A Remarkable Triangle

The second law in the form that suits us best states that in real processes, and thus in engineering practice, the production of entropy is positive  

By applying the first and second laws to processes in which heat and work are exchanged with the environment at P0, T0, we have shown before that this generated entropy is associated with a loss of work according to 

On the other hand, irreversible thermodynamics has provided us with the insight that entropy generation is related to process flow rates like those of volume, V, mass in moles, h, chemical conversion, vl h, and heat, Q, and their so-called conjugated forces A(P/T), -A(p/T), A/T, and A(l/T). Although irreversible thermodynamics does not specify the relationship between these forces X and their conjugated flow rates /, it leaves no doubt about the 

The simple conclusion that we can now draw is that the work lost can be directly related to the process s flows and driving forces. By eliminating Sgen from Equations 5.2 and 5.3, we obtain 

With X, approaching zero, lost work will approach zero, but this result is not very realistic as flows will tend to become zero too. In practice, we deal with an equipment of finite size that we wish to operate in finite time. So, the question arises With these constraints, what is the minimum amount of lost work Thus, it is clear that minimization of lost work and thus of entropy production is a challenging subject with many aspects. 

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