The Road to Entropy
The history of thermodynamics is a story of people and concepts. The cast of characters is large. At least ten scientists played major roles in creating thermodynamics, and their work spanned more than a century. The list of concepts, on the other hand, is surprisingly small; there are just three leading concepts in thermodynamics: energy, entropy, and absolute temperature.
The three concepts were invented and first put to use during a forty-year period beginning in 1824, when Sadi Carnot published his memoir on the theory of heat engines. Carnot was the pioneer, and the conceptual tools he had available to refine his arguments were primitive. But he managed, nonetheless, to invent highly original concepts and methods that were indispensable to his successors.
Carnot died in 1832, and his scientific work almost died with him. His memoir was first ignored and then resurrected, initially by his colleague Émile Clapeyron and later by two second-generation thermodynamicists, Rudolf Clausius and William Thomson. These two men were born almost at the same time as Carnot's revolutionary memoir: they were, so to speak, Carnot's scientific progeny. Just as the generation that had ignored Carnot was passing, Clausius and Thomson came of age, ventured into the world of scientific ideas, and took full advantage of Carnot's powerful, but neglected, message. Now it is Clausius's turn, but first I must digress on some mathematical matters.
To describe a system in the style of thermodynamics, one must first define the system's state with suitable state-determining variables such as the volume V and temperature t (t now stands for Celsius temperature). Small changes in V and t, brought on as the system is put through some process, are represented by dVand dt. These symbols can denote either increases or decreases, and that means dV and dt are implicitly either positive or negative. In an expansion, for example,