Entropy production and lost work for some irreversible processes

Abstract

In this paper we analyze in depth the lost work in an irreversible process (i.e. W _Lost = W _{Re v} − W _Irrev). This quantity is also called ‘degraded energy’ or ‘energy unavailable to do work’. Usually in textbooks one can find the relation W _Lost ≡ TΔS_U , which, for many processes, is not suitable for evaluation of the lost work. Here we find for W _Lost a more general relation in terms of internal and external entropy production, π _int and π _ext, quantities which also enable the Clausius inequality to be written in a simple form. Examples are given for elementary processes.

Acknowledgments

This work is mainly due to useful discussion with Marco Zannetti, Caterina Gizzi Fissore, Michele D’Anna and Corrado Agnes and with my friend Franco Siringo to whose memory this paper is especially dedicated. This version of the paper is due to the many encouraging remarks of the referee, which are welcomed and acknowledged.