Thermodynamics

542 | Thermodynamics9–64E An ideal Ericsson engine using helium as the workingfluid operates between temperature limits of 550 and3000 R and pressure limits of 25 and 200 psia. Assuming amass flow rate of 14 lbm/s, determine (a) the thermal efficiencyof the cycle, (b) the heat transfer rate in the regenerator,and (c) the power delivered.9–65 Consider an ideal Ericsson cycle with air as the workingfluid executed in a steady-flow system. Air is at 27°C and120 kPa at the beginning of the isothermal compressionprocess, during which 150 kJ/kg of heat is rejected. Heattransfer to air occurs at 1200 K. Determine (a) the maximumpressure in the cycle, (b) the net work output per unit mass ofair, and (c) the thermal efficiency of the cycle. Answers:(a) 685 kPa, (b) 450 kJ/kg, (c) 75 percent9–66 An ideal Stirling engine using helium as the workingfluid operates between temperature limits of 300 and 2000 Kand pressure limits of 150 kPa and 3 MPa. Assuming the massof the helium used in the cycle is 0.12 kg, determine (a) thethermal efficiency of the cycle, (b) the amount of heat transferin the regenerator, and (c) the work output per cycle.Ideal and Actual Gas-Turbine (Brayton) Cycles9–67C Why are the back work ratios relatively high in gasturbineengines?9–68C What four processes make up the simple ideal Braytoncycle?9–69C For fixed maximum and minimum temperatures, whatis the effect of the pressure ratio on (a) the thermal efficiencyand (b) the net work output of a simple ideal Brayton cycle?9–70C What is the back work ratio? What are typical backwork ratio values for gas-turbine engines?9–71C How do the inefficiencies of the turbine and thecompressor affect (a) the back work ratio and (b) the thermalefficiency of a gas-turbine engine?9–72E A simple ideal Brayton cycle with air as the workingfluid has a pressure ratio of 10. The air enters the compressorat 520 R and the turbine at 2000 R. Accounting forthe variation of specific heats with temperature, determine(a) the air temperature at the compressor exit, (b) the backwork ratio, and (c) the thermal efficiency.9–73 A simple Brayton cycle using air as the workingfluid has a pressure ratio of 8. The minimumand maximum temperatures in the cycle are 310 and 1160 K.Assuming an isentropic efficiency of 75 percent for the compressorand 82 percent for the turbine, determine (a) the airtemperature at the turbine exit, (b) the net work output, and(c) the thermal efficiency.9–74 Reconsider Problem 9–73. Using EES (or other)software, allow the mass flow rate, pressure ratio,turbine inlet temperature, and the isentropic efficiencies of theturbine and compressor to vary. Assume the compressor inletpressure is 100 kPa. Develop a general solution for the problemby taking advantage of the diagram window method forsupplying data to EES software.9–75 Repeat Problem 9–73 using constant specific heats atroom temperature.9–76 Air is used as the working fluid in a simple idealBrayton cycle that has a pressure ratio of 12, a compressorinlet temperature of 300 K, and a turbine inlet temperature of1000 K. Determine the required mass flow rate of air for anet power output of 70 MW, assuming both the compressorand the turbine have an isentropic efficiency of (a) 100 percentand (b) 85 percent. Assume constant specific heats atroom temperature. Answers: (a) 352 kg/s, (b) 1037 kg/s9–77 A stationary gas-turbine power plant operates on asimple ideal Brayton cycle with air as the working fluid. Theair enters the compressor at 95 kPa and 290 K and the turbineat 760 kPa and 1100 K. Heat is transferred to air at arate of 35,000 kJ/s. Determine the power delivered by thisplant (a) assuming constant specific heats at room temperatureand (b) accounting for the variation of specific heatswith temperature.9–78 Air enters the compressor of a gas-turbine engine at300 K and 100 kPa, where it is compressed to 700 kPa and580 K. Heat is transferred to air in the amount of 950 kJ/kgbefore it enters the turbine. For a turbine efficiency of 86 percent,determine (a) the fraction of the turbine work outputused to drive the compressor and (b) the thermal efficiency.Assume variable specific heats for air.9–79 Repeat Problem 9–78 using constant specific heats atroom temperature.9–80E A gas-turbine power plant operates on a simpleBrayton cycle with air as the working fluid. The air enters theturbine at 120 psia and 2000 R and leaves at 15 psia and1200 R. Heat is rejected to the surroundings at a rate of 6400Btu/s, and air flows through the cycle at a rate of 40 lbm/s.Assuming the turbine to be isentropic and the compresssor tohave an isentropic efficiency of 80 percent, determine the netpower output of the plant. Account for the variation of specificheats with temperature. Answer: 3373 kW9–81E For what compressor efficiency will the gas-turbinepower plant in Problem 9–80E produce zero net work?9–82 A gas-turbine power plant operates on the simple Braytoncycle with air as the working fluid and delivers 32 MW ofpower. The minimum and maximum temperatures in the cycleare 310 and 900 K, and the pressure of air at the compressorexit is 8 times the value at the compressor inlet. Assuming anisentropic efficiency of 80 percent for the compressor and86 percent for the turbine, determine the mass flow rate of airthrough the cycle. Account for the variation of specific heatswith temperature.9–83 Repeat Problem 9–82 using constant specific heats atroom temperature.