Dissipated energy and entropy production for an unconventional heat engine: the stepwise ‘circular cycle’

Abstract

When some entropy is transferred, by means of a reversible engine, from a hot heat source to a colder one, the maximum efficiency occurs, i.e. the maximum available work is obtained. Similarly, a reversible heat pumps transfer entropy from a cold heat source to a hotter one with the minimum expense of energy. In contrast, 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 entropy production. The lost work, i.e. , is also called ‘degraded energy’ or ‘energy unavailable to do work’. The extra work, i.e. , is the excess of work performed on the system in the irreversible process with respect to the reversible one (or the excess of heat given to the hotter source in the irreversible process). Both quantities are analysed in detail and are evaluated for a complex process, i.e. the stepwise circular cycle, which is similar to the stepwise Carnot 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 the increase of the potential energy of the dw's. Each single dw is identified and its increase, i.e. its increase in potential energy, evaluated. In such a way it is found how the energy output of the cycle is distributed among the dw's. The size of the dw's affects entropy production and therefore the lost and extra work. The distribution of increases depends on the chosen removal process.

Keywords:

• entropy production
• thermodynamics
• recovery
• thermal analysis

Acknowledgements

We thankfully acknowledge G. Monroy, P. Ruggiero and M. Zannetti for helpful comments. This paper is dedicated to the memory of Giuliano Martinelli for his pioneering works on energy production and storage.

Notes

Note

1. The quantities Q _in, Q _out and Q _Rev are positive.