Question

8. An ideal air-standard Brayton cycle operates at steady state with compressor indo, cuandowns of 250 K and 25 kPa. The compressor pressure ratio is 10. The turbine intes, empedunes 2 K. For the cycle: (a) the heat addition and work done in each process, in ku kg, (b) the thermal efficiency (c) the back work ratio

Answer 1

Quess - Greven - P. = 25 kPa T = 250k P2 10 P, P₂ = 10 P = 10x25 P2= 250 kPa T3= 180ok solun - a) Heat addition and w.D in each prown, Assumption - 0 Air is ideal gas having constant propertig. 0 M 1.4-1 # T()= (10) (0.4/1.4) - 10 " 1.9307 Tz = 1.934 T 1.9 37% 250 482.67 k # T3 TA = (rp) = (10) 0.4/1.4 TA= T3 1800 932.3k (1039454 (10 30.4/1.9 Compressor :- Compressor follous reversible adiabatic process. 1Q1-2=0 KI -W12= m(ha hi) for unit mass Wrz= Cp (T2-T1) - Wr2 = 1.005 (482.67-250)= 23.83 kJ/kg W1-2=-233.83 Kulkg

Combestion Chamber - W2-3=0 Kilkg Constant pressure Heat addition. 2-3 = (hz-h2) = Cp (T3-T2) = 1.005 (1800 - 482.67) Q2-3 = 1323.91 kolleg 80 Turbine - I sentropic expansion Q3-4 = 0 kolleg adiabatic prouss. W3-4 = (ha-hal = 6 (73-Tq) = 1.005(1800-932.3) W3-4 = 872.03 Kalkg Condenser - Constant pressure Heat rejection. IW,.q=o koleg 21-4 = (hi-ha) = (p (Ti-T8) = 1.005(250-932-3) Q1-4 = - 685.71 Kalkg. (b) Thermal efficiency, - th= Wnet Q2-3 こ Wy - Wc Q2-3 ntha 872.03-233.83 1323.91 = 0.482 In th=48.2%. (c) Back work ratio: - We Wi-2 W3-4 233.83 872.03 = 0.26814 Te = 0.26814 # PLS RATE I