1. The contemplation of the actual working of heat engines, and of their great development in England, with which he was well acquainted, suggested, to the mind of Sadi Carnot, the fundamental principle regulating their operation. He postulated that heat can give rise to mechanical work only in the process of carrying through its effort towards an equilibrium. This idea involves immediately the whole of isothermal thermodynamics, including the modern thermodynamic potentials of physical chemistry; for it asserts that, in isothermal circumstances, the heat that is present takes no part in the interchanges of mechanically available energy in the material system, and therefore that the available energy is conserved by itself (or in part dissipated if the operation is irreversible) without any reference to the heat-changes which accompany its transformations. An argument—perhaps the most original in physical science, whether as regards simple abstract power or in respect of grasp of essential practical principles—which was based on combining direct and reversed simplified engines operating in parallel, then led Carnot from this general postulate to a quantitative thermodynamic relation, fundamental for all departments of natural knowledge: that all reversible cyclic thermal operations, involving supply and abstraction of heat at the same two temperatures, have equal mechanical efficiency, which is the maximum possible. But he allowed himself, in his demonstration, somewhat reluctantly, and perhaps hastily in order to fix the ideas, to adopt the view then current that heat is substantial, so cannot be annulled or created. This point came right later, without trouble, in the corrected expositions by Clausius and W. Thomson, once a net of misconception, arising partly from confusion between total energy and mechanically available energy, had been cleared away. The whole matter ought, however, to be capable of abstract development on broader and more general lines; and the following statement is now advanced to that end. The rough manuscript notes left by Carnot at his death show his own early and very substantial progress towards a more complete doctrine of thermal motive power.
Modeling of the thermo-mechanical efficiency of the bimetal strip heat engines
