HW1b_09 Solution

HW1b_09 Solution - ME 18b, HW 1 Due Tuesday April 7, 2008...

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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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HW1b_09 Solution - ME 18b, HW 1 Due Tuesday April 7, 2008...

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