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

Solu T 3 Qs WT 4 2 t Wc S Given T = 250K P = 25kla = P₂ Pressure ratio (e) = 10 Turbine inlet temperature T3 = 1800k PO For 1-2 Process (isentropic process T Y for air = 1.4 ته انه Ti Pi 1.4-1 0.2857 Ta T (4) T 482.67K Work done in compressor Wr = CP (T₂-T) KJ kg = 1.005 (482.67-250) Wc = 233.833 kJ/kg For 2-3 Process Heat addition (pa Qs (T3-T2) = 1.005 (1800 - 482.67) Qs = 1323.62 KJ / kg

For 3-4 Prouss Y Y-1 r isentropic T3 P3 1.4-1 1.4 > Ty Pu = 0.2857 0.2857 Tz () Tu Ty Tz 0.2857 (10) Ty 1800 1.930634 Tu 932.34 K Work done by Turbine WT = Сео KI Kg (T3 - Tu = 1.005 (1800 ~ 932.34) WT=872.029 KJ) Kg. 어 (b) Thermal efficiency not Work done Net Heat addition WT Wc (872.022 - 233.833) KJ 1 kg 1323.62 KII kg = 0.48215 IT 48.221. Back Work Ratio > BWR Wc Compressor work Turbine Work WT BWR Wc 233.833 WT 872.022 BWR = 0.268