On the Carnot efficiency and the 2nd law of thermodynamics

A review is carried out on the general applicability of the Carnot efficiency of conversion of heat to work in a cycling engine. It is found that the expression for the calculation of such efficiency is correct when applied to cycles where the waste or unused heat from the engine is transferred outside the cycle in each and every cycle. In other words, for such engine, an entirely new amount of heat must be supplied in each and every cycle. If we call such cycle as a Carnot cycle, the 2nd law of thermodynamics is its most logical consequence whereby the efficiency of conversion of heat to work can never exceed the Carnot efficiency. Since the 2nd law of thermodynamics has the status of a law of physics, any attempt to question its validity or define its limitations is considered to be useless. Indeed, the present study confirms that the 2nd law of thermodynamics is a law of physics for the Carnot cycle, as defined above. If one considers a cycle where the waste heat is not transferred outside the cycle, but is recovered, recirculated, and re-used, one finds that the Carnot efficiency is a lower limit for higher efficiencies. The thermodynamic conditions required for a cycle to have the waste heat recovered, recirculated, and re-used are found from elementary analysis, and their validity are confirmed from numerical simulation and a proof-of-principle experiment. The consequences of such finding in terms of world yearly energy saving and climate change mitigation are highlighted.