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Unit Eleven Homework Solutions

1. Consider a 210 MW steam power plant that operates on a simple ideal Rankine cycle. Steam enters the turbine at 10 MPa and 500^oC and is cooled in the condenser to a pressure of 10 kPa. Show the cycle on a T-s diagram with respect to the saturation lines and determine (a) the quality of steam at the turbine exit, (b) the thermal efficiency of the cycle, and (c) the mass flow rate of the steam.
2. Consider a solar-pond power plant that operates on a simple ideal Rankine cycle with refrigerant-134a as the working fluid. The refrigerant enters the turbine as a saturated vapor at 1.6 MPa and leaves at 0.7 MPa. The mass flow rate of the refrigerant is 6 kg/s. Show the cycle on a T-s diagram with respect to the saturation lines and determine (a) the thermal efficiency and (b) the power output of the plant.
3. 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^oC and is cooled in the condenser to a pressure of 10 kPa by running cooling water from a lake through the condenser at a rate of 2000 kg/s. Show the cycle on a T-s diagram with respect to the 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.
4. A steam power plant operates on an ideal regenerative Rankine cycle. Steam enters the turbine at 6 MPa and 450^oC and is condensed in the condenser at 20 kPa. Steam is extracted from the turbine at 0.4 MPa to heat the feedwater in an open feedwater heater. Water leaves the feedwater heater as a saturated liquid. Show the cycle on a T-s diagram and determine (a) the net work per kilogram of steam flowing through the boiler and (b) the thermal efficiency of the cycle.
5. Repeat problem 4 with the open feedwater heater replaced by a closed feedwater heater. Assume that the feedwater leaves the heater at the condensation temperature of the extracted steam and that the extracted steam leaves the heater as a saturated liquid and is pumped to the line carrying the feedwater.
6. A steam power plant operates on an ideal reheat-regenerative Rankine cycle and has a net power output of 80 MW. Steam enters the high-pressure turbine at 10 MPa and 550^oC and leaves at 0.8 MPa. Some of the steam is extracted at this pressure to heat the feedwater in an open feedwater heater. The rest of the steam is reheated to 500^oC and is expanded in the low pressure turbine to the condenser pressure of 10 kPa. Show the cycle on a T-s diagram and determine (a) the mass flow rate of steam flowing through the boiler and (b) the thermal efficiency of the cycle.