exam2_sol_2006

# exam2_sol_2006 - ENGRD 221 Thermodynamics(Prof N Zabaras...

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ENGRD 221 –Thermodynamics (Prof. N. Zabaras) Prelim II 11/16/2006 Page 1 of 10 Thursday November 16, 7:30 pm – 9:30 pm Closed books and notes. You are allowed to have only whatever information fits in the two sides of the `index card’ that was given to you in class. Wireless or any other form of internet/phone connection is strongly prohibited during the exam. Answer all questions. Make sure your answers are legible. Circle your final answer. The TAs and instructor will not respond to any questions during the exam. If you think that something is wrong with one of the problems below, please state your concern in your exam books. Problem 1 (20 points) The figure shows three devices operating at steady state: a pump, a boiler, and a turbine. The turbine provides the power required to drive the pump and also supplies power to other devices. For adiabatic operation of the pump and turbine, and ignoring kinetic and potential energy effects, determine, in kJ per kg of steam flowing: a) (5 points) the work required by the pump b) (5 points) the heat transfer to the boiler c) (10 points) the net work developed by the turbine Useful data: h 1 =125.74 KJ/Kgr, v 1 =1.0043 x 10 -3 m 3 /Kgr. h 3 =2769.1 KJ/Kgr, s 3 =6.6628 KJ/Kgr K At 1 bar, s f =1.3026 KJ/Kgr K, s g =7.3594 KJ/Kgr K, h f =417.46 KJ/Kgr, h g =2675.5 KJ/Kgr.

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ENGRD 221 –Thermodynamics (Prof. N. Zabaras) Prelim II 11/16/2006 Page 2 of 10 Solution: Known: Steady state operating data are provided for a pump, a boiler and a turbine in series. Find: Determine in KJ per Kg of steam flowing (a) the pump work, (b) the net work developed by the turbine and (c) the heat transfer to the boiler. Schematic and given data: Find: (1) Control volumes enclosing the pump, the boiler and the turbine are at steady-state. For the pump and turbine we neglect all heat transfers to or from the surroundings . (2) All kinetic and potential energy effects are negligible. Analysis: For the pump, Eq. 6.53b from the text can be invoked to evaluate the work in the internally reversible process. With data from Table A-2, h 1 =h f (T 1 )=125.74 KJ/Kgr, v 1 =v f (T 1 )=1.0043 x 10 -3 m 3 /Kgr. Then Then using the isentropic pump efficiency, we can compute the following: Mass and energy rate balances reduce to give: Thus
ENGRD 221 –Thermodynamics (Prof. N. Zabaras) Prelim II 11/16/2006 Page 3 of 10 For the boiler, mass and energy rate balances reduce to give: where h 3 is from Table A-3. For the turbine, mass and energy rate balances reduce to give: or on introducing the isentropic turbine efficiency: From Table A-3, s 3 =s 4s =6.6628 KJ/Kgr K. The quality at 4 s is: Then, h 4s =417.46 + 0.885 (2258) = 2415.8 KJ/Kgr. Accordingly, Of this amount, 1 KJ/Kgr is required by the pump leaving Problem 2 (5 points) Compute the coefficient of thermal expansion α and the isothermal compressibility β for an ideal gas.

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exam2_sol_2006 - ENGRD 221 Thermodynamics(Prof N Zabaras...

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