Thermodynamics

548 | ThermodynamicsThe pressure ratio across each turbine stage is the same. Thehigh-pressure turbine exhaust gas enters the regenerator andthen enters the low-pressure turbine for expansion to thecompressor inlet pressure. Determine the thermal efficiencyof this cycle as a function of the compressor pressure ratioand the high-pressure turbine to compressor inlet temperatureratio. Compare your result with the efficiency of the standardregenerative cycle.9–155 A four-cylinder, four-stroke spark-ignition engineoperates on the ideal Otto cycle with a compression ratio of11 and a total displacement volume of 1.8 liter. The air is at90 kPa and 50°C at the beginning of the compressionprocess. The heat input is 1.5 kJ per cycle per cylinder.Accounting for the variation of specific heats of air with temperature,determine (a) the maximum temperature and pressurethat occur during the cycle, (b) the net work per cycleper cyclinder and the thermal efficiency of the cycle, (c) themean effective pressure, and (d) the power output for anengine speed of 3000 rpm.9–156 A gas-turbine plant operates on the regenerativeBrayton cycle with two stages of reheating and two-stages ofintercooling between the pressure limits of 100 and1200 kPa. The working fluid is air. The air enters the first andthe second stages of the compressor at 300 K and 350 K,respectively, and the first and the second stages of the turbineat 1400 K and 1300 K, respectively. Assuming both the compressorand the turbine have an isentropic efficiency of80 percent and the regenerator has an effectiveness of 75 percentand using variable specific heats, determine (a) the backwork ratio and the net work output, (b) the thermal efficiency,and (c) the second-law efficiency of the cycle. Also determine(d) the exergies at the exits of the combustion chamber(state 6) and the regenerator (state 10) (See Figure 9–43 inthe text). Answers: (a) 0.523, 317 kJ/kg, (b) 0.553, (c) 0.704,(d) 931 kJ/kg, 129 kJ/kg9–157 Electricity and process heat requirements of a manufacturingfacility are to be met by a cogeneration plant consistingof a gas turbine and a heat exchanger for steam production.12Compressor100 kPa30°C350°C 25°CHeatCombustionexchangerchamber31.2 MPa 4 500°C Sat. vapor200°CFIGURE P9–157TurbineThe plant operates on the simple Brayton cycle between thepressure limits of 100 and 1200 kPa with air as the workingfluid. Air enters the compressor at 30°C. Combustion gasesleave the turbine and enter the heat exchanger at 500°C, andleave the heat exchanger of 350°C, while the liquid waterenters the heat exchanger at 25°C and leaves at 200°C as a saturatedvapor. The net power produced by the gas-turbine cycleis 800 kW. Assuming a compressor isentropic efficiency of82 percent and a turbine isentropic efficiency of 88 percent andusing variable specific heats, determine (a) the mass flow rateof air, (b) the back work ratio and the thermal efficiency, and(c) the rate at which steam is produced in the heat exchanger.Also determine (d) the utilization efficiency of the cogenerationplant, defined as the ratio of the total energy utilized to theenergy supplied to the plant.9–158 A turbojet aircraft flies with a velocity of 900 km/hat an altitude where the air temperature and pressure are35°C and 40 kPa. Air leaves the diffuser at 50 kPa with avelocity of 15 m/s, and combustion gases enter the turbine at450 kPa and 950°C. The turbine produces 500 kW of power,all of which is used to drive the compressor. Assuming anisentropic efficiency of 83 percent for the compressor, turbine,and nozzle, and using variable specific heats, determine(a) the pressure of combustion gases at the turbine exit,(b) the mass flow rate of air through the compressor, (c) thevelocity of the gases at the nozzle exit, and (d) the propulsivepower and the propulsive efficiency for this engine. Answers:(a) 147 kPa, (b) 1.76 kg/s, (c) 719 m/s, (d) 206 kW, 0.1569–159 Using EES (or other) software, study the effectof variable specific heats on the thermal efficiencyof the ideal Otto cycle using air as the working fluid.At the beginning of the compression process, air is at 100kPa and 300 K. Determine the percentage of error involved inusing constant specific heat values at room temperature forthe following combinations of compression ratios and maximumcycle temperatures: r 6, 8, 10, 12, and T max 1000,1500, 2000, 2500 K.9–160 Using EES (or other) software, determine theeffects of compression ratio on the net workoutput and the thermal efficiency of the Otto cycle for a maximumcycle temperature of 2000 K. Take the working fluid tobe air that is at 100 kPa and 300 K at the beginning of thecompression process, and assume variable specific heats. Varythe compression ratio from 6 to 15 with an increment of 1.Tabulate and plot your results against the compression ratio.9–161 Using EES (or other) software, determine theeffects of pressure ratio on the net work outputand the thermal efficiency of a simple Brayton cycle for amaximum cycle temperature of 1800 K. Take the workingfluid to be air that is at 100 kPa and 300 K at the beginningof the compression process, and assume variable specificheats. Vary the pressure ratio from 5 to 24 with an incrementof 1. Tabulate and plot your results against the pressure ratio.At what pressure ratio does the net work output become a