A regenerative Brayton cycle is schematically shown below. Air at state 1 enters the compressor at 300 K and 1 bar. The pressure ratio is 8, and the compressor and the turbine operate with isentropic efficiencies of 80% and 89%, respectively. The effectiveness of the regenerative heat exchanger is 82%. Hot air at state 4 leaves the combustor at 1200 K. The exhaust of the cycle (state 6) is discharged to the environment. Neglect any pressure drop in the flow path of the air. Per unit mass flow rate of the air, determine (a) the work requirement of the compressor; (b) the work production of the turbine; (c) the heat added to the air in the combustor; (d) the net work production of the cycle; (e) the thermal efficiency of the cycle; (f) the mass flow rate of the air if the net power production of the cycle is 80 kW. Use k = 1.4 in your calculations.

A Rankine cycle with one closed heater and one open heater is schematically shown below. Steam leaving the boiler at 500 °C and 10 MPa (state 8) is expanded in the turbine to 7 kPa (state 11). At the location of 500 kPa (state 9) and 250 kPa (state 10), steam is extracted from the turbine to preheat the water in the open and the closed heaters, respectively. The temperature of the water at state 5 is the condensation temperature of the extracted steam at state 10, all of which condenses within the closed heater. The condensate is then throttled (state 4) through a valve to the condenser pressure. The exit flow of the open heat is saturated liquid. The isentropic efficiencies of the turbine and pumps are 92% and 72% respectively. The rate of heat transfer in the boiler is 5 MW. Determine (a) the steam mass flow rate at state 8; (b) the steam mass flow rate at the extraction points; (c) the power production of the turbine; (d) the thermal efficiency of the cycle.

A simple Brayton cycle with a net power output of 1 MW is combined with a regenerative Rankine cycle operating with steam as the working fluid. Air at 20 °C and 100 kPa enters the compressor where it is pressurized to 1.2 MPa. The isentropic efficiency of the compressor is 80%. The gas turbine operating with an isentropic efficiency of 90% receives hot air at 1000 °C. The exhaust stream of the gas turbine at 110 kPa is sent to a heat exchanger to produce 0.546 kg/s steam at 485 °C and 4.5 MPa. The exhaust gas at 100 kPa is finally discharged to the atmosphere. Steam is extracted from the turbine at 550 kPa. The preheated water leaving the open heater is saturated liquid. The water leaving the condenser is at 36 °C and 9.5 kPa. The isentropic efficiency of the steam turbine is 89%. Both pumps operate with an identical isentropic efficiency of 75%. Determine (a) the mass flow rate of the air; (b) the mass flow rate of the extracted steam; (c) the temperature at state 5; (d) the quality at the exhaust of the steam turbine; (e) the power output of the Rankine cycle; (f) the thermal efficiency of the combined cycle.

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