Faculté de génie Génie mécanique Faculty of Engineering Mechanical Engineering MCG2131 - THERMODYNAMICS II 22 April 2008 Page 1 of 7 Prof. W. Hallett Closed book. Non-programmable calculators only allowed. Steam tables, a psychrometric chart and some equations are provided at the end of the paper; other data are given with the questions. 1. (6 marks total) Descriptive questions - give brief answers in words. No calculations are required. You may write your answers in point form if you wish. (a) (2 marks) For an ideal Otto cycle, sketch (i) a P-v diagram; (ii) a T-s diagram. Label the events in the cycle on each of these diagrams. (b) (2 marks) A sample of moist air is compressed at constant temperature. How does the relative humidity change and why? (c) (2 mark) How does an increase in excess air affect the efficiency of a combustion process? Explain why. 2. (11 marks total) Ethanol (C2H5OH) burns in a domestic furnace at a pressure of 101.3 kpa according to the following stoichiometric equation: C2H5OH + 4.0 (O 2 + 3.76 N 2) 2.0 CO 2 + 3.0 H2O + 1.0 O 2 + 15.04 N 2 The fuel and air enter the furnace at 25 C and the products leave at 40 C. Determine: (a) (2 marks) the dew point of the products; (b) (4 marks) the amount of water condensed from the products and the product composition after condensation, all in kmol/kmol fuel; (c) (5 marks) the heat transfer from the furnace in MJ/kmol fuel. Data: Ethanol: molecular mass M = 46 kg/kmol, higher heating value HHV = 31.6 MJ/kg. CO Product Enthalpies: H O 2 2 2 2 at 40 C (kj/kmol) 579 504 441 433 (kj/kmol) - 43 961 - - O N
22 April 2008 Page 2 of 7 3. (12 marks total) A room is heated and ventilated by the system shown in the sketch. Outside air enters at point 1 at T 1 = 5 C, 1 = 40%, and is mixed with air returning from the room at T 5 = 25 C, 5 = 40%. This air is then heated and humidified with cool liquid water. The pressure is 100 kpa throughout. The mass flow rate of outside air is = 5 kg dry air/min, while the recirculated air mass flow rate is also = 5 kg dry air/min. (a) (5 marks) Determine the temperature and relative humidity of the air at point 2. (b) (2 marks) Assuming that state 4 and state 5 are the same, show all the processes in the system on a sketch of a psychrometric chart. (c) (5 marks) Determine the temperature at point 3 and the heat input required in kw. A psychrometric chart is provided at the end of this paper.
22 April 2008 Page 3 of 7 4. (16 marks total) The sketch shows a fan jet aircraft engine. A large flow of air enters the fan at T 1 = 0 C, P 1 = 100 kpa, and is compressed in the fan to P = 170 kpa. A portion of this air is then split off and is 2 discharged through a nozzle at the back of the engine (the bypass air). The remaining air flow (the core flow) then passes through the rest of the engine, comprising the compressor, the high pressure (HP) turbine which drives the compressor, and the low pressure (LP) turbine which drives the fan. The pressure P 3 = 4200 kpa, and the temperature T 4= 1400 C. Assume that the isentropic efficiencies of the fan, the compressor and both turbines are all = = 0.90. (a) (2 marks) Sketch a T-s diagram for this cycle. (b) (4 marks) If the exit temperature from the fan T 2 = 322.7K, determine the compressor work in kj/kg. (c) (3 marks) Noting that the high pressure turbine drives only the compressor, determine the temperature T 5 at the HP turbine outlet. (d) (4 marks) Calculate the pressure P 5 at the outlet of the HP turbine. (e) (3 marks) If the core mass flow = 140 kg/s, determine the bypass flow. The low pressure turbine specific work is w = 480 kj/kg and the fan specific work is w = -50.2 kj/kg. T LP Use constant specific heat, assuming that for air C P = 1.01 kj/kg K, k = 1.4. The numbers are representative of a large jet engine such as the Rolls-Royce Trent 1000. C T F
22 April 2008 Page 4 of 7 5. (15 marks total) The sketch shows a steam power cycle with one open feedwater heater. The follow cycle states are given: 1: saturated liquid at 50 C 2: P 2 = 0.3 MPa 3: saturated liquid 4: P 4 = 5.0 MPa 5: T = 400 C 5 The isentropic efficiency of both pumps is P = 80%, and the isentropic efficiency of both turbines is = 90%. T (a) (2 marks) Sketch a T-s diagram of the cycle. (b) (4 marks) Determine the low pressure pump specific work w P LP in kj/kg and the enthalpy h 2 at the low pressure pump exit. (c) (4 marks) Determine the high pressure turbine specific work w T HP in kj/kg and the enthalpy h6 at the high pressure turbine exit. (d) (5 marks) Calculate the ratio of the mass flow extracted from the turbine to the mass flow passing through the low pressure pump. Properties tables are appended to this paper. Total marks for this paper: 60
22 April 2008 Page 5 of 7 Steam Tables Saturated Steam - Temperature Table 3 T ( C) P (kpa) v f (m /kg) h f (kj/kg) h g (kj/kg) s f (kj/kgk) s g (kj/kg K) 0.01 0.6113 0.001 0.01 2501.4 0.0000 9.1562 5 0.8721 0.001 20.98 2510.6 0.0761 9.0257 10 1.2276 0.001 42.01 2519.8 0.1510 8.9008 15 1.7051 0.001001 62.99 2528.9 0.2245 8.7814 20 2.339 0.001002 83.96 2538.1 0.2966 8.6672 25 3.169 0.001003 104.89 2547.2 0.3674 8.5580 30 4.246 0.001004 125.79 2556.3 0.4369 8.4533 35 5.628 0.001006 146.68 2565.3 0.5053 8.3531 40 7.384 0.001008 167.57 2574.3 0.5725 8.2570 45 9.593 0.001010 188.45 2583.2 0.6387 8.1648 50 12.349 0.001012 209.33 2592.1 0.7038 8.0763 Saturated Steam - Pressure Table 3 P (kpa) T ( C) v f (m /kg) h f (kj/kg) h g (kj/kg) s f (kj/kgk) s g (kj/kg K) 5 32.88 0.001005 137.82 2561.5 0.4764 8.3951 10 45.81 0.001010 191.83 2584.7 0.6493 8.1502 20 60.06 0.001017 251.4 2609.7 0.8320 7.9085 30 69.10 0.001022 289.23 2625.3 0.9439 7.7686 50 81.33 0.001030 340.49 2645.9 1.0910 7.5939 75 91.78 0.001037 384.39 2663.0 1.2130 7.4564 100 99.63 0.001043 417.46 2675.5 1.3026 7.3594 200 120.23 0.001061 504.70 2706.7 1.5301 7.1271 300 133.55 0.001073 561.47 2725.3 1.6718 6.9919 400 143.63 0.001084 604.74 2738.6 1.7766 6.8959 500 151.86 0.001093 640.23 2748.7 1.8607 6.8213
22 April 2008 Page 6 of 7 Superheated Water Vapour P = 5.0 MPa T ( C) h (kj/kg) s (kj/kg K) Sat 2794.3 5.9734 300 2924.5 6.2084 350 3068.4 6.4493 400 3195.7 6.6459 450 3316.2 6.8186 500 3433.8 6.9759 P = 0.3 MPa T ( C) h (kj/kg) s (kj/kg K) Sat 2725.3 6.9919 150 2761.0 7.0778 200 2865.6 7.3115 250 2967.6 7.5166 300 3069.3 7.7022 400 3275.0 8.0330 Equations and Other Data Isentropic relation for a perfect gas with constant specific heat: Reversible work done on an incompressible liquid in steady flow:
MCG2131 - THERMODYNAMICS II 22 April 2008 Psychrometric Chart for a total pressure of 100 kpa Page 7 of 7