A Historical Epistemology of Thermodynamics. the Mathematics in Sadi Carnot's Theory

Abstract

The mathematical footnote mathematical footnote in Réflexions sur la puissance motrice du feu Réflexions sur la puissance motrice du feu can be considered the highest mathematical level presented by Sadi Carnot Sadi Carnot in his book. It also represents his way of mathematically interpreting physical phenomena and the relationship relationship between physics and mathematics in thermodynamics thermodynamics. Without proposing new concepts or sophisticated functions in trying to explain the modernity of the result obtained by Sadi Carnot Carnot, here we will present an historical analysis of the footnote. Moreover, strictly based on primary sources and documents, we will provide an epistemological interpretation of the arguments that Sadi Carnot used to calculate the formula of the efficiency efficiency of a heat machine heat machine; and centring on the role of shared knowledge, of challenging objects, and of knowledge reorganization. The idea is presenting an integrated history and epistemology of scientific methods which combine epistemological and historical approaches to identify significant historical hypotheses. Such epistemological interpretations are subjected to historical facts of scientific activity and original documents in order to trace their historical development. In this case the discussion regards Carnot's mathematical foundations, considering both the relationship between physics and mathematics and the mathematical (infinitesimal) analysis infinitesimal analysis of the nineteenth century.