Polytropic reversible expansion

Clearly, if A is zero (no heat transfer), then the normal polytropic relation holds. A point of interest is that if Tjp = (1 — A) then rj = 1 and the expansion becomes isentropic (but not reversible adiabatic). 

Perfect (reversible) one-time-expansion adiabatic ERR of our gas, or even imperfect (irreversible) adiabatic or even polytropic (intermediate between adiabatic and isothermal)... 

A very important special case of the polytropic flow equation (5.25) is that describing a reversible, adiabatic expansion, where no heat is exchanged with the surroundings, i.e. an isentropic expansion. In this case, the ratio of specific heats, y, is substituted for n in the mass-flow equation ... 

Achieving sonic flow during an isothermal expansion is a highly improbable eventuality because the rapid heat transfer needed would take a great effort to contrive. Nevertheless, it is a theoretical possibility and has an interest as the limiting case of a reversible polytropic expansion. Accordingly a brief treatment will be provided here for completeness. 

The expander efficiency was calculated with aid of a polytropic expansion coefficient of 1.67, that is, an isotropic efficiency of 70%. A reversible process [22] is totally misleading for determining the potential of such a hybrid system. In addition, the mechanical and electrical transmission losses were evaluated with a transmission efficiency of 95%. 

Both the processes in this section can be considered polytropic. The isothermal expansion of an ideal gas follows Equation (2.49) with 7 = 1 while the reversible, adiabatic expansion of an ideal gas with constant heat capacity has y = k = c lc . Can you think of another example of a polytropic process ... 

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