Lost work, extra work and entropy production for a system with complexity: The stepwise ideal-gas Carnot cycle

Abstract

This paper is an extension of a previous paper [Phil. Mag. 87 (2007) p.569] devoted to lost work and entropy production. Here, we also introduce extra work (i.e. W _Extra=W _in–W _Rev) in an irreversible process and apply both concepts to the analysis of a system with complexity: the stepwise ideal-gas Carnot cycle. A stepwise Carnot cycle is performed by means of N small weights (here called dws), which are first added and then removed from the piston of the vessel containing the gas. The work performed by the gas can be found as an increase in the potential energy of the dws. We identify each single dw and evaluate the rise; i.e. its increase in potential energy. Thus, we find how the energy output of the cycle is distributed among the dws. The size of the dws affects entropy production and, therefore, the lost and extra work. The raising distribution depends on the removal process chosen. Since these processes are N!, there are N! distributions for the raisings of the dws

Keywords:

• entropy
• Carnot cycle
• complexity

Acknowledgement

I am indebted to M. Zannetti and G. Monroy for their useful comments.

Notes

Note

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