the fusion process. Today’s astronomers know this mechanism as “KelvinHelmholtz Contraction.” (The German scientist Hermann von Helmholtz had independently proposed a
similar theory.)
Kelvin concluded that the Sun built up all its heat as it formed. During its life, it radiated that heat away
like a hot coal. He estimated the lifespan of the Sun to be about 30 million years. This remained the
standard solar model among physicists and astronomers until the early 20th century.
Q4. You can estimate the possible age of the Sun with this mechanism as follows. Assume the total
potential energy of a gas cloud of the Sun’s mass that collapses to the size R of the Sun is E = GM2/R.
How long can this radiate energy at the Sun’s current rate 4 1026 watts?
Q5. The energy release in hydrogen fusion is 645,000,000 MJ/kg. Estimate the lifetime of the Sun.
Q6. Looking at Kelvin’s argument as a whole, what did he get right? What did he get wrong?
Q7. Believe it or not, this is how modern astronomy works. People observe the heavens and use
current knowledge of physics and chemistry to try to piece together a consistent picture. What are the
limits of this procedure? Name some contemporary observations that might be straining against such
limits.
Enter Darwin
Kelvin’s solar age disagreed with estimates of the age of the Earth from geologists of the time.
Working from current erosion rates, the geologists had long believed that the Earth must be
considerably older than Kelvin’s estimate, perhaps hundreds of millions of years.
This was a problem: the Earth could not be older than the Sun! Kelvin countered that the geologists
were wrong to assume a steady rate of erosion, since floods and other natural disasters could
accelerate the erosion. But he realized he needed a better estimate of the age of the Earth. As with his
solar theory, he applied thermodynamic arguments.
It was already known that the interior of the Earth consisted of molten rock, with only the outer crust
hardened – this explained volcanic eruptions. Kelvin assumed that the Earth formed as a molten ball,
which then cooled from the outside in. Using temperature data from mines, he was able to work
backward to a time when the Earth would be a solid ball at 7000ºF. His estimate of the age of the
Earth was similar to his other figure: somewhere between 20 and 400 million years.
Kelvin seemed to feel that the soft thinking of the geologists could use a solid dose of mathematical
Copyright 2008 Wayne State University. For educational use only. For permission to use: [email protected]
rigor. He had turned geological information against the geologists, and it supported his theory of the
Sun. He and his physicist supporters were confident of their estimates.
When Charles Darwin and Alfred Russel Wallace proposed their theory of evolution in 1858, they were
following the geologists’ estimates. They felt that hundreds of millions of years – or maybe more –
were needed to explain the origin of the species. The age of the Earth was so important to Darwin that
he had made geological studies of his own. Included in the first edition of On The Origin of the Species
by Natural Selection was an estimate of the time needed to wash away the Weald, a valley in southeast England formed of the eroded remains of a uplifted structure called an anticline. He estimated
that that erosion alone would require 300 million years.
Darwin himself was bowled over by Kelvin’s careful analysis. He could not escape the logic! He was
so troubled that he removed any reference to time scales from later editions of Origin of the Species.
The shy Darwin thought of Kelvin as a “odious spectre” [4].
Kelvin on the other hand had little understanding of biology. Nevertheless, when opponents said that
his time scales were too short to allow for life to develop, he ignored them. Arguments raged among
the followers of both men.
Q8. Which side had the more convincing argument at the time?
Q9. Kelvin lived to 1907, by which time radioactivity was firmly established. It had been shown in 1903
that radium generates enough heat to melt its own weight in ice in one hour. Geologists observed at
that time that the Earth would be heated from within by radioactive decay and, therefore, could be a lot
older than Kelvin thought. Many people criticize Kelvin for refusing to change his mind. Is this
appropriate?
Q10. Both Darwin, a naturalist, and Kelvin, a physicist, had to reach across disciplinary lines in their
work. Was their debate a “territorial” dispute? How might such disputes figure in to today’s research?
Q11. We now know that the Earth is 4.54 billion years old. The Sun may live 10 billion years or more.
Countless laboratory experiments from the molecular level on up support evolution as the central
paradigm of biology. Yet in some quarters the battle against Darwin rages on. Why do you think this
is? What would Kelvin have thought of present-day Creationists and Intelligent Design supporters?
Copyright 2008 Wayne State University. For educational use only. For permission to use: [email protected]
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