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TUTORIAL-GAS POWER CYCLES 1) An engine working on Otto cycle has an air standard efficiency of 56% and rejects 550 KJ of heat. The pressure and temperature of air at the beginning of compression are 0.1 MPa and 500 C. Find (a) the compression ratio (b) net work done per kg of air (c) the pressure and temperature at the end of compression (d) the maximum pressure in the cycle. 2) In an Otto cycle, the condition at the stating of compression is 270 C and 100 KPa. The heat added is 2000 KJ/kg. The compression ratio is 10. Find the pressure and temperature at each point of the cycle, efficiency and m.e.p. 3) Show that for the Otto cycle the compression ratio for maximum specific work output is given by rc= (Tmax /Tmin) 1/2(1-γ) with usual notations. 4) In an air standard diesel cycle the compression ratio is 15. Compression begins at 0.1 MPa and 400 C. the heat added is 1.675 MJ/kg. Find (a) the maximum temperature of the cycle. (b) the work done per kg of air. (c) Cycle efficiency (d) cutoff ratio (e) the maximum pressure (f) m.e.p. 5) An air standard limited pressure cycle has a compression ratio of 15 and compression begins at 0.1 MPa and 400 C. the maximum pressure is limited to 6 MPa and heat added is 2.0 KJ/kg. a) Heat supplied at constant pressure and volume per kg of air. b) Work done per kg of air. c) The cycle efficiency. d) Cutoff ratio and mean effective pressure. 6) In an air standard brayton cycle the compression ratio is 7 and maximum temperature of the cycle is 8000 C. Compression begins at 0.1 MPa and 400 C. a) The heat supplied per kg of air. b) Work done per kg of air. c) The cycle efficiency. d) The temperature at the end of expansion process. 7) A gas turbine power plant based on brayton cycle between the temperatures 270 C and 8000 C. find (a) the pressure ratio at which cycle ratio approaches the Carnot efficiency. (b) The pressure ratio at which the work done per kg of air is optimum. (c) Compare the efficiency at this pressure ratio with the Carnot efficiency for the given temperatures. 8) In brayton based gas turbine power plant the air at the inlet is 270 C and 0.1 MPa. The pressure ratio is 6.25 and maximum temperature is 8000 C. the turbine and compressor each has 80% efficiency. If a regenerator with 80 % effectiveness is added to the plant. Find, a) Compressor and turbine work per kg of air. b) The heat supplied per kg of air. c) Cycle efficiency. 9) A simple gas turbine plant operating on brayton cycle has air inlet temperature of 270 C, pressure ratio 9 and maximum cycle temperature 7270 C. what will be the improvement in cycle efficiency and output if the turbine process is divided into two stages each of compression ratio 3 with intermediate reheating to 7270 C. [ans. -18.3%, 30.6%] 10) A gas turbine power plant draws air at 1.013 bar, 100 C and has a pressure ratio 5.5 .The Maximum temperature in the cycle is 7500 C. compressor and turbine having isentropic efficiency of 82% and 85%. A heat X’ger with 70% efficiency is fitted between the compressor outlet and combustion chamber. For an airflow of 40 Kg/s. find a) Overall cycle efficiency b) Turbine work. c) The air fuel ratio if the calorific value of fuel is 45.22 MJ/kg [ans. 30.4%, 4272 KW, 115] 11) An ideal air cycle consist of isentropic compression , constant volume heat transfer, isothermal expansion to original pressure and constant pressure heat transfer to original temperature. Find the cycle efficiency in terms of compression ratio (rc) and isothermal expansion ratio (re). In such a cycle the pressure and temperature at the start of the compression is 1 bar and 400 C, the compression ratio is 8 and the maximum temperature is 100 bar. Find the cycle efficiency and m.e.p. [ans. 51.5%, 3.45 bar] 12) Show that mean effective pressure for the Otto cycle is given by ( )