Question

8. An ideal air-standard Brayton cycle operates at steady state with compressor inlet conditions of 250 K and 25 kPa. The compressor pressure ratio is 10. The turbine inlet temperature is 1800 K. For the cycle: (a) the heat addition and work done in each process, in kJ/kg, (b) the thermal efficiency (c) the back work ratio (35 points)

Answer 1

m mm = 25 kipa PL PL P3 PG 2 Sol Given dala:- compressor inlet temperature (7,5 - 950k pressure CPD compressor pressure ratio CM) : 10 - turbine inlet temperature CT3)= 1800 K Given temperature CT, ) - 250K iscentropic process (1)-(2) "] 1-4-1 = 300 [10] 109 Wtor T Qin 4 K-1 K 2 Encamp acut K-1 к 5 :: T2 - = 579. 209 k • Tz - 579. 20922 Given turbine inlet temperature CT3] = 1800k Ty K-1 . K PIN [en Py P3 T3 K-1 . Ty = T3 Pyk P3 1.4-) 1.9 1800[767

= 932. 305 k 932. 305 K Ty = hoffe done by the turbine (total cycle) CP [CTz- T4] - CT2-T;]] - 1.005 [C1800 - 932• 305) -(579.209 - 3 - 300)] .: wicycle = 591.428 kylng 591.428 kJ/kg .. Wcycle heat addition din CP CT3-T2] -- = 1.005(1800 - 579.209) = 1226.894 kylng .: ein + 1226.894 kg Ing Therefore Ncycle thermal efficiency Coh2 in 591.428 1226-894 = 0.48 20 = 48.2%. - Thermal Efficiency C276 3 = 48.2%

Therefore Back wolk ralio (BWR) - Workinput to the compressor work output of the turbine I comp in Weurbout T2-TI CP CT2-T CP CT4 -T4) T3-TY 519-209 - 300 1800 - 932.305 = 0.3217 .: Back work ratio CBWR) (BWR) = 0.3217