Question

A coal-fired steam power plant produces 175 MW of electric power. The power plant operates on a Rankine cycle with turbine inlet conditions of 7 MPa and 550oC and a condenser pressure of 15 kPa. The turbine efficiency and pump efficiency are both 0.8. The coal has a heating value (energy released when the fuel is burned) of 29,300 kJ/kg. Assuming that 85 percent of this energy is transferred to the steam in the boiler and that the electric generator has an efficiency of 96 percent, determine

(a) the overall plant efficiency (the ratio of net electric power output to the energy input as fuel) and

(b) the required rate of coal supply

c) fill the table

stream	state	T(C)	P(kPa)	H(kj/kg)
1
2
3
4

Answer 1

Solution Obtain the properties of steam at 15k Pa VI - V -0.001014 m/kg hi hy = 265.94 kJ /kg hfg: 2372.3 kJ/kg SE -0.7549 kJ / kgk Sta = 7.2522 kJ / kg k. Determine the work on the pump (wglm = V (P2 - P.) -0.001014 ( 7000-15) = 7.08279 kJ/kg Determine the enthalpy at state 2 he e hi + (Wolm -925.94 +7.08279 =233022 kJ /kg Obtain the properties of the steam at 7 MPa 'and 550°c he - 3530.8 kJ/kg Sq: 6.949kJ/kgki As the process 3-4 is isentropic process, ولع ول Sf + Ny Sfo = 6.949 0.7549 +7.522 X4 = 6.949 xu=0.854 Determine the enthalpy at state 4 hu=hp + Xu har =925.94 +0.854 (23723) 52251.88 kJ/kg

Determine the heat input to the cycle 9 in hi-he -3530.8. 233.022 - 3297.778 kJ/kg Determine the heat output from the cycle yout = hu-hi 22251.88 - 225.94 -2025.94 kJ / kg " Determine the thermal efficiency n=1 - Yout qin =1 - 2025.94 3 297.778 - 38.56% Determine the overall efficiency п: 1, x1 x out -0.3856 80.85x0.96 - 31477 b) Determine the required rate of coal Qin = W -175000 0.3147 = 556085.1605 kW

Determine the mass flow rate of the coal 7MPA -556085.1605 Din 29300 1 Rout -18.979 kg/s = 0.018979 kg / = 68.324 ton In c) Refer to saturated water - pressure table and interpret h, and vi at pressure CP, = 15k Pad hicho=225.94 kJ /kg V-V-0.001014 m3 /kg Expres the specific work input to the cycle (Wpin I. Wpin - Vi (Px-P) Here press we af state ! i Pr. pressure at state, and Refer to interpret saturated water pressure table the value of hag at pressure. CP4 =15 kPa) hog - 1992.4 kJ/kg heat output of the ideal Express the specific Rankine cycle (gout). yout = hu-hi

substitute 2, 252.68 kJ/kg for hy and 225.94 kJ lng for hi q=2,252.68 kJ/kg - 225.94 kJ/kg : 2,026.74 kJ/kg Express the thermal efficiency of the cycle (new qin 7th = 1 - Gout Substitute 2026.74kJ /kg for your and 3,298.57k3/ng for qin nh: 1 - 2026.74 kilka 3,298.57 kJ/kg. -0.3855 Express the overall efficiency of the ideal Rankine cycle Cloverall) Поvеrаl - Пm x Поmb stan noverall = 0.38551 0.85 40.96 -0.3146 Express the rate of heat input to the cycle Coin) Qin - Wnet noverall Here, the net work output of the cycle is Water Substitute 175,000 kils for Whet and 0.3146 for noverall Qin -175,000ksts 0.3146 =556126185/s

in of coal rate the power flow Express plant the may linout) Qin mout = It Vout of coal is tout fir ain and 29,300k Ilka Here, the substitute Hout calorific value 556,261 kils inout - 556,261kJ 29,300kJ/kg =18. 98 x (7600 tons!") = 68.32 tons In Therefore, the mass flow rate of coal is 68.32 tons/h.