From Asimov's Biographical Encyclopedia of Science and Technology
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CARNOT, Nicolas Léonard Sadi (kahr-noh)
French physicist
Born: Paris, June 1, 1796
Died: Paris, August 24, 1832
Carnot came of a distinguished French family. His father had been a leading government figure under the First Republic and under Napoleon I. He had been called the Organizer of Victory because of the manner in which he managed to train and equip the raw recruits called to arms against the circling hostile powers of Europe. Carnot's younger brother was a politician of liberal views who was later to oppose Napoleon III. His brother's son was eventually to serve as one of the presidents of France's Third Republic. Among this group of politicians was Nicolas, a scientist. He was educated by his father to begin with, entered the École Polytechnique in 1812 and graduated in 1814. He had been trained as a military engineer and fought against the armies invading France in 1814. With Napoleon's fall his father was exiled and his own advancement was out of the question. He remained an army officer, however.
In 1824 he published his only work, a partial title of which is On the Motive Power of Fire. The book was enough to secure his place in the history of science. In it he defined work as "weight lifted through a height." (This is now made more general by defining it as "force acting through a distance against resistance," a definition advanced by Coriolis.)
Carnot was interested in the amount of work that could be obtained from a heat engine. The steam engine invented by Watt, although far better than any previous model, was quite inefficient. In Carnot's time an efficiency of 5 to 7 percent was all that could be expected, meaning that 93 to 95 percent of the heat energy of the burning fuel was wasted. Carnot was interested in determining how far this mark might be improved.
He was able to demonstrate that the maximum efficiency depended upon the temperature difference in the engine. In the case of the ordinary steam engine, the temperature of the steam (T1) was the hottest part of the engine, the temperature of the cooling water (T2) the coldest. The maximum fraction of the heat energy that could be converted into work, even if the machine operated with perfect efficiency, would then be:
(T1 - T2) / T2
(T_1 and T_2 in this equation represent absolute temperature, a concept that was to be made clear and explicit by Kelvin some fifteen years after Carnot's death. Indeed it was Kelvin who brought Carnot's till-then-neglected work to the attention of science in 1848.)
Carnot was the first to consider quantitatively the manner in which heat and work are interconverted. He was thus the founder of the science of thermodynamics ("heat movement"). He was not correct in his views as to the nature of heat flow, for he held to the caloric theory of Lavoisier. This, however, did not affect the validity of his results.
Carnot's equation makes it clear that what counts in maximum work production are the maximum and minimum temperatures. It does not matter what happens to the temperature in between, whether it drops slowly, quickly, smoothly, or in stages. The dependence on two extreme points only and independence of the path between is characteristic of thermodynamic function. G. H. Hess a decade later showed this to be true about the heat accompanying chemical reactions.
It is possible from Carnot's equation to deduce what is now called the second law of thermodynamics and Carnot was the first to be vouchsafed a glimpse of that great generalization. He might well have gone on to bring it into the full light of day. Unfortunately, he died in a cholera epidemic at the age of thirty-six and his work was neglected. It was left to such men as Clapeyron and Clausius, a generation later, to develop Carnot's notions.
BOLTZMANN, Ludwig Edward
(bohlts' mahn)
Austrian physicist
Born: Vienna, February 20, 1844
Died: Duino, near Trieste (then in Austria, now in Italy), September 5, 1906
Boltzmann, the son of a civil servant, received his Ph.D. from the University of Vienna in 1866. His work on the kinetic theory of gases was done independently of Maxwell and they share the credit.
Beginning in 1871, Boltzmann increased the rigor of the mathematical treatment and emphasized the statistical interpretation of the second law of thermodynamics, thus founding “statistical mechanics.” He showed that Clausius' concept of increasing entropy could be interpreted as increasing degree of disorder, laying the groundwork for the later achievements of Gibbs.
He was a firm proponent of atomism at a time when Ostwald was mounting the final campaign against it. Boltzmann also advanced a mathematical treatment that explained the manner in which, according to the experimental observations of Stefan (whom Boltzmann, in his college years, served as assistant), quantity of radiation increased as the fourth power of the temperature. This is therefore sometimes called the Stefan-Boltzmann law.
Boltzmann turned down a chance to succeed Kirchhoff at Berlin but in 1894 succeeded to Stefan's post in Vienna.
Though Boltzmann lived longer than Maxwell, his life too was cut short. In his case it was suicide, brought on by recurrent episodes of severe mental depression accentuated, perhaps, by opposition to his atomistic notions by Ostwald and others.
His equation relating entropy and disorder was engraved on the headstone of his grave.