Question

(2) Steam generated in a Rankine steam power cycle at a pressure of 8 MPa and temperature 600°C is fed to a turbine. Exhaust from the turbine enters a condenser at 100 kPa, where it is condensed to saturated liquid, which is then pumped to the boiler. (a) (20 pts.) What is the thermal efficiency n of an ideal Rankine cycle operating at these conditions? (b) (5 pts.) If the net power production of the cycle is 80,000 kW, what is the steam mass flow rate (in kg/s)? (c) (15 pts.) What is the thermal efficiency of the power cycle if the turbine efficiency and pump efficiency are 75%?

Answer 1

Given Data - Boiler pressure P1 = Py = 8 MPa Condenser pressure P2 = P3 = 100 kPa Turbine inlet Ti = Gooc solution T T-S Diagram h = enthalpy of superheated vapor at 600°c and O MPa 4 a MPa 3 100KPA 2 m= 3639.5 kJ/kg S S;= specific entropy of super hected vapor at Good and & MPa s=7.019 kJ/gK Si= (isentropic process 1>2) 7.019 = sf + H2X Sfg @look Pa @ lookPa = S2 7.019 = 1.303+ Xzx 6.057 H2= 70019-1.303 Gi057 2. 0.943 2

• h₂= hf+42x hfg @ look la @ look pa - 417.5+0.9434 2257.9 h2 = 2548.28 83 kJ/kg hz=hf 417.5 kJ kJ/kg @look la = O pump work Wp O dl Look Po f Wp= 0.001043 X (2000-100 wp= 0.2397 kJ/kg Wp= hu-hz 0.2397 = hy - 41705 hy = 425.7397 kJ/kg Heat supplied Qs = hi-hy = 363915– 42507397 Qs 3213.76 KJ/kg Net work , Whet = Wy-Wp ( 1 - 2 - WP =(3639.5–2548.2837 – 2.2397

Wnet = 108 2.97 kJ/kg a thermal efficiency na Whet = Qs 1082.97.= 0.3369 3213.76 33.6 Aus b Net power = 80,000 kW (Wnet) nx Whet Power 80,000 mx 1082.97 73.87 kg/sec mass flow rate C T 14 turbine e efficiency 74 n ܝܪܨ hi ha hi-h2 3639.5-hi 3639.5 2548.283 2621 2 0.75= 크 hi = 2821.08 kJ/kg

Up puru efficiency hy-43 hy-h3 3 0.75= 425.74 - 417.5 417.5 hy. hy'= 428.406 kJ/kg Actual turbine work => Wq ha ha ha ha = 818.41K3/kg pump work Wp = ha-ha -10.986 kJ/kg Whet Wq - Wp = 807.42 kJ/kg Whet = y= 207.42 3213.76 S Ans Y = 25.12%