Question

Superheated steam at 20 MPa, 560^oC enters the turbine of a vapor power plant. The pressure at the exit of the turbine is 0.7 bar, and liquid leaves the condenser at 0.4 bar at 75^oC. The pressure is increased to 20.1 MPa across the pump and the specific enthalpy is 338.14 kJ/kg. The turbine isentropic efficiency is 81%. Cooling water enters the condenser at 20^oC with a mass flow rate of 70.7 kg/s and exits the condenser at 38^oC. For the cycle,

1. Draw a schematics of the vapor power plant. Label each component and show the direction of the processes.
2. Draw the T − s diagram showing all the states that the working fluid undergoes.
3. Determine the mass flow rate of the steam.
4. Find the thermal efficiency of the vapor power plant.

Answer 1

(Q) Given data For state 1: Temperolure (T.) - 560°C Pressure (P) = 20MPa = 200 bar For state 2 : Pressure (P2) = 0.7 bar For state 3 : Temperature (Ts) = 750 Pressure (P3) = 0.4bar For state 4 : Pressure (P) = 20.1 MPa = 201 bar Specific enthalpy (hu) = 338.14 Kulkg Turbine Isentropic efficiency (127) = 81% mass flow rate of cooling water through condenser (Mcw) = 70.7 kg/s Inlet temperature (Tin) = 200 condenser cooling water < outlet temperature (Tout) = 38°C Turbine 2 + Boiler to waterman condenser It water 5 in 3 4 Pump Vapor power plant T Pu-20lbar Pi=200 bar 45 P2=0.7bar 25 2 Ps=0.4bay T-S diagram

From steain tables at P, = 200bay and T, = 5600 Specific enthalpy Chi) = 3423 kJ/kg Specific entropy (S,) = 6.3105 Kuikg.k water in a cycle is expansion Isentropically from state i to 25 S. - Szs = 6.3705 KJ/Kg.K From steam tables at P2=0.7 bar Sf2 = 1.192 kJ/kg.K Sfg2 = 6.288 kulkgK hfas = 376.8 kJIKE hig25 = 2283.3 kJ/kg. Szs = Sf2s + H₂s Segas 6.3105 = 1.12+ x (6.288) Kas = 0.8235 has = hfs + H₂s heges = 376.8+(0.8235) 2283.3 has = 2257.1 Kulkg I Sentropic efficiency of Turbine " hi ha ho has h₂=h, n, (hi-has) = 3423-0.81(3423-2257.1) h₂ = 2478.6 kJ/kg. From Steam tables at P₂ = 0.4 bar and T3 = 75°c Specific enthalpy (hz) = 313.93 kJ/kg. Already given Specific enthalpy (hy) = 338.14 kJ/kg.

From steam tables at Tin=20c hin - 83.96 Kilkg hout = 159.21 Kuikg at Tout = 38°c Heat and balance siate at Condensex to a control volume m (hz-hy) = řew (hout -hin) mass flow rate of steam (m) m = mcw (hout -hin) h-hz 70.7(159-21-83.96) 2478.6-313.93 m = 2.45 kgls mass flow rate of the steam (m) is 2.45kg/s. Work done Thermal efficiency (Meycle) = Heat supplied Wy - Wp Qio m (Chi-h2) - (h4-13) mh-h) (3423-2478-6) - (33814-313-93) 3423-338-14 -cycle Reycle = 0.2982 Mcycle 29.82% Thermal efficiency of the vapor power plant is 29182:.
Answer:

1. Mass flow rate of steam is 2.45kg/s.

2. Thermal efficiency of vapor power plant is 29.82%.