Equipartitioning entropy generation

This chapter establishes a direct relation between lost work and the fluxes and driving forces of a process. The Carnot cycle is revisited to investigate how the Carnot efficiency is affected by the irreversibilities in the process. We show to what extent the constraints of finite size and finite time reduce the efficiency of the process, but we also show that these constraints still allow a most favorable operation mode, the thermodynamic optimum, where the entropy generation and thus the lost work are at a minimum. Attention is given to the equipartitioning principle, which seems to be a universal characteristic of optimal operation in both animate and inanimate dynamic systems. 

Example 5.7 Equipartition principle Heat exchanger For a heat exchanger operating at steady state, the total entropy generation P is obtained by integrating over the surface area... 

The above equation implies that the extremum is a minimum. Thus, with a constant transfer coefficient, the distribution of the driving force that minimizes the entropy generation under the constraint of a specified duty is a uniform distribution. The minimal dissipation for a specified duty implies the equipartition of the driving force and entropy generation along the time and space variables of the process. 

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