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Mechanical Engineering
Donald Siegel

ME 235 EXAM II, November 21, 2011 K. Kurabayashi and D. Siegel, ME Dept. Exam Rules: Open Book and one page of notes allowed. Solve each problem on a new page. Put your name at the top of each page. Print Name: __________________________________ I have observed the honor code and have neither given nor received aid on this exam. Signature:____________________________________________ 1. [40 points] A steam engine based on a n adiabatic turbine is shown to the right. The boiler tank has a volume of 100 L and initially contains saturated liquid at 100 kPa. Heat is now added by the burner. A pressure regulator separates the boiler from the turbine. This regulator only opens when the boiler pressure reaches 700 kPa , and maintains a constant exit pressure of 700 kPa. When the regulator opens, saturated vapor from the boiler enters the turbine at 700 kPa and is discharged to the atmosphere as   saturated vapor at 100 kPa. The burner is turned off when Burner   no more liquid is present in the boiler. Determine: a) The initial mass of water in the tank b) The amount of water which has left the tank by the time the burner switches off c) The total heat transfer to the boiler during this process d) The total turbine work 2. [25 points] A refrigerator makes ice cubes out of a tray of 0.25 kg liquid water at 10ºC under a constant, but unknown pressure. Assume the refrigerator works in a Carnot cycle between –8ºC and 35ºC. (Hint 1: You may treat liquid water and ice as incompressible substances. Hint 2: Liquid and solid water do NOT have the same specific volume.) a) Find the amount of heat that must be transferred from the water to freeze it to –8ºC b) Find the refrigerator’s coefficient of performance c) Calculate the amount of work input to the refrigerator d) The refrigerator has a motor -compressor rated at 750 W. How much time does it take to freeze the ice to -8ºC assuming it is the only cooling load? (Hint: it will be quick!) 3 3 3. [35 points] A piston cylinder has the water volume separated into V A = 0.2 m and V = 0B3 m by a stiff membrane (see figure at right). The initial state in A is 1000 kPa quality x = 0.75 and in B it is 1600 kPa and 250 °C. Now, the system is heated by a heater at 300°C, the membrane ruptures, and the water comes to a uniform state with 200 °C. (Hint: The weight m apd the atmospheric pressure P togeth0r exert a constant external force on the piston throughout the process.) a) What is the final pressure? b) Find the final volume. c) Find the work in the process. d) Find the heat transfer in the process . e) Find the entropy generation in the process .     Solutions 1. C.V. Boiler tank. Heat transfer, no work and flow out. Continuity Eq.6.15: m 2- m 1= − me Energy Eq.6.16: m 2u2 - m1u1 = QCV - m e e State 1: Table B.1.2, 100 kPa => 1= 0.001 043, u1 = 417.36 kJ/kg => m 1 = V/v1 = 0.1/0.001 043 = 95.877 kg State 2: Table B.1.2, 700 kPa => 2= vg = 0.2729, u2 = 2572.5 kJ/kg => m2 = V/vg = 0.1/0.2729 = 0.366 kg, Exit state: Table B.1.2, 700 kPa => he = 2763.5 kJ/kg From continuity eq.: me = m 1 - m2 = 95.511 kg "#$%&'(()!'&*!+#&&,'%! Q C! = m 2u2- m 1u1+ mehe = 0.366 × 2572.5 - 95.877 × 417.36 + 95.511 × 2763.5 !"#= 224 871 kJ = 224.9 MJ ! -'./0.',)!,1)!'2#0&,!#3!4#$(!5&60,!'!$)3$5%)$',#$!&))*7!,#!2'()!5/)!/08)7!#0,!#3!'! # C.V. Turbine, steady state, inlet state is boiler tank exit state.#$!4#$(7!5&!'!-'$,! Turbine exit state: Table B.1.2, 100 kPa => he = 2675.5 kJ/kg!#3!E=:!F;!G#4!20/1! W = m (h - h ))7!5,!,'()!53!,157!57!,1)!#&.9!/##.5&%!.#'*H! turb e in ex = 95.511 × (2763.5 - 2675.5) = 8405 k
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