Problem 1 As you learned in chapter 6 while understanding the basics of the Second Law...

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Problem 1 As you learned in chapter 6 while understanding the basics of the Second Law of Thermodynamics, a steam power plant can be represented as a heat engine by assembling the devices shown in the figure on the right, where qin is supplied from a source and qout is rejected to a sink. Please answer the following questions. Wpump.in - Pump Boiler Turbine Condenser Yout Wturb,out a. Assume that all devices shown in the figure are adiabatic and reversible. Water enters the pump as saturated liquid and leaves the pump at 1 MPa and approximately at the same temperature it entered, leaves the boiler as saturated vapor, enters the turbine and leaves the turbine as a saturated mixture with quality 85% and a pressure equal to 20 kPa. Also changes in kinetic and potential energy on any device may be assumed to be negligible compared to changes in other properties, and there are no fluid pressure losses as it passes through the boiler and the condenser, or as it travels from one device to the next. On a T-v and T-s diagrams represent the processes that correspond to each device such that it operates as a cycle; do not include any property values except for pressures that correspond to the boiler and condenser and temperatures. Label your states with numbers and do not omit including the process lines. In your diagram, is there any change in entropy for the water as it passes through the pump and turbine? Explain. b. In part (a) you were told that the boiler and the condenser were adiabatic and reversible. What condition needs to happen to make the statement true? c. Next, you want to determine if the cycle as given to you could be a real cycle, reversible cycle or impossible cycle. Support your answer with computations using concepts learned in chapter 7. List your assumptions. d. Next, you decide to compute the thermal efficiency of the cycle to verify that your conclusion in part (c) is correct. Support your answer with computations using concepts learned in chapter 6. List your assumptions. e. You as an engineer realized that you want to have a cycle with better thermal efficiency for the same boiler and condenser pressures. You realize by looking at your governing equations for each device and for the efficiency of the heat engine that decreasing the value for qout may bring benefit to your goal however you do not know by how much. Thus, you decided to investigate how cycle efficiency changes with qout for better of for worse. What parameter would you change at the exit of the turbine if you wish to increase or decrease qout? Support your answer with an equation and appropriate explanations. List your assumptions. Note that no computations are required beyond understanding the expressions that you wrote. Problem 2 Do not start the solution of this problem until you finished Problem 1. Now that you know the answer for part (e) of Problem 1, you decide to study the effect of quality of the saturated mix on cycle thermal efficiency. Using the definition of thermal efficiency as a function of heat supplied to the cycle and heat rejected from the cycle you find that a computation for the thermal efficiency is possible using enthalpy values for the inlet and exit of the devices (h1, h2, h3 and ha) provided you make reasonable assumptions. As part of your job, you must present to your management results showing an equation and a plot in which you will show the governing equation for the thermal efficiency as a function of the quality of the saturated mix at the exit of the turbine when it ranges from 65% to 100% in intervals of 1%. To generate your plot, you may use MATLAB or any other software; please include a screenshot of your code and a computer generate code. Using your plot, what is the theoretical quality that will lead to the maximum thermal "theoretical" efficiency? Using your plot, comment whether the trends in the plots can be explained with theory. Will the cycle be reversible, irreversible, or impossible when the quality at the exit of the turbine is 70% and when it is 92%? In your plot include the names of the variables on the axis with units, the quality needs to be plotted on the horizontal axis. Hints: you discovered in your governing equation that you need the value for the enthalpy at the exit of the pump, hz. To determine h you can use equation (3-9) from your textbook, not the approximation in equation 3-8. Alternatively, you can obtain the same when you apply an energy balance for an adiabatic pump with negligible changes in kinetic and potential energy and expand the enthalpy variable in terms of the properties that define it (h = u + Pv). Next consider that during the pumping process the change in temperature for the water is negligible; from this you can get an expression to compute h which will be identical to the expression you found with the first hint. Problem 1 As you learned in chapter 6 while understanding the basics of the Second Law of Thermodynamics, a steam power plant can be represented as a heat engine by assembling the devices shown in the figure on the right, where qin is supplied from a source and qout is rejected to a sink. Please answer the following questions. Wpump.in - Pump Boiler Turbine Condenser Yout Wturb,out a. Assume that all devices shown in the figure are adiabatic and reversible. Water enters the pump as saturated liquid and leaves the pump at 1 MPa and approximately at the same temperature it entered, leaves the boiler as saturated vapor, enters the turbine and leaves the turbine as a saturated mixture with quality 85% and a pressure equal to 20 kPa. Also changes in kinetic and potential energy on any device may be assumed to be negligible compared to changes in other properties, and there are no fluid pressure losses as it passes through the boiler and the condenser, or as it travels from one device to the next. On a T-v and T-s diagrams represent the processes that correspond to each device such that it operates as a cycle; do not include any property values except for pressures that correspond to the boiler and condenser and temperatures. Label your states with numbers and do not omit including the process lines. In your diagram, is there any change in entropy for the water as it passes through the pump and turbine? Explain. b. In part (a) you were told that the boiler and the condenser were adiabatic and reversible. What condition needs to happen to make the statement true? c. Next, you want to determine if the cycle as given to you could be a real cycle, reversible cycle or impossible cycle. Support your answer with computations using concepts learned in chapter 7. List your assumptions. d. Next, you decide to compute the thermal efficiency of the cycle to verify that your conclusion in part (c) is correct. Support your answer with computations using concepts learned in chapter 6. List your assumptions. e. You as an engineer realized that you want to have a cycle with better thermal efficiency for the same boiler and condenser pressures. You realize by looking at your governing equations for each device and for the efficiency of the heat engine that decreasing the value for qout may bring benefit to your goal however you do not know by how much. Thus, you decided to investigate how cycle efficiency changes with qout for better of for worse. What parameter would you change at the exit of the turbine if you wish to increase or decrease qout? Support your answer with an equation and appropriate explanations. List your assumptions. Note that no computations are required beyond understanding the expressions that you wrote. Problem 2 Do not start the solution of this problem until you finished Problem 1. Now that you know the answer for part (e) of Problem 1, you decide to study the effect of quality of the saturated mix on cycle thermal efficiency. Using the definition of thermal efficiency as a function of heat supplied to the cycle and heat rejected from the cycle you find that a computation for the thermal efficiency is possible using enthalpy values for the inlet and exit of the devices (h1, h2, h3 and ha) provided you make reasonable assumptions. As part of your job, you must present to your management results showing an equation and a plot in which you will show the governing equation for the thermal efficiency as a function of the quality of the saturated mix at the exit of the turbine when it ranges from 65% to 100% in intervals of 1%. To generate your plot, you may use MATLAB or any other software; please include a screenshot of your code and a computer generate code. Using your plot, what is the theoretical quality that will lead to the maximum thermal "theoretical" efficiency? Using your plot, comment whether the trends in the plots can be explained with theory. Will the cycle be reversible, irreversible, or impossible when the quality at the exit of the turbine is 70% and when it is 92%? In your plot include the names of the variables on the axis with units, the quality needs to be plotted on the horizontal axis. Hints: you discovered in your governing equation that you need the value for the enthalpy at the exit of the pump, hz. To determine h you can use equation (3-9) from your textbook, not the approximation in equation 3-8. Alternatively, you can obtain the same when you apply an energy balance for an adiabatic pump with negligible changes in kinetic and potential energy and expand the enthalpy variable in terms of the properties that define it (h = u + Pv). Next consider that during the pumping process the change in temperature for the water is negligible; from this you can get an expression to compute h which will be identical to the expression you found with the first hint.