Clausius proposed a reversible thermodynamic cycle made up of three isothermal processes and three adiabatic processes to establish the theorem of the equivalence of the transformation of heat to work and the transformation of heat at a higher temperature to a lower temperature. Then, he derived the Clausius equality and the concept of entropy (later called thermal entropy to prevent confusion). Similarly, this study uses a reversible reversed thermodynamic cycle made up of three isobaric processes and three isochoric processes to establish the theorem of the equivalence of the transformation of work to heat and the transformation of work at a higher pressure to a lower pressure, and then derives a corresponding equality for a reversed thermodynamic cycle and the concept of work entropy. The work entropy is shown to be equal to the system volume which is the core physical quantity of a reversed thermodynamic cycle. Although this is not a new quantity, the work entropy gives the volume a new physical interpretation corresponding to thermal entropy. Next, by analogy with the definition of exergy (later called thermal exergy to prevent confusion), the work exergy is defined as the maximum heat output that can be transformed from the work in a system at pressure p though a reversed p-V cycle under ambient pressure. Furthermore, the work exergy of the working medium is defined as the sum of the heat that the working medium outputs though a series of reversed p-V cycles and the heat that the working medium outputs directly as the temperature varies, as the working medium changes reversibly from any state to the state in balance with the environment. The physical meanings of the work entropy and the work exergy are illustrated with comparisons to the thermal entropy and the thermal exergy. When it changes reversibly from any state to the state in balance with the environment, the working medium with more thermal entropy will have more unavailable energy T-0(S-T-S-T0) and, thus, less thermal exergy, if the system outputs work through a reversible thermodynamic cycle. In contrast, the working medium with more work entropy will have less unavailable energy p(0)(V-0-V) and, thus, more work exergy, if the system outputs heat through a reversible reversed thermodynamic cycle. Thus, the work entropy can measure the unavailable energy of the working medium while the work exergy can measure the available energy of the working medium. The "pressure-work entropy diagram" can be used to intuitively analyze a reversed thermodynamic cycle. Finally, a least action principle is proposed for reversible thermodynamic processes. When the heat-to-work action, Delta S/Q reaches a minimum, the optimal heat-to-work process is obtained that is the combination of an isothermal process and an adiabatic process. When the work-to-heat action, Delta V/W reaches a maximum, the optimal work-to-heat process is obtained that is the combination of an isobaric process and an isochoric process.
