The irreversible simple cycle

A closed cycle [CHT]i, with state points 1,2,3,4, is shown in the T,s diagram of Fig. 3.7. The specific compressor work input is given by 

The important point here is that the efficiency is a function of the temperature ratio 6 as well as the pressure ratio r (and d, whereas it is a function of pressure ratio only for the reversible cycle, [CHT]r. 

The isentropic temperature rise for maximum specific work (J , ) is obtained by differentiating Eq. (3.11) with respect to x and equating the differential to zero, giving 

In their graphical interpretations, using isentropic rather than polytropic efficiencies, Hawthorne and Davis plotted the following non-dimensional quantities, all against the parameter. v =  

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