To determine The power produced by the turbine, heat supplied in the boiler, and thermal efficiency. Explanation The given cycle is the simple Rankine cycle with water as the working fluid and operated at the boiler and condenser temperatures of 200 ° C and 40 ° C respectively. Refer Table A-4, “Saturated water-Temperature table”. The saturation pressures corresponding to the temperatures of 300 ° C and 40 ° C is as follows. P 1 = P @ 40 ° C = 7.3851 kPa P 2 = P @ 300 ° C = 8588 kPa The simple Rankine cycle involves following processes and following conditions: Processes: 1. Process 1 to 2 – Isentropic compression in a Pump 2. Process 2 to 3 – Heat addition at constant pressure in a Boiler 3. Process 3 to 4 – Isentropic expansion in a Turbine 4. Process 4 to 1 – Heat rejection at constant pressure in a Condenser Conditions: The pressure is constant for the process 2 to 3 and the process 4 to 1. P 2 = P 3 and P 4 = P 1 The entropy is constant for the process 1 to 2 and the process 3 to 4. s 1 = s 2 and s 3 = s 4 Here, water is the working fluid. Write the formula for work done by the pump during process 1-2. w p,in = v 1 ( P 2 − P 1 ) (I) Here, the specific volume is v , the pressure is P . Write the formula for enthalpy ( h ) at state 2. h 2 = h 1 + w p,in (II) Write the formula for power produced by the turbine ( W ˙ T, out ) . w T, out = h 3 − h 4 (III) The quality of water at the exit of the turbine is expressed as follows. x 4 = s 4 − s f , 4 s f g , 4 (IV) The enthalpy and entropy at state 4 is expressed as follows. h 4 = h f , 4 + x 4 h f g , 4 (V) Here, the enthalpy is h , the entropy is s , the quality of the water is x , the suffix f indicates the fluid condition, the suffix f g indicates the change of vaporization phase; the suffix 4 indicates the state 4. Write the formula for heat in ( q in ) and heat out ( q out ) of the cycle. q in = h 3 − h 2 (VI) q out = h 4 − h 1 (VII) Write the formula for thermal efficiency of the cycle ( η th ) . η th = 1 − q out q in (VIII) At state 1: The water exits the condenser as a saturated liquid at the temperature of 40 ° C . Hence, the enthalpy at state 1 is as follows. h 1 = h f @ 40 ° C Refer Table A-4, “Saturated water-Temperature table”. The enthalpy ( h 1 ) and specific volume ( v 1 ) at state 1 corresponding to the temperature of 40 ° C is 167.53 kJ/kg and 0.001008 m 3 /kg respectively. At state 3: (Turbine inlet) The steam enters the turbine without any superheating i.e. the quality ( x 3 ) of the steam is 1 . Hence, the steam is at the state of saturated vapor. Refer Table A-4, “Saturated water-Temperature table”. The enthalpy ( h 3 = h g ) and entropy ( s 3 = s g ) at state 3 corresponding to the temperature of 300 ° C is as follows. h 3 = h g @ 250 ° C = 2749.6 kJ/kg s 3 = s g @ 250 ° C = 5.7059 kJ/kg ⋅ K At state 4: (Condenser inlet) Refer Table A-4, “Saturated water-Temperature table”. Obtain the following properties corresponding to the temperature of 40 ° C . h f , 4 = 167.53 kJ/kg h f g , 4 = 2406

8th Edition

ISBN: 9780073398174

Author: Yunus A. Cengel Dr., Michael A. Boles

Publisher: McGraw-Hill Education

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Chapter 10.9, Problem 14P

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The power produced by the turbine, heat supplied in the boiler, and thermal efficiency.

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Thermodynamics: An Engineering Approach

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