Thermodynamics

514 | ThermodynamicsT, K13003002s12aq inq out34aFIGURE 9–37T-s diagram of the gas-turbine cyclediscussed in Example 9–6.4ssAnalysis (a) The T-s diagram of the cycle is shown in Fig. 9–37. The actualcompressor work and turbine work are determined by using the definitions ofcompressor and turbine efficiencies, Eqs. 9–19 and 9–20:Compressor:Turbine:Thus,w comp,in w s 244.16 kJ>kg 305.20 kJ>kgh C 0.80w turb,out h T w s 10.852 1606.60 kJ>kg2 515.61 kJ>kgr bw w comp,in 305.20 kJ>kgw turb,out 515.61 kJ>kg 0.592That is, the compressor is now consuming 59.2 percent of the work producedby the turbine (up from 40.3 percent). This increase is due to theirreversibilities that occur within the compressor and the turbine.(b) In this case, air leaves the compressor at a higher temperature andenthalpy, which are determined to beThus,andw comp,in h 2a h 1 S h 2a h 1 w comp,inh th w netq inThat is, the irreversibilities occurring within the turbine and compressorcaused the thermal efficiency of the gas turbine cycle to drop from 42.6 to26.6 percent. This example shows how sensitive the performance of agas-turbine power plant is to the efficiencies of the compressor and theturbine. In fact, gas-turbine efficiencies did not reach competitive valuesuntil significant improvements were made in the design of gas turbines andcompressors.(c) The air temperature at the turbine exit is determined from an energy balanceon the turbine:Then, from Table A–17, 300.19 305.20 605.39 kJ>kg1and T 2a 598 K2q in h 3 h 2a 1395.97 605.39 790.58 kJ>kgw net w out w in 515.61 305.20 210.41 kJ>kg210.41 kJ>kg 0.266 or 26.6%790.58 kJ>kgw turb,out h 3 h 4a S h 4a h 3 w turb,outT 4a 853 K 1395.97 515.61 880.36 kJ>kgDiscussion The temperature at turbine exit is considerably higher than thatat the compressor exit (T 2a 598 K), which suggests the use of regenerationto reduce fuel cost.