Carnot and the fields formulation of elementary thermodynamics

Thermodynamics centers on the fact that work and heat are not functions of state. However, the natural formalism to capture this fact was not incorporated into thermodynamics because it was formulated before the development of vector field notation. One reason for reexamining this omission is provided by the work of Sadi Carnot that initiated thermodynamics. His results, which he derived from his grand principle, were not obtained by what is now called the 2nd law of thermodynamics or by the 1st law of thermodynamics. Instead they were obtained by a (co)vector formula, albeit expressed in words not symbols. Carnot’s formula allowed him to obtain several standard results of thermodynamics, including the Clausius-Clapeyron equation. The formula also implies the Maxwell relations.