Action and entropy in heat engines: An action revision of the Carnot cycle

Action (@) is a state property with physical dimensions of angular momentum (mrv=mr²ω). But it is scalar, rather than a vector, with a finite phase angle for change (mr²ωδθ). We have shown (Entropy 21,454) that molecular entropy (s) is a logarithmic function of mean values of action (s = kln[e^u(@_t/ħ)³(@_r/ħ)^2,3(@_v/ħ)], where k is Boltzmann’s constant, ħ Planck's quantum of action, u the kinetic molecular freedom; mean action values for translation (@_t), rotation (@_r) and vibration (@_v) are easily calculated from molecular properties. This is a novel development from statistical mechanics, mindful of Nobel laureate Richard Feynman’s favored principle of least action. The heat flow powering each engine cycle is reversibly partitioned between external mechanical work with compensating internal changes in the action and chemical potential of the working fluid. Equal entropy changes at the high temperature source and the low temperature sink match equal action and entropy changes in the working fluid. Asymmetric variations in quantum states with volume occur isothermally but constant action (mr²ω) is maintained during the adiabatic or isentropic phases. The maximum work possible per reversible cycle (-ΔG) is the net variation in the configurational Gibbs function of the working fluid between the source and sink temperatures. The engine’s inertia compensates so that external kinetic work performed adiabatically in the expansion phase is restored to the working fluid during the adiabatic compression, allowing its enthalpy to return to the same value, as claimed by Carnot. Restoring Carnot’s non-sensible heat or calorique as action as a basis for entropy will be discussed in the context of designing more efficient heat engines, including that powering the Earth’s climate cycles where we introduce the concept of vortical entropy for cyclones and anticyclones.