Thermodynamics

h C w s h 4a2s h 1(9–19)2a4sw a h 2a h 1 2sChapter 9 | 513The thermal efficiency could also be determined fromh th 1 q outq inwhereq out h 4 h 1 789.37 300.19 489.2 kJ>kgDiscussion Under the cold-air-standard assumptions (constant specific heatvalues at room temperature), the thermal efficiency would be, from Eq. 9–17,h th,Brayton 1 11 1 0.448r 1k12>k11.412>1.4p8which is sufficiently close to the value obtained by accounting for the variationof specific heats with temperature.TPressure dropduring heataddition3Deviation of Actual Gas-Turbine Cyclesfrom Idealized OnesThe actual gas-turbine cycle differs from the ideal Brayton cycle on severalaccounts. For one thing, some pressure drop during the heat-addition and heatrejectionprocesses is inevitable. More importantly, the actual work input to thecompressor is more, and the actual work output from the turbine is lessbecause of irreversibilities. The deviation of actual compressor and turbinebehavior from the idealized isentropic behavior can be accurately accountedfor by utilizing the isentropic efficiencies of the turbine and compressor asandh T w a h 3 h 4a(9–20)w s h 3 h 4swhere states 2a and 4a are the actual exit states of the compressor and theturbine, respectively, and 2s and 4s are the corresponding states for the isentropiccase, as illustrated in Fig. 9–36. The effect of the turbine and compressorefficiencies on the thermal efficiency of the gas-turbine engines isillustrated below with an example.1Pressure dropduring heatrejectionFIGURE 9–36The deviation of an actual gas-turbinecycle from the ideal Brayton cycle as aresult of irreversibilities.sEXAMPLE 9–6An Actual Gas-Turbine CycleAssuming a compressor efficiency of 80 percent and a turbine efficiency of85 percent, determine (a) the back work ratio, (b) the thermal efficiency,and (c) the turbine exit temperature of the gas-turbine cycle discussed inExample 9–5.Solution The Brayton cycle discussed in Example 9–5 is reconsidered. Forspecified turbine and compressor efficiencies, the back work ratio, the thermalefficiency, and the turbine exit temperature are to be determined.