Deviation of Actual Gas-Turbine Cycles from Idealized Ones The actual gas-turbine cycle differs from the ideal Brayton cycle on several accounts. For one thing, some pressure drop during the heat-addition and heat- rejection processes is inevitable. More importantly, the actual work input to the compressor is more, and the actual work output from the turbine is less because of irreversibilities. The deviation of actual compressor and turbine behavior from the idealized isentropic behavior can be accurately accounted for by utilizing the isentropic efficiencies of the turbine and compressor as (9–19) and (9–20) where states 2a and 4a are the actual exit states of the compressor and the turbine, respectively, and 2s and 4s are the corresponding states for the isen- tropic case, as illustrated in Fig. 9–36. The effect of the turbine and com- pressor efficiencies on the thermal efficiency of the gas-turbine engines is illustrated below with an example. h T = w a w s  h 3 - h 4a h 3 - h 4s h C = w s w a  h 2s - h 1 h 2a - h 1 Chapter 9 | 513 The thermal efficiency could also be determined from where Discussion Under the cold-air-standard assumptions (constant specific heat values at room temperature), the thermal efficiency would be, from Eq. 9–17, which is sufficiently close to the value obtained by accounting for the varia- tion of specific heats with temperature. h th,Brayton = 1 - 1 r 1k-12>k p = 1 - 1 8 11.4-12>1.4 = 0.448 q out = h 4 - h 1 = 789.37 - 300.19 = 489.2 kJ> kg h th = 1 - q out q in s T 2s 3 1 2a Pressure drop during heat addition Pressure drop during heat rejection 4s 4a FIGURE 9–36 The deviation of an actual gas-turbine cycle from the ideal Brayton cycle as a result of irreversibilities. EXAMPLE 9–6 An Actual Gas-Turbine Cycle Assuming a compressor efficiency of 80 percent and a turbine efficiency of 85 percent, determine (a) the back work ratio, (b) the thermal efficiency, and (c) the turbine exit temperature of the gas-turbine cycle discussed in Example 9–5. Solution The Brayton cycle discussed in Example 9–5 is reconsidered. For specified turbine and compressor efficiencies, the back work ratio, the ther- mal efficiency, and the turbine exit temperature are to be determined.