(a) Explanation Write the expression for the mass flow rate into the first stage of the turbine. m ˙ 1 = { W ˙ c y c l e ( h 1 − h 2 ) + ( 1 − y ′ ) ( h 2 − h 3 ) + ( 1 − y ′ − y ″ ) ( h 3 − h 4 ) − ( 1 − y ′ − y ″ ) ( h 6 − h 5 ) − ( h 8 − h 7 ) } (I) Here, the net power developed in the turbine is W ˙ c y c l e , the fraction of the flow at location 2 is y ′ , the specific enthalpy at point 2 is h 2 , the specific enthalpy at point 8 is h 8 , the fraction of the flow at location 3 is y ′ ′ , the specific enthalpy at point 3 is h 3 , the specific enthalpy at point 6 is h 6 , the specific enthalpy at point 7 is h 7 , the specific enthalpy at point 5 is h 5 , the specific enthalpy at point 1 is h 1 and the specific enthalpy at point 4 is h 4 . Write the expression for the fraction of the flow at location 2 at control volume. y ′ = h 9 − h 8 h 2 − h 10 (II) Write the expression for the fraction of the flow at location 3 at control volume. y ′ ′ = h 7 − ( 1 − y ′ ) h 6 − y ′ h 11 h 3 − h 6 (III) 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 (IV) Here, the variables denote by x and y are specific entropy and specific enthalpy. Write the expression for the specific enthalpy at state 4. h 4 = h f 4 + x 4 h f g 4 (V) Here, the dryness fraction at state 4 is x 4 , the saturated specific enthalpy liquid at state 4 is h f 4 and the saturated specific enthalpy liquid and vapor at state 4 is h f g 4 . Write the expression for the specific enthalpy at state 6. h 6 = h 5 + v 5 ( p 6 − p 5 ) (VI) Here, the specific volume at state 5 is v 5 , the pressure at state 5 is p 5 and the pressure at the state 6 is p 6 . Write the expression for the specific enthalpy at state 8. h 8 = h 7 + v 7 ( p 8 − p 7 ) (VII) Here, the specific volume at state 7 is v 7 , the pressure at state 7 is p 7 and the pressure at the state 8 is p 8 . Conclusion: Refer to table A-4E “Properties of superheated water vapor” to obtain the specific enthalpy and specific entropy at pressure p 1 = 1400 lbf / in 2 and temperature T 1 = 1000 ° F as 1493.5 Btu / lb and 1.6094 Btu / lb ⋅ ° R . Refer to table A-4E “Properties of superheated water vapor” to obtain the specific enthalpies and specific entropies at pressure p 2 = 500 lbf / in 2 as 1298.3 Btu / lb , 1356.7 Btu / lb and 1.5585 Btu / lb ⋅ ° R , 1.6112 Btu / lb ⋅ ° R . Since, the temperature is constant for state 1 and 2 so the specific entropies are also same. Show the temperature at 1.5585 Btu / lb ⋅ ° R and 1.6112 Btu / lb ⋅ ° R as in Table (1). Specific entropy, Btu / lb ⋅ ° R specific enthalpy Btu / lb 1.5585 Btu / lb ⋅ ° R 1298.3 Btu / lb 1.6094 Btu / lb ⋅ ° R ? 1.6112 Btu / lb ⋅ ° R 1356.7 Btu / lb Substitute 1.5585 Btu / lb ⋅ ° R for x 1 , 1.6094 Btu / lb ⋅ ° R for x 2 , 1.6112 Btu / lb ⋅ ° R for x 3 , 1298.3 Btu / lb for y 1 , and 1356.7 Btu / lb for y 3 in Equation (IV). y 2 = { [ ( 1.6094 Btu / lb ⋅ ° R − 1.5585 Btu / lb ⋅ ° R ) ( 1356.7 Btu / lb − 1298.3 Btu / lb ⋅ K ) ] ( 1.6112 Btu / lb ⋅ ° R − 1.5585 Btu / lb ⋅ ° R ) + 1298.3 Btu / lb } = ( 2.9725 ) 0.0527 + 1298.3 Btu / lb = 56.404 + 1298.3 Btu / lb ≈ 1354.71 Btu / lb From above calculation the specific enthalpy at state 2 is 1354.71 Btu / lb . Refer to table A-4E “properties of superheated water vapor” to obtain the specific enthalpies and specific entropies at pressure p 3 = 120 lbf / in 2 as 1196.2 Btu / lb , 1224.4 Btu / lb and 1.5950 Btu / lb ⋅ ° R , 1.6288 Btu / lb ⋅ ° R . Since, the temperature is constant for state 1 and 3 so the specific entropies are also same. Show the temperature at 1.5950 Btu / lb ⋅ ° R and 1.6288 Btu / lb ⋅ ° R as in Table (1). 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 (IV). 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 } = ( 0.4060 ) 0.0338 + 1196.2 Btu / lb = 12.011 + 1196.2 Btu / lb ≈ 1208.21 Btu / lb From above calculation the specific enthalpy at state 3 is 1208.21 Btu / lb . Refer to table A-3E “properties of saturated water (liquid-vapor): pressure table” to obtain the specific enthalpy of saturated liquid, specific enthalpy of saturated liquid and vapor and specific entropy at pressure p 4 = 2 lbf / in 2 as 94.02 Btu / lb , 1022.08 Btu / lb and 1.6094 Btu / lb ⋅ ° R . Substitute 0.8221 for x 4 , 94.02 Btu / lb for h f 4 and 1022 (b) To determine The rate of the heat transfer through the steam generator. (c) To determine The thermal efficiency of the cycle.

8th Edition

ISBN: 9781119391630

Author: MORAN

Publisher: WILEY

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Chapter 8.6, Problem 65P

(a)

To determine

The mass flow rate into the first turbine stage.

(b)

To determine

The rate of the heat transfer through the steam generator.

(c)

To determine

The thermal efficiency of the cycle.

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Chapter 8.6, Problem 64P

Chapter 8.6, Problem 66P

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FUND OF ENGINEERING THERMO W/WILEY PLU

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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