Dissipated Energy and Entropy Production for an Unconventional Heat Engine: The Stepwise "Circular Cycle"

International audienceWhen some entropy is transferred, by means of a reversible engine, from a hot heat source to a colder one, we have the maximum of efficiency. Similarly the reversible heat pumps transfer entropy from a cold heat source to a hotter one with the minimum expense of energy. On the contrary if we are faced with non reversible devices there is some Lost Work for heat engines, and some Extra Work for heat pumps. These quantities are both related to the Entropy production. The Lost Work, i.e. WLost=WRev-WIrrev , is also called 'degraded energy' or 'Energy unavailable to do work'. The Extra Work, i.e. WExtra= WIrrev- WRev, is the excess of work performed on the system in the irreversible process with respect to the reversible one. In this paper, which follows two previous ones on the Lost Work [Phil. Mag. 87, 569 (2007), Phil. Mag. 88 4177-4187 (2008)] both quantities are analyzed in deep and are evaluated for a process with complexity, i.e. the stepwise Circular Cycle. The stepwise Circular Cycle is a cycle performed by means of N small weights dw which are first added and then removed from the piston of the vessel containing the gas or vice versa. The work performed by the gas can be found as increase of the potential energy of the dw's. We identify each single dw and thus evaluate its rising i.e. its increase in potential energy. We find how the energy output of the cycle is distributed among the dw's