Chapter 20, Problem 78GP

A gas turbine operates under the Brayton cycle, which is depicted in the PV diagram of Fig. 20-28. In process ab the air-fuel mixture undergoes an adiabatic compression. This is followed, in process bc, with an isobaric (constant pressure) heating, by combustion. Process cd is an adiabatic expansion with expulsion of the products to the atmosphere. The return step, da, takes place at constant pressure. If the working gas behaves like an ideal gas, show that the efficiency of the Brayton cycle is

$e=1-{\left(\frac{P_b}{P_a}\right)}^{\frac{1-y}{y}}.$

FIGURE 20-28

Problem 78.