A. Entropy generation is proportional to lost work

We begin with a brief look at why in EGM we must rely on heat transfer and fluid mechanics, not just thermodynamics. Consider the open thermodynamic system (control volume) shown in Figure 1, where, for simplicity, only one of the heat transfer interactions \(\dot{Q}_{i}\) (i = 0, 1, ..., n) is shown. Each heat transfer interaction \(\dot{Q}_{i}\) is accompanied by the entropy transfer \(\dot{Q}_{i}\) /T_i, where T_i is the absolute temperature of the boundary point crossed by \(\dot{Q}_{i}\). The thermodynamic analysis of the system is based on three statements, mass conservation, the first law, and the second law Bejan (1988).

\[\label{eq1} \frac{\partial \mbox{M}}{\partial t} = \sum\limits_{\rm in}\dot{m} - \sum\limits_{\rm out}\dot{m}\tag{1}\]

\[\label{eq2} \frac{\partial \mbox{E}}{\partial \mbox{t}} = \sum\limits_{{\rm i} = 0}^ {\rm n} \dot {Q}_{i} - \dot{\rm W} + \sum\limits_{{\rm in}}\dot{m}\left(h + 1/2V^{2} + {\rm gz}\right) - \sum\limits_{out}\dot{m}\left(h + 1/2V^{2} + gz\right)\tag{2}\]

\[\label{eq3} \frac{\partial S}{\partial t} \geq \sum\limits_{i = 0}^{n}\frac{\dot{Q}_{i}}{T_{i}} + \sum\limits_{in}\dot{m}s - \sum\limits_{out}\dot{m}s\tag{3}\]