Our history now turns from mechanics, the science of motion, to thermodynamics, the science of heat. The theory of heat did not emerge as a quantitative science until late in the eighteenth century, when heat was seen as a weightless fluid called “caloric.” The fluid analogy was suggested by the apparent “flow” of heat from a high temperature to a low temperature. Eighteenth-century engineers knew that with cleverly designed machinery, this heat flow could be used in a “heat engine” to produce useful work output.
The basic premise of the caloric theory was that heat was “conserved,” meaning that it was indestructible and uncreatable; that assumption served well the pioneers in heat theory, including Sadi Carnot, whose heat engine studies begin our story of thermodynamics. But the doctrine of heat conservation was attacked in the 1840s by Robert Mayer, James Joule, Hermann Helmholtz, and others. Their criticism doomed the caloric theory, but offered little guidance for construction of a new theory.
The task of building the rudiments of the new heat science, eventually called thermodynamics, fell to William Thomson and Rudolf Clausius in the 1850s. One of the basic ingredients of their theory was the concept that any system has an intrinsic property Thomson called “energy,” which he believed was somehow connected with the random motion of the system's molecules. He could not refine this molecular interpretation because in the midnineteenth century the structure and behavior—and even the existence—of molecules were controversial. But he could see that the energy of a system—not the heat—was conserved, and he expressed this conclusion in a simple differential equation.
In modern thermodynamics, energy has an equal partner called “entropy.” Clausius introduced the entropy concept, and supplied the name, but he was ambivalent about recognizing its fundamental importance. He showed in a second simple differential equation how entropy is connected with heat and temperature, and stated formally the law now known as the second law of thermodynamics: that in an isolated system, entropy increases to a maximum value. But he hesitated to go further. The dubious status of the molecular hypothesis was again a concern.