(a) To determine The heat addition of steam entering the first-stage turbine. Explanation The T − s diagram with given state is shown below. Figure-(1) Write the expression for the specific entropy at point 2s. s 2 s = s f + x 2 s 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 2 s corresponding to point 2s. Write the expression for the specific enthalpy at point 2 h 2 s = h f + x 2 s 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 2 s corresponding to point 2s. Write the expression for the isentropic efficiency for 1 st turbine. η T 1 = h 1 − h 2 h 1 − h 2 s (III) Here, the specific enthalpy at point 1 is h 1 and at point 2 is h 2 . Write the expression for the specific entropy at point 3. s 3 s = s f + x 3 s s f g (IV) 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 s corresponding to point 3s. Write the expression for the specific enthalpy at point 3s. h 3 s = h f + x 3 s h f g (V) 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 isentropic efficiency for 2 nd turbine. η T 2 = h 2 − h 3 h 2 − h 3 s (VI) Here, the specific enthalpy at point 3 is h 3 and at point 2 is h 2 . Write the expression for the enthalpy at point 5. h 5 s = h 4 + v 4 ( p 5 − p 4 ) (VII) 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 isentropic efficiency for 1 st pump. η P 1 = h 5 s − h 4 h 5 − h 4 (VIII) Here, the specific enthalpy at point 4 is h 4 and at point 5 is h 5 . Write the expression for the enthalpy at point 7s. h 7 s = h 6 + v 6 ( p 7 − p 6 ) (IX) Here, the pressure at the point 7s 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 7s is h 7 s and the specific enthalpy at state 6 is h 6 . Write the expression for the isentropic efficiency for 2 nd pump. η P I I = h 7 s − h 6 h 7 − h 6 (X) Here, the specific enthalpy at point 7 is h 7 and at point 6 is h 6 . Write the expression for the heat addition for 1 st stage turbine. Q ˙ 1 st = h 1 − h 7 (XI) Here, the enthalpy at point 1 is h 1 . Conclusion: Refer to Superheated steam table to obtain specific enthalpy as 3321.4 kJ / kg and the specific entropy 6.5282 kJ / kg ⋅ K at temperature 480 ° C and pressure 10 MPa . Refer to saturated steam table to obtain specific enthalpy of liquid as 697.22 kJ / kg , specific enthalpy of vaporization 2066.3 kJ / kg , and the specific entropy of liquid 1.9922 kJ / kg ⋅ K and specific entropy of vaporization as 4.7158 kJ / kg ⋅ K and specific volume 1.108 × 10 − 3 m 3 / kg at pressure 7 bar and specific enthalpy of 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 6.5282 kJ / kg ⋅ K for s 2 s , 1.9922 kJ / kg ⋅ K for s f and 4.7158 kJ / kg ⋅ K for s f g in Equation (I). 6.5282 kJ / kg ⋅ K = ( 1.9922 kJ / kg ⋅ K ) + x 2 s × ( 4.7158 kJ / kg ⋅ K ) x 2 s = ( 6.5282 kJ / kg ⋅ K ) − ( 1.9922 kJ / kg ⋅ K ) ( 4.7158 kJ / kg ⋅ K ) = 0.9619 Substitute 697.22 kJ / kg for h f , 0.9619 for x 2 s and 2066.3 kJ / kg for h f g in Equation (II). h 2 s = 697.22 kJ / kg + 0.9619 × 2066.3 kJ / kg = 697.22 kJ / kg + 1987.57 kJ / kg = 2684.8 kJ / kg Substitute 0.8 for η T 1 , 3321.4 kJ / kg for h 1 and 2684.8 kJ / kg for h 2 S in Equation (III) (b) To determine The thermal efficiency. (c) To determine The heat transfer from the working fluid passing through the condenser.

8th Edition

ISBN: 9781119391630

Author: MORAN

Publisher: WILEY

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Chapter 8.6, Problem 38P

(a)

To determine

The heat addition of steam entering the first-stage turbine.

(b)

To determine

The thermal efficiency.

(c)

To determine

The heat transfer from the working fluid passing through the condenser.

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Chapter 8.6, Problem 37P

Chapter 8.6, Problem 39P

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