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Water undergoes an ideal Rankine cycle with a condenser pressure of 1 kPa and a

ID: 2199428 • Letter: W

Question

Water undergoes an ideal Rankine cycle with a condenser pressure of 1 kPa and a boiler pressure of 10MPa. Due to the metallurgical concerns, the turbine cannot handle temperature above 900 degrees Celsius. The steam is expanded isentropically in two stage, first to a pressure of 4.5 MPa in the hight-pressure stage, then to a 2-phase mixture in the low-pressure stage. A) find the quality of the mixture exiting the turbine (Answer: 0.891). B) The total work developed in both stages of the turbine, Wt, in kj/kg (Answer: 2532.2kj/kg) C) the mass flowrate required if the turbine must generate 10 MW of power (Answer: 3.95 kg/s). Could you also include a T vs S diagram to help me find out where I went wrong.

Explanation / Answer

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

At 10 MPa, 900 deg C, we get h1 = 4360 kJ/kg, s1 = 7.63 kJ/kg-K

At 4.5 MPa and s2 = s1 = 7.63 kJ/kg-K, we get h2 = 3970 kJ/kg, quality = spuperheated

At s3 = s2 = 7.63 kJ/kg-K and P3 = 1 kPa we get h3 = 2140 kJ/kg and quality = 0.848

a) As found from table, x3 = 0.848

b) W = (h1 - h2) + (h2 - h3) = h1 - h3 = 4360 - 2140 = 2220 kJ/kg

c) m*2220 = 10*10^3

m = 4.5 kg/s