Calculating polytropic efficiencies is a basic task used for quantifying performance of power cycles involving compression and/or expansion. The incremental definition of a “polytropic curve” of gases by Gustav Zeuner in 1905 may be the oldest mention of the word “polytropic” in a thermodynamic context .
In Turbomachinery blading, the typical changes of state are nearly adiabatic and polytropic. L. S. Dzung was probably the first defining an incremental polytropic efficiency in 1944 . Recursive integration of this has become the best thermodynamic quality measure of a blading.
Thus, we face now two definitions of a polytropic change of state, which are theoretically identical for ideal gases but different for real gases and vapors. In educational context, this is disturbing and forcing to a logical detour. We trace the historic roots and show that the initial incremental definition is the physically healthier one. Recursive integration allows direct application to turbomachinery with any finite pressure ratio and to any real fluid.