Question

Consider a power plant with water as the working fluid that operates on a Rankine cycle. It has a net power output of 40 MW. Superheated steam enters the turbine at 8 MPa and 600°C (h = 3642 kJ/kg; s = 7.0206 kJ/kg K) and is cooled in the condenser at a pressure of 10 kPa by running cooling water from a lake through the tubes of the condenser. The isentropic efficiency of the turbine is 85%. The pump has an isentropic efficiency of 100%.
(a) Show the cycle on a T-s diagram (a right schematic is fine - you do not need to calculate the temperatures at each point);
(b) Determine the work done by the turbine and the pump in KJ/kg;
(c) the mass flow rate of water used by the power plant;
(d) the thermal efficiency of the cycle;
(e) the back work ratio

Answer 1

Fra No Page 1 ta) T 873 k. h₂ = 3642 KJ ling Khayk 3 S3 = 7.0 206 S3=Sus 2 P2 = P3 = 8 MPa Чs Ч P = P4 = py=1 = 10kpa S (Misen -0.85 Turbine At 10 kPa : sp = 0.65173 K lagik Sg = 8- 1953 Klaga hf = 192.62 KJ /hgk, hg = 2584.2 KI/kg Vf=0.00101036 m3kg We have, S3=Sus =>7.0206 = 0.65173 + x[8.1453 -0.6173) - x = 0.85 hys = 2225.463 = 0.85 = 3642-2225.463 » hus 192.62 t 0.85 (2589.2 - 192. 92:62) KJ/kg hz-hy 3642-hy Misen) Turbine hz-hus =) hy = 2437.74 KJ Ang by the turbine (KI/kg) = hz-hy = 3642-2437.74 = 1204.259 kJ/kg (6) Work done

Engen 2 (c) Wpamp v dp = v 182 p.) = (p2-2) = 0.00101 x (8X102-10) 8.0699 Kiling Net work power output ins (W Turbine Wpump) 40x lol mis (1204.259 - 8.0699 =) ins 33.439 kg/s (d) nt of heat supplied 3 Net power Yoxlo Rate ins (hz - hz) We have, h₂ h = 8.0699 h = h + 8.0699 = 192.62+8.0699 = 22 200.6899 KJ 3 Yoxlo 1th = 33.4398 ( 3642 - 200.6899 = 0. 3476 or 34.76% (e) Back work ratio = Wpump = 8.0699 WTurebine 1204.259 = 6.70 1 x 10