After Carnot

The man who rescued Carnot’s workfrom what certainly would otherwise have
been oblivion was E´ mile Clapeyron, a former classmate of Carnot’s at the E´ cole
Polytechnique. It was Clapeyron who, in a paper published in the Journal de
l’E´ cole Polytechnique in 1834, put Carnot’s message in the acceptable language
of mathematical analysis. Most important, Clapeyron translated into differential
equations Carnot’s several verbal accounts of how to calculate his efficiency function
F(t).
Clapeyron’s paper was translated into German and English, and for ten years
or so it was the only linkbetween Carnot and his followers. Carnot’s theory, in
the mathematical translation provided by Clapeyron, was to become the point of
departure in the 1840s and early 1850s for two second-generation thermodynamicists,
a young German student at the University of Halle, Rudolf Clausius,
and a recent graduate of Cambridge University, William Thomson (who became
Lord Kelvin). Thomson spent several months in 1845 in the Paris laboratory of
Victor Regnault. He scoured the Paris bookshops for a copy of Carnot’s memoir
with no success. No one remembered either the bookor its author.
In different ways, Clausius and Thomson were to extend Carnot’s workinto
the science of heat that Thomson eventually called thermodynamics. One of Clapeyron’s
differential equations became a fixture in Thomson’s approach to thermodynamics;
Thomson found a way to use the equation to define an absolute
temperature scale. Later, he introduced the concept of energy, and with it resolved
a basic flaw in Carnot’s theory: its apparent reliance on the caloric theory.
Among Clausius’s contributions was an elaboration of Carnot’s heat engine analysis,
which recognized that heat is not only dropped in the heat engine from a
high temperature to a low temperature but is also partially converted to work.
This was a departure from Carnot’s water engine analogy, and in later research
it led to the concept of entropy.