Homework Set 13

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Pennsylvania State University *

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300

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Mechanical Engineering

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Feb 20, 2024

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ME 300 Homework Set 13 ME 300. Engineering Thermodynamics Zhu 1 Due 11:59 pm Friday, Apr. 28, 2023. Submit to Canvas (100 points + 30 extra points) In homework 13, you will analyze Rankine cycle and vapor-compression cycle. For these cycles, the working fluid is typically H 2 O or R-134. These working fluid is not ideal gas. Problem 1 (50 points) A steam power plant based on Rankine cycle has net power of 200 MW. Saturated vapor enters the turbine at 10 MPa. Saturated liquid leaves the condenser at 0.005 MPa. Both the turbine and pump are adiabatic. The turbine has isentropic efficiency of 85%, and the pump is ideal. For the cycle, determine: a. (8 points) Draw a T-s diagram for the isentropic and actual process. Label the points on the diagram to match those in the cycle sketch below. b. (7 points) The mass flow rate of the working fluid (steam). c. (7 points) The power output of the turbine in Watts. d. (7 points) The net heat transfer to the working fluid in the boiler, per unit mass of the working fluid ! ̇ ! in kJ/kg. e. (7 points) The thermal efficiency for the ideal cycle (where the isentropic efficiencies of the turbine and the pump are both 100%). f. (7 points) The actual thermal efficiency of the cycle. g. (7 points) The mass flow rate of the cooling fluid (assume subcooled water with a Cp of 4.184 kJ/kgK) If this cooling fluid enters the condenser at 15 ˚C and leaves at 25 ˚C.
ME 300 Homework Set 13 ME 300. Engineering Thermodynamics Zhu 2 Problem 2 (50 points) Modified from Text 9.115 Consider an ideal vapor-compression cycle using R-134a and operating between pressures of 0.30 and 1.68 MPa. The refrigerant flow rate is 0.035 kg/s. Use NIST resource to evaluate relevant properties. (a). (5 points) Draw the T-s diagram for the cycle, (b). (5 points) Determine ࠵? ̇ $ , (c). (5 points) Determine ࠵? ̇ % , (d). (5 points) Determine ࠵? ̇ &’ , (e). (5 points) Determine ࠵? ()*(&+ , (f). (5 points) Determine ࠵? ,)-. 01#0 . Problem 3 (30 extra points) We add superheat and reheat to the cycle in Problem 1. Steam enters the first turbine stage at 10 MPa, 760 K, and leaves at 0.5 MPa. Subsequently, it is reheated to 700 K and enters the second turbine stage. It leaves the second turbine stage at 0.005 MPa. Saturated liquid leaves the condenser at 0.005 MPa. The turbines have isentropic efficiency of 85%, and the pump is ideal. The power plant has 200 MW net power. Determine: a. (10 points) Draw a sketch of the system, and label all the components. Number the flow, starting with 1 at the pump inlet. b. (8 points) Draw a T-s diagram for the isentropic and actual process. Label the points in the diagram to match the sketch of the system. c. (8 points) The mass flow rate of the working fluid (steam). Compare to the answer you got in problem 1. Is it less, the same or greater? d. (8 points) The thermal efficiency of the ideal cycle (when the isentropic efficiencies of the turbines and the pump are 100%). Compare to the answer you got in problem 1. Is it less, the same or greater? e. (8 points) The actual thermal efficiency of the cycle. Compare to the answer you got in problem 1. Is it less, the same or greater? f. (8 extra points) The mass flow rate of the cooling fluid (assume subcooled water with a Cp of 4.184 kJ/kgK) If this cooling fluid enters the condenser at 15 ˚C and leaves at 25 ˚C. Compare to the answer you got in problem 1. Is it less, the same or greater?
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