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Transcript
ME 200 Thermodynamics – Spring 2016 PREPARING FOR EXAM 3 I. Class Notes, Examples and Quizzes Review all class notes, examples and quizzes from Lectures 1 - 34. Do you understand all of the concepts that were presented and discussed? Could you solve the examples and quizzes without looking at the solutions? II. Homework Problems Be able to solve all of the special problems until Lecture 34 (SP1 – SP34) without having to look at the solutions. Do all of the supplemental text problems listed on the syllabus that are assigned through Lecture 34. Solutions for SP1 – SP34 and an answer key for the supplemental text problems are provided on Blackboard for each section. III. Old Exams The ME 200 website (https://engineering.purdue.edu/ME200/) has previous exams (Exam 3) for Fall 2011 and Spring 2013. Try to solve the old exams in the time normally allotted for a onehour exam. There also is a posted solution for Exam 3 from last semester. You can review this but it would better if you tried to solve it without looking at the solution. IV. Some Additional Practice Problems 1. A small air conditioner cools a space at 20oC at a rate of 2.5 kW and rejects heat to the outdoors at a temperature 35oC. What is the rate of entropy production for a COP of 5? 2. An inventor claims that a process produces a work output that is equal to the heat input when going from one state to another. Does this claim violate the Kelvin-Planck Statement of the 2nd Law? Explain. 3. An engineer has devised a system that employs a heat engine (HE) and heat pump (HP) and produces a net power output ( W net ) as depicted. Is this net power delivery rate possible for the given conditions? Justify your answer using an entropy balance with calculations. High Temperature Reservoir @ 300 C HP increases increases increases increases increases increases increases increases increases increases HE Wnet 100 kW Q M ,HP 500 kW Medium Temperature Reservoir @ 50C 4. Does entropy increase, decrease, or remain constant for each case? Justify with property relations or entropy balances. Ideal gas with constant P and increasing v Incomp. liquid with constant T and decreasing P Incomp. liquid with constant h and decreasing P Ideal gas with constant h and decreasing P 2-phase mixture with constant h and decreasing P Ideal gas undergoing an isothermal compression 2-phase substance condensed at constant pressure Closed system undergoing a rev. adiabatic process Closed reversible system undergoing heat rejection Adiabatic, irreversible process Q H ,HE 1000 kW Q H ,HP 1000 kW Low Temperature Reservoir @ -50C decreases decreases decreases decreases decreases decreases decreases decreases decreases decreases same same same same same same same same same same 1 5. Heat transfer at a rate of 10 kW is needed for a process operating at 300 K. How would the total rate of entropy generation change with increasing temperature of the heat source for the same heat transfer rate? a) increases, b) decreases, c) doesn’t change, d) can’t tell. Utilize an entropy balance to justify. Source at TH Q 10 kW Process at 300 K 6. Liquid water treated as an incompressible fluid is flowing through a horizontal, adiabatic, and internally reversible diffuser. What happens to the following quantities as the water flows through the device? Use basic equations to justify. Velocity: Enthalpy: Entropy: Temperature: Pressure: increases increases increases increases increases decreases decreases decreases decreases decreases constant constant constant constant constant 7. Refrigerant enters an adiabatic and irreversible throttling valve as a saturated liquid where it is throttled to a low pressure and then evaporated inside a heat exchanger at constant pressure before it exits as a saturated vapor. Depict the process that the refrigerant undergoes on a T-s Heat Exchanger diagram with respect to the 3 1 Throttle 2 dome, showing the individual Saturated Saturated Liquid at Vapor at state points that are indicated X High Pressure Low Pressure in the figure below. 8. A steady stream of air is compressed adiabatically to a higher pressure. Would the exit temperature from the compressor be higher for a reversible or irreversible compressor for the same inlet condition and exit pressure? Explain why. Depict on a T-s diagram. 9. Is there any circumstance where an irreversible process could ever be isentropic? entropy balance to justify. Use an 10. Consider a piston-cylinder device with 1 kg of air initially at a temperature 20oC and a pressure of 2 bar. It has been claimed that after a total of 25 kJ of heat has been transferred to the air in a constant pressure process, the final temperature is 30oC. The temperature of the source of the heat addition is 300oC. Using this data, determine: a) the specific work done by the air and b) whether the stated process and conditions violate sat. water vapor the 2nd Law. at P1 = 5 MPa 11. Saturated water vapor at 5 MPa enters an adiabatic throttle and exits at 1.5 MPa. What is the entropy production per unit mass of water vapor flowing? What if the throttle were replaced with an adiabatic and reversible turbine? Depict the two processes on a T-s diagram with respect to the dome and constant pressure lines. 1 2 P2 = 1.5 MPa 2 12. An inventor claims to have devised a steady-flow compressor, which requires no shaft-power input. It is claimed that CO2 at 15 bar and 50oC can be compressed to 20 bar, where it will emerge at -5oC, simply by a transfer of energy as heat from this device. The patent application states that the device will handle 2 kg CO2 per second and is driven by a “cold source” at –95oC (-140oF). They further state that the CO2 enters and leaves the device at very low velocity, and that no Inlet Outlet significant elevation changes are involved. Can these claims be valid? Assume ideal gas but allow for variable specific heats. Heat Transfer Depict the process on a T-s diagram showing constant pressure lines. -140 F 13. At steady state, steam with a mass flow rate of 5 kg/s enters a turbine at 400oC and 40 bar and expands to 4 bar. The power developed by the turbine is 2127 kW. The steam then passes through a heat exchanger with a negligible change in pressure, exiting at 400oC. Air enters the heat exchanger in a separate stream at 1.4 bar, 550oC and exits at 1.2 bar, 325oC. Determine the total rate of entropy production. Neglect changes in kinetic and potential energy and assume the turbine is adiabatic. 14. A 1 kg piece of copper at 30oC is dropped in a large lake that is at 15oC. Determine the total entropy production. (Assume that the copper has a constant specific heat of 0.39 kJ/kg-K and treat the lake as a reservoir at constant and uniform temperature.) Lake Copper Block 15. Liquid water flowing in a pipe at a rate of 0.12 kg/s is heated using an electrical resistance heater as depicted below. At steady flow and steady state conditions, electrical power is dissipated in the resistor at a rate of 10 kW and heats the water from 15C to 35C with negligible change in water pressure. The resistor is at a uniform and constant temperature of 50C. The pipe is approximately adiabatic and changes in kinetic and potential energy are negligible. Water can be treated as an incompressible substance with a constant specific heat of 4.18 kJ/kg-K. With this information, do the following: a) Determine the total rate of entropy generation for this process, in kW/K. b) Determine the rate of entropy generation for the water alone, in kW/K. c) Determine the rate of entropy generation for the resistor alone, in kW/K. For each part, you need to show your system, list assumptions, and start with basic equations. T = 50C Water: 0.12 kg/s T1 = 15C P1 = 300 kPa + 10 kW T2 = 35C P2 = 300 kPa 3 16. Two liquid water streams are mixed together in a steady-state, steady-flow process at constant pressure. One stream has a temperature of 60oC and mass of flow rate of 1 kg/s, while the other enters at 10oC and 0.1 kg/s. Heat transfer occurs to an environmental temperature of 20oC, such that the exit temperature of the liquid water is 48oC. Determine the rate of entropy production. Neglect changes in kinetic & potential energy. 17. Air enters a nozzle at 4 bar, 277oC, and 60 m/s and exits at 0.75 bar. Assuming ideal gas behavior, variable specific heats and a reversible and adiabatic process, determine the exit temperature of the air. 18. Air is expanded reversibly in a closed piston-cylinder from an initial state of 0.05 m3, 10 bar, and 600K to a final pressure of 2 bar. The piston is located in an environment of 25C. Determine the expansion work (kJ) for two cases: a) adiabatic expansion (assume variable specific heats) and b) isothermal expansion (assume constant specific heats). 19. As shown below, a turbine is located between two tanks. Initially, the smaller tank contains air at 3.0 MPa and 280C within a volume of 100 m3. The larger tank is evacuated and has a volume of 1000 m3. The air then flows from the smaller tank, through the turbine, and into the larger tank until equilibrium is attained. Determine the maximum work output (kJ) if there are no irreversibilities. Show your system, list assumptions, and start with basic equations. Initially: air at 3 MPa, 280C Initially evacuated Turbine 100 m3 1000 m3 Hints: Choose a system that remains closed throughout the process! Calculate specific volumes before and after. The volume of the turbine and piping is negligible, and heat transfer to the surroundings is negligible. Air at these conditions can be treated as an ideal gas, but you must consider the temperature dependence of specific heats. 4