A Continued Fraction Expression for Carnot Efficiency

A new and interesting continued fraction expression is derived for Carnot efficiency. The derivation is based on a series combination of a set of Carnot heat engines, wherein heat rejected by a member of the series is absorbed by the following member of the series. Our analysis of this combination of Carnot heat engines shows that mathematical consistency is maintained only if the efficiency of Carnot heat engine is zero. This calls the attention of researchers to look back at the puzzling definition of Carnot efficiency that says the efficiency of ideal heat engine (Carnot heat engine) is less than one, in spite of the fact that each of the steps involved in the cycle of operation is hundred percent efficient.