How Kelvin and Clausius discovered Carnot’s ideas

In textbooks dealing with thermodynamics, the story is often recounted that Carnot’s groundbreaking memoir Réflexions sur la Puissance Motrice du Feu (Reflections on the Motive Power of Fire) went unnoticed by the scientific world when it was published, and lay forgotten for 24 years until Lord Kelvin seized on its significance and brought Carnot’s seminal work – in which lay the seeds of the second law of thermodynamics – into the spotlight of publicity.

This popular account, although broadly accurate, is incomplete in one important respect. It neglects the vital role played by Clapeyron.

Benoît Émile Clapeyron (1799-1864)

Sadi Carnot (1796-1832) and Émile Clapeyron (1799-1864) were contemporaries. Both were engineers by training, and both had studied at the École Polytechnique in Paris. When Carnot published his memoir (at his own expense) in 1824, Clapeyron had already left Paris and was teaching at an engineering school in St. Petersburg, Russia. He returned to Paris just two years before Carnot’s untimely death during a cholera epidemic in 1832. By that time, Sadi Carnot’s little book had long since disappeared from the booksellers’ shelves. But Clapeyron had evidently obtained a copy, and had clearly recognised the importance of his compatriot’s work. Clapeyron’s own Mémoire sur la Puissance Motrice de la Chaleur (Memoir on the Motive Power of Heat), published in Journal de l’École Polytechnique in 1834, contains a full restatement of Carnot’s theoretical principles – albeit in a more analytical form.

While Carnot’s privately published booklet quickly faded into obscurity, Clapeyron’s memoir published in an academic journal did not. It was read in scientific circles and remained available in scientific libraries, and so kept Carnot’s powerful ideas alive. In 1837, Clapeyron’s memoir was translated into English and formed one of the papers presented in Volume I of Taylor’s Scientific Memoirs. This was how Lord Kelvin became aware of Carnot’s work – we know this because the following footnote appears in the historic paper On an Absolute Thermometric Scale which Lord Kelvin published in Philosophical Magazine in October 1848:

“Carnot’s Theory of the Motive Power of Heat – Published in 1824 in a work entitled Réflexions sur la Puissance Motrice du Feu, by M. S. Carnot. Having never met with the original work, it is only through a paper by M. Clapeyron, on the same subject, published in the Journal de l’École Polytechnique, Vol. XIV, 1834, and translated in the first volume of Taylor’s Scientific Memoirs, that the Author has become acquainted with Carnot’s Theory.”

William Thomson, later Lord Kelvin (1824-1907)

At the end of 1848, Lord Kelvin succeeded in obtaining a copy of Carnot’s original work, and the following year published a lengthy paper entitled An account of Carnot’s Theory of the Motive Power of Heat in the Transactions of the Edinburgh Royal Society, XVI, 1849.

Curiously, just as Lord Kelvin came to discover Carnot’s masterwork through the agency of Émile Clapeyron’s memoir, so did another key figure in the development of thermodynamics – Rudolf Clausius.

In his first and most famous paper On the Motive Power of Heat, and on the Laws which can be deduced from it for the Theory of Heat published in Annalen der Physik  in 1850, Clausius cites Carnot’s memoir on the opening page and adds this footnote:

“Réflexions sur la Puissance Motrice du Feu, par S. Carnot. Paris, 1824. I have not been able to obtain a copy of this work, and am acquainted with it only through the work of Clapeyron and Thomson [Lord Kelvin]”

Rudolf Clausius (1822-1888)

Clapeyron’s memoir had been translated into German in 1843 and published in the same journal in which Clausius’ 1850 paper appeared – Annalen der Physik – so it likely to be this translation to which Clausius refers. It is doubtful whether Carnot had much inkling of how crucially important his ideas would be to the development of thermodynamics. But there is no doubt that Clapeyron immediately saw value in them. In the introduction to his memoir, Clapeyron describes Carnot’s ideas as ‘both fertile and beyond question‘ and ‘worthy of the attention of theoreticians‘.

He was right. The two foremost theoreticians of the day certainly found Carnot’s fertile ideas worthy of attention. And we have Émile Clapeyron to thank for enabling Lord Kelvin and Rudolf Clausius to discover them.

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