Question

Consider a power plant with water as working fluid that operates on a reheat Rankine cycle and has a net power output of 75 MW. Steam enters the high-pressure turbine at 10 MPa and 400°C and the low-pressure turbine at 1 MPa and 400°C. Water leaves the condenser as a saturated liquid at a pressure of 100 kPa. The isentropic efficiency of the high-pressure turbine is 85% and the low-pressure turbine in 100%. The pump has an isentropic efficiency of 90%. (a) Show the cycle on a T-s diagram showing the location of the states correctly (a right schematic is fine - you do not need to calculate the temperatures at each point); (b) Determine the work done by the two turbines and the pump in KJ/kg; (c) the mass flow rate of water; (d) the thermal efficiency of the cycle (45 points)

Answer 1

Wnet = 75MW P = 10 MPa h = 3099.05 kilkg T, 400°c S = 6.2 158 Kilkgk 1 | from steam stable lo - impa . = Pz. Az = 3262.82 KJ 1 Kg Sz = 7.4634 KJ 1 KGK from Steam table T3 = 400c 7₂ = 100%. = 85% Mp=90 S =525 = 6. 2158 k3 lkg k. At P2 = Impa. h = 762.33 kJ 11g. ha = 2776.28 kJ 1 kg Sf = 2.1367 kJ 1kg k. Sg = 6.5828 kJ 1 kg k 525= St + x (Sg - Sf) 6.2158 = 2.1367 tr (6.5828 - 2.1367). [x=0.9175 has = hf & xe (hy - hf) has - 762.33 +0.9175 has = 2610.13 kilky 2776 28 - 762.33) hi ha - 3099.05 - hz M = 0.85 = hi has 3099.05 - 2610.13 The = 2683.467 kJ 1 kg Wr = hi ha = 3099.05 - 2683.467 = 415.583 kilka

1 T2 = 100Y. S₂ = Sy = 7.4634 KB) Kg k. At P = lоо кра. hurt = 417.31 - 417.31 sut = 1,3020 Lug - 2675.27. bug sug = 7.3589. VaR = 0.00 1043. melkg Sus sug state u is superheated region. hy =?? from steam table. At P=100 kPa. s = 7,4634. KIIKK. I super heated table. At s = 7.3610 h = 2676.01 s = 7.6146 h = 2776.81. Interpolation. hy - 26 76.01 - 2226.81- 2676.01 7.4634 -7.36 10 7.6146-7.3610 thu = 2716.71 kJ 1kg WT₂ = hz- hy = 32 62.82-27 16.71 | Wp = 546. 11 ks 1kg Ihs = hur = 417.31 kJ 1 kg

has hs = Vet X (P. – Py). has his = 0.001043 * (lox 103 - 100) hos hs = 10.3257. KJ 1 kg (WP)ison = 10.3257 kJ 1 kg ne = 90%. og = (Wplisen (Wp) Actual 10. 3257 (Wp) Actual = o. 9 al - N. 473 kJ) les (WP) Actual = hehs = 11.473. 5 = hut = 417.31 KJ 1 Kg honths = 11.473 kJ lig The = 11.473 + 417.31 = 428.78 KJ 1kg

lomra dywizo 25 lookpa b) = 415.583 RJ11g Already calculated WT2 = subill kilkg Wp = 11.473 kJ 1 kg c) Wines = 75x103 kW = in Wnet. Wnet = WT, +Wrz tWp = 415.583 +546.11 – 11.473. Whet = 950 122 kJ / kg 75x103 = mx950.22 in = 78.929 kg is

Whet h Qadd. cladd = (hi-ho) + (he-tho) - (30 99,05 429.78) + 3262-82- 2681.46 Q add = 3249.63 kJ 1 kg 1th = What a 950.22 Qadd 3249.63 1th = 29.24 1th = 29.24%