On the structure of Carnot's theory of heat

A simple connection is pointed out between the theory of heat formulated in Sadi Carnot's: Réflexions sur la puissance motrice du feu (1824) and the later Kelvin-Clausius thermodynamics. In both theories two well-defined quantities, a heat function and a work function, exist and can be calculated by integrating along a reversible path. In thermodynamics the work function (energy) is conserved, whereas the heat function (entropy) increases by irreversible processes. In Carnot's theory the heat function is conserved, whereas the work function decreases, so that in this theory the irreversible process is characterized by a loss of work.