(a) Explanation The T − s diagram with given state is shown below. Figure-(1) Write the expression for the specific entropy at point 3. s 3 = s f + x 3 s f g (I) Here, the specific entropy of the saturated water is s f and the specific entropy of the water vapor mixture is s f g and the dryness fraction is x 3 corresponding to point 3. Write the expression for the specific enthalpy at point 3 h 3 = h f + x 3 h f g (II) Here, the specific enthalpy of the saturated water is h f and the specific enthalpy of the water vapor mixture is h f g and the dryness fraction is x 3 corresponding to point 3. Write the expression for the enthalpy at point 5. h 5 = h 4 + v 4 ( p 5 − p 4 ) (III) Here, the pressure at the point 5 is p 5 , the pressure at the point 4 is p 4 , the specific volume at point 4 is v 4 , the specific enthalpy at state 5 is h 5 and the specific enthalpy at state 4 is h 4 . Write the expression for the enthalpy at point 7. h 7 = h 6 + v 6 ( p 7 − p 6 ) (IV) Here, the pressure at the point 7 is p 7 , the pressure at the point 6 is p 6 , the specific volume at point 6 is v 6 , the specific enthalpy at state 7 is h 7 and the specific enthalpy at state 6 is h 6 . Write the expression for the fraction of the mass of steam entering in to feed water heater before entering into second stage turbine. y = ( h 6 − h 5 ) ( h 2 − h 5 ) (V) Write the expression for te turbine work. W T m ˙ = ( h 1 − h 2 ) + ( 1 − y ) ( h 2 − h 3 ) (VI) Write the expression for the pump work. W P m ˙ = ( h 7 − h 6 ) + ( 1 − y ) ( h 5 − h 4 ) (VII) Write the expression for the heat addition for 1 st stage turbine. Q ˙ 1 st m ˙ = h 1 − h 7 (VIII) Here, the enthalpy at point 1 is h 1 . Write the expression for thermal efficiency. η t h = W T m ˙ − W P m ˙ Q ˙ 1 st m ˙ (IX) Conclusion: Refer to Superheated steam table to obtain specific enthalpy as 3506.2 kJ / kg and the specific entropy 6.6840 kJ / kg ⋅ K at temperature 560 ° C and pressure 12 MPa and specific enthalpy as 2823.3 kJ / kg , specific entropy 2.1387 kJ / kg ⋅ K , specific enthalpy of liquid as 762.81 kJ / kg , and specific volume of liquid 1.1273 × 10 − 3 m 3 / kg at pressure 1 MPa . Refer to saturated steam table to obtain specific enthalpy of liquid as 151.53 kJ / kg , specific enthalpy of vaporization 2415.9 kJ / kg , and the specific entropy of liquid 0.521 kJ / kg ⋅ K and specific entropy of vaporization as 7.8094 kJ / kg ⋅ K and specific volume of liquid 1.0064 × 10 − 3 m 3 / kg at pressure 6 kPa . Substitute 6.6840 kJ / kg ⋅ K for s 3 , 0.521 kJ / kg ⋅ K for s f and 7.8094 kJ / kg ⋅ K for s f g in Equation (I). 6.6840 kJ / kg ⋅ K = ( 0.521 kJ / kg ⋅ K ) + x 3 × ( 7.8094 kJ / kg ⋅ K ) x 3 = ( 6.6840 kJ / kg ⋅ K ) − ( 0.521 kJ / kg ⋅ K ) ( 7.8094 kJ / kg ⋅ K ) = 0.7892 Substitute 151.53 kJ / kg for h f , 0.7892 for x 3 and 2415.9 kJ / kg for h f g in Equation (II). h 3 = 151.53 kJ / kg + 0.7892 × 2415.9 kJ / kg = 151.53 kJ / kg + 1935 kJ / kg = 2086.57 kJ / kg Substitute 151.53 kJ / kg for h 4 , 1 (b) To determine The mass flow rate into the first turbine stage. (c) To determine The rate of entropy production in the open feed water heater.

8th Edition

ISBN: 9781119391630

Author: MORAN

Publisher: WILEY

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Chapter 8.6, Problem 40P

(a)

To determine

The cycle efficiency.

(b)

To determine

The mass flow rate into the first turbine stage.

(c)

To determine

The rate of entropy production in the open feed water heater.

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Chapter 8.6, Problem 39P

Chapter 8.6, Problem 41P

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