ME1002 Engineering Thermodynamics Examples Sheet 2 PDF

ME1002 – ENGINEERING THERMODYNAMICS EXAMPLES SHEET 2 1. 1.0 m3 of air has initial conditions of 0.1 MPa and 18°C. It undergoes the following cycle of reversible processes: (1) Isentropic compression to 5 MPa; (2) isobaric expansion to 0.1 m3; (3) Isentrop...

ME1002 – ENGINEERING THERMODYNAMICS EXAMPLES SHEET 2 1. 1.0 m3 of air has initial conditions of 0.1 MPa and 18°C. It undergoes the following cycle of reversible processes: (1) Isentropic compression to 5 MPa; (2) isobaric expansion to 0.1 m3; (3) Isentropic expansion to 1.0 m3; (4) constant volume cooling back to 0.1 MPa. Calculate the temperatures at the ends of each process, and the thermal efficiency of the cycle. ( = 1.4) 2. A steam power plant operates on a Rankine cycle and is supplied with steam at 3.0 MPa and 300°C. The steam exhausts to a condenser at a pressure of 0.01 MPa. Calculate (a) the dryness fraction of the steam entering the condenser, (b) the work and heat transfers per kg, and (c) the efficiency of the cycle. 3. An air-standard Otto cycle has a compression ratio of 8. At the beginning of the compression process, the air is at 100 kPa and 17°C. If 800 kJkg-1 of energy is transferred to the air during the heat addition process, determine (a) the maximum pressure and temperature in the cycle, (b) the net work output and (c) the thermal efficiency. (CP = 1.005 kJkg-1K-1, CV = 0.718 kJkg-1K-1) 4. An air-standard Diesel cycle has a compression ratio of 18 and a cut-off ratio of 2. At the beginning of the compression process, the working fluid is at 26.7°C, 0.1 MPa and 1.9 litres volume. Determine (a) the temperature and pressure at the end of each process, (b) the work output and (c) the thermal efficiency. (R = 287 Jkg-1K-1,  = 1.4) 5. A reciprocating engine operates on a Carnot cycle with air as the working fluid. The maximum cylinder volume is 1.0 litres and the minimum cylinder volume is 0.15 litres. The isothermal compression ceases when the cylinder volume is 0.5 litres. If the minimum cycle temperature is 25°C and the minimum cycle pressure is 0.1MPa, determine the heat transfers involved, the net work output, and the thermal efficiency. ( = 1.4, R = 287 Jkg-1K-1) 6. A steam power plant operates on a Rankine cycle with a single reheat stage. The steam leaves the boiler at 12MPa and enters the condenser at 0.1 MPa. The reheater pressure is 25% of the boiler pressure, and the steam temperature at the inlets of both turbine stages is 500°C. Calculate all the work and heat transfers in the cycle, and the efficiency of the power plant. 7. An internal combustion engine with a compression ratio of 8.5 operates on an air- standard Otto cycle. The minimum and maximum temperatures in the cycle are 21°C and 1550°C respectively. The minimum pressure in the cycle is 0.1 MPa and the maximum cycle volume is 1.4 litres. Calculate (a) the pressure and temperature at the end of each process, (b) the cycle efficiency, and (c) the mean effective pressure. ( = 1.4, R = 287Jkg-1K-1) 8. An air-standard Diesel cycle operates with a compression ratio of 20 between maximum and minimum cycle temperatures of 1657°C and 18°C respectively. Calculate (a) the cut- off ratio, (b) all work and heat transfers for each process, and (c) the cycle efficiency. (CP = 1004.5 Jkg-1K-1, CV = 717.5 Jkg-1K-1) 1 9. A power plant operates on an ideal Brayton cycle with a pressure ratio of 10. The compressor and turbine inlet temperatures are 25°C and 900°C respectively. Calculate (a) the work and heat transfers per unit mass, (b) the back work ratio, and (c) the efficiency of the cycle. Also calculate the mass flow rate required to produce a power output of 40 kW, the rate of heat input required for this output, and the total power consumption of the compressor. ( = 1.4, R = 287Jkg-1K-1) 10. A flat insulating panel 0.8 m wide by 1.5 m high consists of two 4 mm thick outer layers of material with k = 0.78 Wm-1K-1 separated by a 10 mm thick inner layer with k = 0.026Wm-1K-1. Heat is transferred from a fluid on one side at 20°C with a combined radiative and convective heat transfer coefficient of 10 Wm-2K-1 into a fluid on the other side at -10°C with a combined radiative and convective heat transfer coefficient of 40 Wm-2K-1. Calculate the temperatures of all surfaces in the insulating structure, and the rate of heat transfer through the panel. Answers: 1. 891.4K, 1456.5K, 579.8K, 63.5% 2. (a) x = 0.785; (b) w12 = –3.02 kJkg-1, q23 = 2799.1 kJkg-1, w34 = 923.6 kJkg-1, q41 = – 1878.5 kJkg-1; (c) 32.9% 3. (a) 4910 kPa, 1780.8K; (b) 451.8 kJkg-1; (c) 56.5% 4. (a) 679.7°C, 5.72 MPa; 1632.5°C, 5.72 MPa; 518.1°C, 0.264 MPa; (b) 1.34 kJ; (c) 63.2% 5. Q23 = 112.2 J, Q41 = –69.3 J, WNET = 42.9 J,  = 38.2% 6. qin = 3409.5 kJkg-1, qout = –2211 kJkg-1, win = –12.4 kJkg-1, wout = 1210.9 kJkg-1,  = 35.2% 7. (a) 0.1 MPa, 294.15K; 2.0 MPa, 692.4K; 5.27 MPa, 1823.15K; 0.263 MPa, 774.6K; (b) W12 = –473.7 J, Q23 = 1345.2 J, W34 = 1247.4 J, Q41 = –571.5 J; (c) 0.626 MPa. 8. (a) 2.0; (b) q12 = 0 kJkg-1, w12 = –483.5 kJkg-1; q23 = 969.5 kJkg-1, w23 = 277 kJkg-1; q34 = 0 kJkg-1, w34 = 833.5 kJkg-1; q41 = –342.4 kJkg-1, w41 = 0 kJkg-1; (c)  = 64.7% 9. (a) q12 = 0 kJkg-1, w12 = –278.7kJkg-1; q23 = 600.2kJkg-1, w23 = 0 kJkg-1; q34 = 0 kJkg-1, w34 = 568.1kJkg-1; q41 = –310.8 kJkg-1, w41 = 0 kJkg-1; (b) 49.1%; (c)  = 48.2%, 0.138 kgs-1, 83 kW, 19.6 kW. 10. Q = 69.2 W. 2