A critique of Sadi Carnot's work and a mathematical theory of the caloric

TL;DR

This paper critically examines Sadi Carnot's foundational work in thermodynamics, contrasting it with modern theories, and develops a mathematical framework based on caloric theory's principles.

Contribution

It provides a mathematical formulation of Carnot's work grounded in caloric theory, highlighting differences with modern thermodynamics.

Findings

Carnot's work can be mathematically modeled using caloric theory

Caloric theory's dQ as a perfect differential offers new insights

Contrasts between classical and modern thermodynamics are clarified

Abstract

In this work, Sadi Carnot;s fundamental work is critically examined, and contrasted with modern thermodynamics. A mathematical theory of his work is given on the basis of the observation that in caloric theory dQ is a perfect differential.