Traditional Isentropic-Eta method bases actual work on reversible work: ΛS = 0. Proposed Free-Energy-Eta method bases actual work on Gibbs Free-Energy change:
ΛG = ΛH − T* ΛS.
T is exit stream temperature, causing Free-Energy-Eta results to match Isentropic-Eta results at unity efficiency.
Free-Energy-Eta method for an engine:
Free-Energy-Eta = (Actual Work Output) / (ΛG);
Engine-Sout = (Hin − Hout) * (1 − Free-Energy-Eta) / (Free-Energy-Eta * Tout) + Sin.
As Turbine Free-Energy-Eta goes to 0, (Hin − Hout) goes to 0, keeping results finite.
Free-Energy-Eta method for a fluid driver:
Free-Energy-Eta = ΛG / (Actual Work Input);
Driver-Sout = (Hout − Hin) * (1 − Free-Energy-Eta)/ Tout + Sin.
As driver Free-Energy-Eta goes to 0, Sout goes to (Hout − Hin)/ Tout + Sin. For an air compressor (driver), zero Free-Energy-Eta corresponds to ∼0.3 Isentropic-Eta.