a) Explanation Draw the T-s diagram for the ideal Rankine cycle as shown in Figure (1). Write the expression for the specific work input to the system. w p,in = v 1 ( P 2 − P 1 ) / η P (I) Here, pressure at state 1 is P 1 , pressure at state 2 is P 2 , efficiency of pump in the steam power plant is η P and specific volume of steam at state 1 is v 1 . Write the expression for the enthalpy of steam at state 2. h 2 = h 1 + w p , in (II) Here, specific enthalpy of steam at state 1 is h 1 , and specific enthalpy of steam at state 2 is h 2 . Write the expression for the specific enthalpy of steam at state 4. h 4 = h f + x 4 h f g (III) Here, specific enthalpy of vaporization of steam at 1 , 250 psia is h f g , specific volume of liquid at 2 psia is h f . Write the expression for the specific entropy of steam at state 4. s 4 = s f + x 4 s f g (IV) Here, specific enthalpy of vaporization of steam at 1 , 250 psia is s f g , specific volume of liquid at 2 psia is s f . The temperature at the inlet of turbine is determined through a series of trial and error since the values are not direct. Hence, Write the expression for the quality of steam just before entering the turbine for trial 1. x 4 s = s 4 s − s f s f g (V) Here, the specific entropy of the steam just before entering the turbine is s 4 s . Write the expression for the specific enthalpy of steam just before entering the turbine for trial 1. h 4 s = h f + x 4 s h f g (VI) Here, specific enthalpy of steam just before entering the turbine is h 4 s . Write the expression for the efficiency of turbine for trial 1. η T 1 = h 3 − h 4 h 3 − h 4 s (VII) Conclusion: Refer to Table A-5E, “Saturated water-Pressure table”, obtain the following properties at the pressure of 2 psia . h g = 94 .02 Btu / lbm h f g = 1021.7 Btu / lbm v g = 0 .016230 ft 3 / lbm s f =0 .17499 Btu / lbm ⋅ K s f g =1 .7444 Btu / lbm ⋅ K Substitute 0.016230 ft 3 / lbm for v 1 , 2 psia for P 1 , 0.85 for η P , and 1 , 250 psia for P 2 in Equation (I). w p,in = 0.016230 ft 3 / lbm ( 1250 − 2 ) psia ( 1 Btu 5.404 psia ⋅ ft 3 ) / 0.85 = 4.4 Btu / lbm Substitute 94 .02 Btu / lbm for h 1 , and 4 .4 Btu / lbm for w p,in in Equation (II). h 2 = 94 .02 Btu / lbm + 4 .4 Btu / lbm = 98 .42 Btu / lbm Substitute 94 .02 Btu / lbm for h f , 1021 .7 Btu / lbm for h f g , and 0.9 for x 4 in Equation (III). h 4 = 94 .02 Btu / lbm + 0.9 ( 1021 .7 Btu / lbm ) = 1 , 013.6 Btu / lbm Substitute 0 .17499 Btu / lbm ⋅ K for s f , 1 .7444 Btu / lbm ⋅ K for s f g , and 0.9 for x 4 in Equation (IV). s 4 = 0 .17499 Btu / lbm ⋅ K + 0.9 ( 1 .7444 Btu / lbm ⋅ K ) = 1 .74495 Btu / lbm ⋅ K From Figure (1), the entropy of steam at state 3 ( s 3 ) is the same as entropy value of s 4 s . s 3 = s 4 From Table A-6E, “Superheated water”, select the initial enthalpy ( h 3 ) and initial entropy ( s 3 ) at the pressure of 1250 psia and temperature of 900 ° F as 1,439 Btu / lbm and 1 b) To determine The rate of heat addition to the cycle c) To determine The thermal efficiency of the Rankine cycle

8th Edition

ISBN: 9780073398174

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

Publisher: McGraw-Hill Education

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Chapter 10.9, Problem 21P

To determine

The temperature at the inlet of turbine

To determine

The rate of heat addition to the cycle

To determine

The thermal efficiency of the Rankine cycle

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Chapter 10 Solutions

Thermodynamics: An Engineering Approach

Ch. 10.9 - Why is the Carnot cycle not a realistic model for...Ch. 10.9 - Prob. 2P Ch. 10.9 - A steady-flow Carnot cycle uses water as the...Ch. 10.9 - A steady-flow Carnot cycle uses water as the...Ch. 10.9 - Consider a steady-flow Carnot cycle with water as...Ch. 10.9 - Consider a simple ideal Rankine cycle with fixed...Ch. 10.9 - Consider a simple ideal Rankine cycle with fixed...Ch. 10.9 - Consider a simple ideal Rankine cycle with fixed...Ch. 10.9 - How do actual vapor power cycles differ from...Ch. 10.9 - The entropy of steam increases in actual steam...

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