of the hotter reservoir. (Note: This equation probably came from Kelvin.) No thermal engine operating any other cycle can be more efficient, given the same operating temperatures. The Carnot cycle is the most efficient possible engine, not only because of the (trivial) absence of friction and other incidental wasteful processes; the main reason is that it assumes no conduction of heat between parts of the engine at different temperatures. Carnot knew that the conduction of heat between bodies at different temperatures is a wasteful and irreversible process, which must be eliminated if the heat engine is to achieve maximum efficiency. Regarding the second point, he also was quite certain that the maximum efficiency attainable did not depend upon the exact nature of the working fluid. He stated this for emphasis as a general proposition: For his "motive power of heat", we would today say "the efficiency of a reversible heat engine", and rather than "transfer of caloric" we would say "the reversible transfer of entropy ∆S" or "the reversible transfer of heat at a given temperature Q/T". He knew intuitively that his engine would have the maximum efficiency, but was unable to state what that efficiency would be. He concluded: and In an idealized model, the caloric transported from a hot to a cold body by a frictionless heat engine that lacks of conductive heat flow, driven by a difference of temperature, yielding work, could also be used to transport the caloric back to the hot body by reversing the motion of the engine consuming the same amount of work, a concept subsequently known as thermodynamic reversibility. Carnot further postulated that no caloric is lost during the operation of his idealized engine. The process being completely reversible, executed by this kind of heat engine is the most efficient possible process. The assumption that heat conduction driven by a temperature difference cannot exist, so that no caloric is lost by the engine, guided him to design the Carnot-cycle to be operated by his idealized engine. The cycle is consequently composed of adiabatic processes where no heat/caloric ∆S = 0 flows and isothermal processes where heat is transferred ∆S > 0 but no temperature difference ∆T = 0 exist. The proof of the existence of a maximum efficiency for heat engines is as follows: As the cycle named after him doesn't waste caloric, the reversible engine has to use this cycle. Imagine