information:extraction, stylistic:tone
Phase transitions

Later in his book, Carnot considered a heat engine operating very close to the boiling point of water, alcohol, or some other working fluid. The transition between the liquid and vapor phases involves a sudden change in density (and therefore in the volume occupied by the fluid) while a latent heat is needed to transform some amount of the fluid from one phase to the other. By requiring that the volume change associated with such a transition not be available to construct what he characterized as a perpetual motion device, Carnot arrived at what would later be formalized mathematically as the " Clausius–Clapeyron relation ". In the Feynman Lectures on Physics, theoretical physicist Richard Feynman stresses that this result is due to Carnot and gives a modernized version of Carnot's original argument.

In 1849, James Thomson (the elder brother of Lord Kelvin), applied Carnot's reasoning to the freezing of water (i.e., the phase transition between liquid water and ice), and concluded that it predicted that the melting point of ice must decrease if an external pressure is applied to it, an effect that no one had ever proposed or studied before. James Thomson's prediction was later confirmed experimentally by his brother (the future Lord Kelvin), who found that the data agreed fully with Carnot's analysis. Kelvin later said of Carnot's argument that "nothing in the whole range of Natural Philosophy is more remarkable than the establishment of general laws by such a process of reasoning."