Entropy production and lost work for some irreversible processes

In this paper we analyze in depth the lost work in an irreversible process (i.e. W-Lost = W-Rev - 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 T Delta S-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, pi(int) and pi(ext), quantities which also enable the Clausius inequality to be written in a simple form. Examples are given for elementary processes.