dtheoptimaltimepathofanOttocyclewithfrictionandheatleakage.Optimalityisdefinedbymaximizationoftheworkpercycle;thesystemisconstrainedtooperateatafixedfrequency,sothemaximumpower-isobtained.Theresultisanimprovementofaboutintheeffectiveness(second-lawefficiency)ofaconventionalnear-sinusoidalengine.Finite-timethermodynamicsisanextensionofconventionalthermodynamicsrelevantinprincipleacrosstheentirespanofthesubject,fromthemostabstractleveltothemostapplied.Theapproachisbasedontheconstructionofgeneralizedthermodynamicpotentials()forprocessescontainingtimeorrateconditionsamongtheconstraintsonthesystem()andonthedeterminationofoptimalpathsthatyieldtheextremacorrespondingtothosegeneralizedpotentials.Heretofore,workonfinite-timethermodynamicshasconcentratedonratheridealizedmodels(-)andonexistencetheorems(),allontheabstractsideofthesubject.Thisworkisintendedasastepconnectingtheabstractthermodynami