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1
ME 18b, HW 1
Due Tuesday April 7, 2008 (by 4 pm)
Suggested Solutions
1.1
Thermal efficiency for an Ideal Rankine cycle. (11.14)
Suppose you wish to design a solar powered Rankine cycle plant using water as a working fluid.
If
the solar collector exit has saturated water vapor at a pressure of 900 kPa and the condenser operates at 10
kPa determine the following: (a) the operating temperatures of the evaporator and the condenser. (b) The
thermal efficiency of this ideal power plant. (c) Compare this to the thermal efficiency of a Carnot Cycle
plant.
Solution:
Water ideal Rankine cycle, see diagram below.
Using CATT 3 for thermodynamic properties:
State 3: Sat vapor at P3 = 900 kPa
⇒
T3 = 175°C, h3 = 2774 kJ/kg,
s3 = 6.623 kJ/kg K
State 1: Sat liquid at P1 = 10 kPa
⇒
T1 = T4 = 46°C, v1 = 0.00101 m3/kg, h1 = 192 kJ/kg
(a) Evaporator Temp = 175°C, Condenser Temp = 46°C
Process: Turbine is adiabatic and reversible so second law gives
s4 = s3 = 6.623 kJ/kg K and P4 = 10 kPa => h4 = 2097 kJ/kg
The energy equation gives
wT = h3  h4 = 2774  2097 = 677 kJ/kg
Process: Pump and incompressible liquid gives work into pump
wP = v1(P2  P1) = 0.00101(900  10) = 0.90 kJ/kg
h2 = h1 + wP = 192 + 0.90 = 193 kJ/kg
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 Spring '08
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