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FACULTY OF ENGINEERING AND COMPUTER SCIENCE DEPARTMENT OF MECHANICAL AND INDUSTRIAL ENGINEERING COURSE NUMBER Thermodynamics II EXAMINATION MECH 351 DATE Final SECTION TIME & PLACE December 10, 2008 Room: All Sections # OF PAGES 14:00 – 17:00 H531 and H535 PROFESSORS 13 LAB INSTRUCTOR I. Hassan and L. Kadem MATERIALS ALLOWED oX NO o YES (PLEASE SPECIFY) CALCULATORS ALLOWED o NO ox YES (non programmable) SPECIAL INSTRUCTIONS: Answer the following four questions. State clearly any assumptions you make. Draw a clear sketch of the problem. Return the Exam paper with the answers’ book. Assume constant specific heats with temperature for N2 and O2 in question 3-I, and use the given values in the Data Sheet, Page 5. Name: _______________________________ I.D.: ______________________ Surname, given names 1 Question no. 1 (30 Points) A steam power plan operates on an ideal reheat-regenerative Rankine cycle with one reheater and two open feedwater heaters. Steam enters the high-pressure turbine at 10 MPa and 600ºC and leaves the low-pressure turbine at 7.5 kPa. Steam is extracted from the turbine at 1.8 and 0.3 MPa, and it is reheated to 550 ºC at a pressure of 1 MPa. Water leaves both feedwater heaters as saturated liquid. Heat is transferred to the steam in the boiler at a rate of 400 MW. Show the cycle on a T-s diagram, relative to the saturation line, and determine: (a) The mass flow rate of steam through the boiler. (b) The net power output of the plant. (c) The thermal efficiency of the cycle.. Question no. 2 (20Marks): A gas-turbine power plant operates on the simple Brayton cycle with air as the working fluid and delivers 15 MW of power (Hint: turbine power minus compressor power). The minimum and maximum temperatures in the cycle are 310 and 900K, and the pressure of air at the compressor exits 8 times the value at the compressor inlet. Consider an adiabatic efficiency of 80 percent for the compressor and 86 percent for the turbine, and assume k =1.4 for air. Sketch the cycle on T-s and P-v diagrams and determine: (a) The mass flow rate of air through the cycle. (b) The thermal efficiency of the cycle. 9 Question no. 3 (25 Marks) I- An insulated tank that contains 1 kg of O2 at 15°C and 300 kPa is connected to a 2 m3 uninsulated tank that contains N2 at 50°C and 500 kPa (see figure below). The valve connecting the two tanks is opened and the two gases form a homogeneous mixture at 25°C. Considering ideal gas mixture, determine: a- The final pressure in the tank. b- The heat transfer. 2 II- Atmospheric air enters an air-conditioning system at 30oC and 70 percent relative humidity with a volume flow rate of 4 m3/min and is cooled to 20oC at a pressure of 1 atm, as shown in the figure. The system uses refrigerant-134a as the cooling fluid that enters the cooling section at 350kPa with a quality of 20 percent and leaves as a saturated vapor. a- Sketch the process on the psychrometric chart. b- What is the heat transfer from the air to the cooling coils, in kW? c- If any water is condensed from the air, how much water will be condensed from the atmospheric air per min? d- Determine the mass flow rate of the refrigerant, in kg/min. 3 Question no. 4 (25 Marks) Methane gas (CH4) at 25 ºC is burned steadily with dry air that enters the combustion chamber at 17 ºC. The volumetric analysis of the products on a dry basis is 5.20% CO2, 0.33% CO, 11.24 O2, and 83.3% N2. Determine: a- The percentage of theoretical air used. b- The heat transfer rate from the combustion chamber per kmol of CH4 if the combustion products leave at 700K. 4 s THERMODYNAMICS DATA SHEET R = 8.315 kJ/kmole°K 1 bar = 100kPa 1 gm/cm3 = 103 kg/m3 Molar masses and specific heats: Air: M = 29 Cp= 1.005kJ/kg°K O2: M = 32 Cp= 0.918kJ/kg°K N2: M = 28 Cp= 1.039kJ/kg°K Enthalpy of Formation: 5 Note: Cp = Cv + R and k = Cp/Cv 6 7 8 9 10 . 11 Formula Sheet – Thermodynamics II T2 V1 T1 V2 K 1 T P ; 2 2 T1 P1 K 1 K K P V ; 2 1 ; P1 V2 W Vmax Vmin MEP= ; where K= cycle Ws W CP ; P ;T a ; Wa Ws CV Wnet Qin Ni m ; Average molar mass M m = m = yi M i ; gas constant: Nm Nm P V N R Rm u Ru 8.314 KJ /( Kmol.K ) ; PV ZNRuT ; (Zm yi Zi ) ; i i i yi ; Mm Pm Vm Nm Mole number: Ni mi ; Mole fraction: yi Mi Dalton’s law: Pm Pi (Tm .Vm ) ; Amagat’s law: Vm Vi (Tm .Pm ) ; U m = mfiU i , U m = yi U i (same for h and s); Cv,m mfiCv,i ; C v,m yi C v,i , same for Cpm Real gasses: h (h2 h1 ) ideal Ru Tcr (Z h 2 Z h1 ) ; u (h2 h1 ) Ru (Z 2T2 Z1T1 ) ; s (s2 s1 )ideal R(Zs2 Zs1 ) ; . Air conditioning energy balance: Q in . . . . . m air . ; m=NM ; m fuel Enthalpy of combustion . out . Air fuel ratio: AF . W in mi hi Q W out me he , m m a Pvi Ptotal mair,act N air,act Ni ; Percentage of theoretical air: or Ntotal mair,th N air,th : hc=H prod H react ; HHV LHV (mhf ) H2O ; g First law analysis of reacting systems: Q W Np (h f h h) p Nr (h f h h)r Entropy generation of reacting systems: S gen N p s p N r s r yP N p s o i T , Po Ru ln i m Po yP N r s o i T , Po Ru ln i m Po Pr od 12 react Summary of Final Answers Question No 1: Required (a) Turbine power output. Numerical Final Answer (b) Cooling water temperature rise. (c) Heater mass flow rate. (d) Heat supply, process heater. (e) Boiler heat transfer and utilization factor. Question No 2: Required (a) The mass flow rate of air. Numerical Final Answer b) The thermal efficiency. Question No 3: IRequired (a) Final Pressure. Numerical Final Answer b) Heat Transfer. IIRequired (a) Heat transfer from the air in kW. (b) How much water will be condensed, if an. (c) Determine the mass flow ate of the refrigerant, in kg/min. Numerical Final Answer Question No 4: Required (a) The mole fraction and the partial pressure of CO2. (c) The air-fuel ratio. (d) The heat transfer rate from the combustion chamber . 13 Numerical Final Answer