Carnots Analysis of Optimal Heat-Engine Efficiency

3 CARNOT S ANALYSIS OF OPTIMAL HEAT-ENGINE EFFICIENCY 

The question of possible limits on the production of work from heat engines was taken up brilliantly by a young French military engineer, Sadi Carnot (Sidebar 4.1). Carnot s monograph of 1824, Reflections on the Motive Power of Fire, pointed to the answers to these questions in a remarkably bold and incisive (if abstract) way. Carnot introduces the question of the motive power (ability to cause movement) of fire (heat) in its most general terms  

Every one knows that heat can produce motion. That it possesses vast motive-power no one can doubt, in these days when the steam-engine is everywhere so well known. .. The question has often been raised whether the motive power of heat is unbounded, whether the possible improvements in steam-engines have an assignable limit—a limit which the nature of things will not allow to be passed by any means whatever or whether, on the contrary, these improvements may be carried on indefinitely. .. We propose now to submit these questions to a deliberate examination. 

Carnot s ensuing analysis of the steam engine culminated in an idealized engine of highest possible efficiency that could be represented as an abstract mathematical Carnot cycle in a PV diagram. Understanding the logic of this supreme thermodynamic abstraction is our first task. 

The gas first undergoes reversible isothermal expansion at th, with energy change (as required by the first law) 

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