The boiler and condenser pressures of a steam plant operating on the ideal Ranki

Question

The boiler and condenser pressures of a steam plant operating on the ideal Rankine cycle are 30 bar and 0.04 bar respectively. The steam is superheated to 350 C in a super-heater before it is expanded isentropically in the turbine. The steam is condensed to a saturated liquid and then pumped isentropically to the boiler pressure to complete the cycle. Calculate (a) the work output of the turbine (kJ/kg), (b) the feed pump work (kJ/kg), (c) the heat rejected in the condenser (kJ/kg), and (d) the thermal efficiency of the plant. Sketch the cycle on a T-s diagram and an h-s diagram for water.

Explanation / Answer

For steam properties, see http://www.irc.wisc.edu/properties/

At 30 bar, 350 C, we get h1 = 3120 kJ/kg and s1 = 6.74 kJ/kg-K

At s2 = s1 = 6.74 kJ/kg-K and P2 = 0.04 bar, we get h2 = 2030 kJ/kg

At P3 = 0.04 bar and quality = 0 (sat. liq.), we get h3 = 121 kJ/kg and s3 = 0.422 kJ/kg-K

At s4 = s3 = 0.422 kJ/kg-K and P4 = 30 bar, we get h4 = 124 kJ/kg

a) W_turb = (h1 - h2) = (3120 - 2030) = 1090 kJ/kg

b) Pump work W_pump = (h4 - h3) = (124 - 121) = 3 kJ/kg

c) Heat rejected in condensor = (h2 - h3) = (2030 - 121) = 1909 kJ/kg

d) Net work = W_turb - W_pump = 1090 - 3 = 1087 kJ/kg

Heat supplied = (h1 - h4) = (3120 - 124) = 2996 kJ/kg

Efficiency = 1087 / 2996 = 0.3628 or 36.28 %

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