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 ) (I) Here, pressure at state 1 is P 1 , pressure at state 2 is P 2 , 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 1250 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 1250 psia is s f g , specific volume of liquid at 2 psia is s f . Conclusion: Refer to Table A-4E, “Saturated water-Temperature table”, obtain the following properties at the pressure of 2 psia . h f = 94 .2 Btu / lbm h f g = 1021 .7 Btu / lbm v f = 0 .01623 ft 3 / lbm s f = 0 .17499 Btu / lbm ⋅ R s f g = 1 .74444 Btu / lbm ⋅ R From Table A-4E, “Saturated water-Temperature table”, select the enthalpy ( h 1 ) and specific volume ( v 1 ) at the pressure of 2 psia as 94 .02 Btu / lbm and 0.016230 ft 3 / lbm respectively. Substitute 0.016230 ft 3 / lbm for v 1 , 2 psia for P 1 , and 1250 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 ) = 3.74 Btu / lbm Substitute 94 .02 Btu / lbm for h 1 , and 3 .74 Btu / lbm for w p,in in Equation (II). h 2 = 94 .02 Btu / lbm + 3 .74 Btu / lbm = 97 .76 Btu / lbm Substitute 94 .02 Btu / lbm for h f , 1021 .7 Btu / lbm for h f g , and 0 b) To determine The rate of heat input to the boiler c) To determine The thermal efficiency of the Rankine cycle

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Author: CENGEL

Publisher: INTER MCG

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Chapter 10.9, Problem 20P

To determine

The minimum turbine inlet temperature in the Rankine cycle

To determine

The rate of heat input to the boiler

To determine

The thermal efficiency of the Rankine cycle

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Chapter 10.9, Problem 19P

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