Thermo 2 Practice problem on rankine cycle 1. A steam power plant operates on the cycle shown below. If the isentropic efficiency of the turbine is 87 percent and the isentropic efficiency of the pump is 85 percent, determine (a) the thermal efficiency of the cycle and (b) the net power output of the plant for a mass flow rate of 15 kg/s. Answers: (a) 0.361, (b) 18.9 MW
2. Consider a steam power plant operating on the ideal Rankine cycle. Steam enters the turbine at 3 MPa and 350°C and is condensed in the condenser at a pressure of 10 kPa. Determine (a) the thermal efficiency of this power plant, (b) the thermal efficiency if steam is superheated to 600°C instead of 350°C, and (c) the thermal efficiency if the boiler pressure is raised to 15 MPa while the turbine inlet temperature is maintained at 600°C. Answers: (a) 0.334,(b) 0.373,(c) 0.43 3. Consider a steady-flow Carnot cycle with water as the working fluid. The maximum and minimum temperatures in the cycle are 350 and 60°C. The quality of water is 0.891 at the beginning of the heatrejection process and 0.1 at the end. Show the cycle on a T-s diagram relative to the saturation lines, and determine (a) the thermal efficiency, (b) the pressure at the turbine inlet, and (c) the net work output. Answers: (a) 0.465, (b) 1.40 MPa, (c) 1623 kJ/kg 4. Consider a coal-fired steam power plant that produces 300 MW of electric power. The power plant operates on a simple ideal Rankine cycle with turbine inlet conditions of 5 MPa and 450°C and a condenser pressure of 25 kPa. The coal has a heating value (energy released when the fuel is burned) of 29,300 kJ/kg. Assuming that 75 percent of this energy is transferred to the steam in the boiler and that the electric generator has an efficiency of 96 percent, determine the overall plant efficiency (the ratio of net electric power output to the energy input as fuel) and (b) the required rate of coal supply. Answers: (a) 24.5 percent, (b) 150 t/h 5. Consider a steam power plant that operates on a simple ideal Rankine cycle and has a net power output of 45 MW. Steam enters the turbine at 7 MPa and 500°C and is cooled in the condenser at a pressure of 10 kPa by running cooling water from a lake through the tubes of the condenser at a rate of 2000 kg/s. Show the cycle on a T-s diagram with respect to saturation lines, and determine (a) the thermal efficiency of the cycle, (b) the mass flow rate of the steam, and (c) the temperature rise of the cooling water. Answers: (a) 38.9 percent, (b) 36 kg/s, (c) 8.4°C
Thermo 2 Practice problem on rankine cycle 6. A smaller power plant produces 25 kg/s steam at 3 MPa, 600◦C, in the boiler. It cools the condenser with ocean water coming in at 12◦C and returned at 15◦C, so the condenser exit is at 45◦C. Find the net power output and the required mass flow rate of ocean water. 7. A heat engine has a solar collector receiving 0.2 kW/m2, inside of which a transfer medium is heated to 450 K. The collected energy powers a heat engine that rejects heat at 40◦C. If the heat engineshould deliver 2.5 kW, what is the minimum size (area) of the solar collector? 8. A car engine burns 5 kg of fuel (equivalent to adding QH) at 1500K and rejects energy to the radiator and exhaust at an average temperature of 750 K. Assume the fuel has a heating value of 40 000 kJ/kg and find the maximum amount of work the engine can provide. 9. It is proposed to build a 1000 MW electric power plant with steam as the working fluid. The condensers are to be cooled with river water. The maximum steam temperature is 550◦C, and the pressure in the condensers will be 10 kPa. Estimate the temperature rise of the river downstream from the power plant.
10. A 10 m3 tank of air at 500 kPa and 600 K acts as the high-temperature reservoir for a Carnot heat engine that rejects heat at 300 K. A temperature difference of 25◦C between the air tank and the Carnot-cycle high temperature is needed to transfer the heat. The heat engine runs until the air temperature has dropped to 400 K and then stops. Assume constant specific heat capacities for air and determine how much work is given out by the heat engine. 11. In a steam power plant 1000 Btu/s is added at 1200 F in the boiler, 580 Btu/s is taken out at 100 F in the condenser, and the pump work is 20 Btu/s. Find the plant’s thermal efficiency. Assuming the same pump work and heat transfer to the boiler as given, how much turbine power could be produced if the plant were running in a Carnot cycle?
