(a) Explanation The below figure show the T − s diagram of Rankine cycle with open feed water heater. Figure-(1) Write the expression for enthalpy at point 2. h 2 = h 1 − η t ( h 1 − h 2 s ) (I) Here, the enthalpy at point 1 is h 1 , the enthalpy at point 2s is h 2 s and the isentropic efficiency of turbine is η t . Write the expression for the entropy at point 3s. s 3 s = s f 3 s + x 3 s s f g 3 s (II) Write the expression for enthalpy at point 3s. h 3 s = h f 3 s + x 3 h f g 3 s (III) Here, the enthalpy of liquid at point 3s is h f 3 s , the dryness fraction at point 3 is x 3 , the enthalpy of liquid vapor mixture is h f g 3 s . Write the expression for enthalpy at point 3. h 3 = h 2 − η t ( h 2 − h 3 s ) (IV) Write the expression for pump work during process 4-5. W p 1 = − v 4 ( p 5 − p 4 ) (V) Here, the pressure at point 5 is p 5 , the pressure at point 4 is p 4 , and the specific volume is v 4 . Write the expression for enthalpy at point 5. h 5 = h 4 − ( − W p 1 η p 1 ) (VI) Here, the specific enthalpy at point 4 is h 4 , and the isentropic efficiency of pump 1 is η p 1 . Write the expression for pump work during the process 6-7. W p 2 = − v 6 ( p 7 − p 6 ) (VII) Write the expression for enthalpy at point 7. h 7 = h 6 − ( − W p 2 η p ) (VIII) Here, the specific enthalpy at point 6 is h 6 , and the isentropic efficiency of pump 2 is η p . Write the expression for fraction of extraction steam. y = h 6 − h 5 h 2 − h 7 (IX) Write the expression for the total turbine work. W ˙ T = m ˙ [ ( h 1 − h 2 ) + ( 1 − y ) ( h 2 − h 3 ) ] (X) Write the expression for the total pump work. W ˙ p = m ˙ [ h 5 − h 4 ] (XI) Write the expression for net power output. W ˙ n e t = W ˙ T + W ˙ p (XII) Conclusion: Refer table A-4E, “Properties of superheated water vapor” to obtain the enthalpy and the entropy at point p 1 = 1400 lbf / in 2 and T 1 = 1000 ° F as h 1 = 1493.5 Btu / lb and s 1 = 1.6094 Btu / lb . ° R . Since the process 1-2s is isentropic process so s 1 = s 2 s . Since 2s and 2 point on same constant pressure line on the T − s diagram so p 2 s = p 2 . Refer table A-4E“Properties of superheated water vapor”, obtain the specific enthalpy at the pressure 120 lbf / in 2 and specific entropy 1.6094 Btu / lb ° R by using interpolation method of two variables. Write the formula of interpolation method of two variables. y 2 = ( x 2 − x 1 ) ( y 3 − y 1 ) ( x 3 − x 1 ) + y 1 (V) Here, the variables denote by x and y are specific entropy and specific entalpy. Show the specific entropy at pressure 120 lbf / in 2 and specific entropy 1.6094 Btu / lb ° R as in Table. Specific entropy, Btu / lb ° R specific enthalpy, Btu / lb 1.5950 Btu / lb ° R 1196.2 Btu / lb 1.6094 Btu / lb ° R ? 1.6288 Btu / lb ° R 1224.4 Btu / lb Substitute 1.5950 Btu / lb ° R for x 1 , 1.6094 Btu / lb ° R for x 2 , 1.6288 Btu / lb ° R for x 3 , 1196.2 Btu / lb for y 1 , and 1224.4 Btu / lb for y 3 in Equation (V). y 2 = ( 1.6094 Btu / lb ° R − 1.5950 Btu / lb ° R ) ( 1224.4 Btu / lb − 1196.2 Btu / lb ) ( 1.6288 Btu / lb ° R − 1.5950 Btu / lb ° R ) + 1196.2 Btu / lb = ( 0.0144 Btu / lb ° R ) ( 28.2 Btu / lb ) 0.0338 Btu / lb ° R + 1196.2 Btu / lb = 12.0142 Btu / lb + 1196.2 Btu / lb = 1208.2 Btu / lb From above calculation the specific enthalpy at point 2s is 1208.2 Btu / lb . Substitute 1493.5 Btu / lb for h 1 , 0.85 for η t and 1208.2 Btu / lb for h 2 s in Equation (I). h 2 = 1493.5 Btu / lb − ( 0.85 ) ( 1493.5 Btu / lb − 1208.2 Btu / lb ) = 1493.5 Btu / lb − ( 0.85 ) ( 285.3 Btu / lb ) = 1493.5 Btu / lb − 242.505 Btu / lb = 1250.995 Btu / lb Refer table A-4E, “Properties of superheated water vapor”, obtain the specific entropy at the pressure 120 lbf / in 2 and specific enthalpy 1250.99 Btu / lb by using interpolation method of two variables. Write the formula of interpolation method of two variables. y 2 = ( x 2 − x 1 ) ( y 3 − y 1 ) ( x 3 − x 1 ) + y 1 (V) Here, the variables denote by x and y are specific enthalpy and specific entropy. Show the specific entropy at pressure 120 lbf / in 2 and specific enthalpy 1224.4 Btu / lb and 1251.2 Btu / lb in Table. Specific enthalpy, Btu / lb specific entropy, Btu / lb ° R 1224.4 Btu / lb 1.6288 Btu / lb ° R 1250.99 Btu / lb ? 1251.2 Btu / lb 1.6590 Btu / lb ° R Substitute 1224.4 Btu / lb for x 1 , 1250.99 Btu / lb for x 2 , 1251.2 Btu / lb for x 3 , 1.6288 Btu / lb ° R for y 1 , and 1.6590 Btu / lb ° R for y 3 in Equation (V). y 2 = ( 1250.99 Btu / lb − 1224.4 Btu / lb ) ( 1.6590 Btu / lb ° R − 1.6288 Btu / lb ° R ) ( 1251.2 Btu / lb − 1224.4 Btu / lb ) + 1.6288 Btu / lb ° R = ( 26.59 Btu / lb ) ( 0.0302 Btu / lb ° R ) 26.8 Btu / lb + 1.6288 Btu / lb ° R = 0.0299 Btu / lb ° R + 1.6288 Btu / lb ° R = 1.6587 Btu / lb ° R From above calculation, the specific entropy at point 2 is 1 (b) To determine The rate of heat transfer. (c) To determine The thermal efficiency of the cycle.

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118832301

Author: SHAPIRO

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Chapter 8.6, Problem 56P

(a)

To determine

The mass flow rate of steam.

(b)

To determine

The rate of heat transfer.

(c)

To determine

The thermal efficiency of the cycle.

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Chapter 8.6, Problem 55P

Chapter 8.6, Problem 57P

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Fundamentals of Engineering Thermodynamics

Ch. 8.6 - Prob. 1E Ch. 8.6 - Prob. 2E Ch. 8.6 - Prob. 3E Ch. 8.6 - Prob. 4E Ch. 8.6 - Prob. 5E Ch. 8.6 - Prob. 6E Ch. 8.6 - Prob. 7E Ch. 8.6 - 8. What is the relationship between global climate...Ch. 8.6 - Prob. 9E Ch. 8.6 - Prob. 10E

Ch. 8.6 - Prob. 11E Ch. 8.6 - Prob. 12E Ch. 8.6 - Prob. 13E Ch. 8.6 - Prob. 1CU Ch. 8.6 - Prob. 2CU Ch. 8.6 - 3. The component of the Rankine cycle in which the...Ch. 8.6 - 4. A cycle that couples two vapor cycles so the...Ch. 8.6 - 5. The ratio of the pump work input to the work...Ch. 8.6 - 6. A shell-and-tube-type recuperator in which the...Ch. 8.6 - Prob. 7CU Ch. 8.6 - Prob. 8CU Ch. 8.6 - Prob. 9CU Ch. 8.6 - Prob. 10CU Ch. 8.6 - 11. An example of an external irreversibility...Ch. 8.6 - Prob. 12CU Ch. 8.6 - Prob. 13CU Ch. 8.6 - Prob. 14CU Ch. 8.6 - 15. A direct-contact–type heat exchanger found in...Ch. 8.6 - 16. The component of a regenerative vapor power...Ch. 8.6 - Prob. 17CU Ch. 8.6 - 18. A Rankine cycle that employs an organic...Ch. 8.6 - Prob. 19CU Ch. 8.6 - Prob. 20CU Ch. 8.6 - Prob. 21CU Ch. 8.6 - Prob. 22CU Ch. 8.6 - Prob. 23CU Ch. 8.6 - 24. The purpose of deaeration is ______________. Ch. 8.6 - Prob. 25CU Ch. 8.6 - Prob. 26CU Ch. 8.6 - Prob. 27CU Ch. 8.6 - Prob. 28CU Ch. 8.6 - 29. The total cost associated with a power plant...Ch. 8.6 - Prob. 30CU Ch. 8.6 - Prob. 31CU Ch. 8.6 - Prob. 32CU Ch. 8.6 - Prob. 33CU Ch. 8.6 - Prob. 34CU Ch. 8.6 - Prob. 35CU Ch. 8.6 - Prob. 36CU Ch. 8.6 - Prob. 37CU Ch. 8.6 - Prob. 38CU Ch. 8.6 - Prob. 39CU Ch. 8.6 - 40. For a vapor power cycle with and , the...Ch. 8.6 - Prob. 41CU Ch. 8.6 - Prob. 42CU Ch. 8.6 - Prob. 43CU Ch. 8.6 - Prob. 44CU Ch. 8.6 - Prob. 45CU Ch. 8.6 - Prob. 46CU Ch. 8.6 - Prob. 47CU Ch. 8.6 - Prob. 48CU Ch. 8.6 - Prob. 49CU Ch. 8.6 - 50. In a binary cycle, energy discharged by heat...Ch. 8.6 - Prob. 1P Ch. 8.6 - Prob. 2P Ch. 8.6 - Prob. 3P Ch. 8.6 - Prob. 6P Ch. 8.6 - 8.7 Water is the working fluid in an ideal Rankine...Ch. 8.6 - Prob. 8P Ch. 8.6 - 8.10 Water is the working fluid in an ideal...Ch. 8.6 - Prob. 12P Ch. 8.6 - Prob. 13P Ch. 8.6 - 8.14 On the south coast of the island of Hawaii,...Ch. 8.6 - Prob. 15P Ch. 8.6 - 8.17. Water is the working fluid in a Rankine...Ch. 8.6 - 8.19 Water is the working fluid in a Rankine...Ch. 8.6 - Prob. 20P Ch. 8.6 - Prob. 21P Ch. 8.6 - 8.22 Superheated steam at 8 MPa and 480°C leaves...Ch. 8.6 - Prob. 23P Ch. 8.6 - Prob. 25P Ch. 8.6 - Prob. 26P Ch. 8.6 - 8.27 Steam is the working fluid in the ideal...Ch. 8.6 - Prob. 28P Ch. 8.6 - Prob. 29P Ch. 8.6 - Prob. 30P Ch. 8.6 - Prob. 31P Ch. 8.6 - 8.32 An ideal Rankine cycle with reheat uses water...Ch. 8.6 - Prob. 33P Ch. 8.6 - 8.34 Steam at 4800 lbf/in.2, 1000℉ enters the...Ch. 8.6 - Prob. 35P Ch. 8.6 - Prob. 37P Ch. 8.6 - 8.38 For the cycle of Problem 8.37, reconsider the...Ch. 8.6 - Prob. 39P Ch. 8.6 - Prob. 40P Ch. 8.6 - Prob. 41P Ch. 8.6 - Prob. 42P Ch. 8.6 - Prob. 43P Ch. 8.6 - Prob. 44P Ch. 8.6 - Prob. 45P Ch. 8.6 - Prob. 46P Ch. 8.6 - Prob. 47P Ch. 8.6 - 8.48 For the cycle of Problem 8.47, investigate...Ch. 8.6 - Prob. 49P Ch. 8.6 - Prob. 50P Ch. 8.6 - Prob. 51P Ch. 8.6 - 8.52 As indicated in Fig. P8.52, a power plant...Ch. 8.6 - Prob. 53P Ch. 8.6 - Prob. 54P Ch. 8.6 - Prob. 55P Ch. 8.6 - Prob. 56P Ch. 8.6 - Prob. 57P Ch. 8.6 - Prob. 58P Ch. 8.6 - Prob. 59P Ch. 8.6 - Prob. 60P Ch. 8.6 - Prob. 61P Ch. 8.6 - Prob. 63P Ch. 8.6 - Prob. 64P Ch. 8.6 - Prob. 65P Ch. 8.6 - Prob. 66P Ch. 8.6 - 8.67 Water is the working fluid in a Rankine cycle...Ch. 8.6 - Prob. 68P Ch. 8.6 - Prob. 69P Ch. 8.6 - Prob. 70P Ch. 8.6 - 8.72 Water is the working fluid in a...Ch. 8.6 - Prob. 73P Ch. 8.6 - Prob. 74P Ch. 8.6 - Prob. 75P Ch. 8.6 - 8.76 A binary vapor power cycle consists of two...Ch. 8.6 - A binary vapor cycle consists of two Rankine...Ch. 8.6 - Prob. 78P Ch. 8.6 - Prob. 79P Ch. 8.6 - Prob. 80P Ch. 8.6 - 8.81 Figure P8.81 shows a combined heat and power...Ch. 8.6 - 8.82 Figure P8.82 shows a cogeneration cycle that...Ch. 8.6 - Prob. 83P Ch. 8.6 - 8.84 The steam generator of a vapor power plant...Ch. 8.6 - 8.85 Determine the exergy input, in kJ per kg of...Ch. 8.6 - 8.86 In the steam generator of the cycle of...Ch. 8.6 - Prob. 87P Ch. 8.6 - 8.88 Determine the rate of exergy input, in Btu/h,...Ch. 8.6 - Prob. 89P Ch. 8.6 - Prob. 90P Ch. 8.6 - Prob. 91P Ch. 8.6 - 8.92 Figure P8.92 provides steady-state operating...Ch. 8.6 - 8.93 Steam enters the turbine of a simple vapor...

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