(a) Explanation Figure-(1) shows the T - s diagram for the Rankine cycle. Figure-(1) The x -axis shows the entropy change and y -axis shows the temperature. Write the expression for first stage turbine efficiency. η T 1 = h 1 − h 2 h 1 − h 2 s (I) Here, specific enthalpy at state 2 is h 2 , specific enthalpy at state 1 is h 1 , specific enthalpy of vaporization is h 2 s and first stage turbine efficiency is η T 1 . Write the expression for entropy at state 2. s 2 = s f − ( s f g ) ( h 2 − h f h f g ) (II) Here, specific entropy at state 3 is s 2 , specific enthalpy at state 2 is h 2 , specific enthalpy at saturated liquid state is h f , specific enthalpy of vaporization is h f g , specific entropy at saturated liquid state is s f , and specific entropy of vaporization is s f g . Write the expression for dryness fraction at state 3s. x 3 s = s 2 − s f ( s f g ) (III) Here, specific entropy at state 3 is s 3 , specific entropy at saturated liquid state is s f , dryness fraction is x 3 s , and specific entropy of vaporization is s f g . Write the expression for enthalpy at state 3s. h 3 s = h f + x 3 s h f g (IV) Here, specific enthalpy at state 3s is h 3 s , specific enthalpy at saturated liquid state is h f , specific enthalpy of vaporization is h f g and the dryness fraction is x 3 s . Write the expression for second stage turbine efficiency. η T 2 = h 2 − h 3 h 2 − h 3 s (V) Here, specific enthalpy at state 2 is h 2 , specific enthalpy at state 3 is h 3 , specific enthalpy of vaporization is h 3 s and second stage turbine efficiency is η T 2 . Write the expression for enthalpy at state 3. h 3 = h f + x 3 h f g (VI) Here, specific enthalpy at state 3 is h 3 , specific enthalpy at saturated liquid state is h f , specific enthalpy of vaporization is h f g and dryness fraction is x 3 . Write the expression for entropy at state 3. s 3 = s f + x 3 ( s f g ) (VII) Here, specific entropy at state 3 is s 3 , specific entropy at saturated liquid state is s f , dryness fraction is x 3 , and specific entropy of vaporization is s f g . Write the expression for entropy at state 4. s 3 = s f + x 4 s ( s f g ) (VIII) Here, specific entropy at state 3 is s 3 , specific entropy at saturated liquid state is s f , dryness fraction is x 4 s , specific entropy of vaporization is s f g . Write the expression for enthalpy at state 3. h 4 s = h f + x 4 s h f g (IX) Here, specific enthalpy at state 4 s is h 4 s , specific enthalpy at saturated liquid state is h f , specific enthalpy of vaporization is h f g and dryness fraction is x 4 s . Write the expression for third stage turbine efficiency. η T = h 3 − h 4 h 3 − h 4 s (X) Here, specific enthalpy at state 3 is h 3 , specific enthalpy at state 4 is h 4 , specific enthalpy of saturated vapour is h 4 s and third stage turbine efficiency is η T . Write the expression for the pump work for the process (5-6). W p 1 = − v f ( p 6 − p 5 ) (XI) Here, pump work is W p 1 , volume at saturated vapor phase is v f , pressure at state 5 is p 5 and pressure at state 6 is p 6 . Write the energy equation for the pump for the process (5-6 s ). h 5 = w p 1 + h 6 s (XII) Here, specific enthalpy at state 5 is h 5 and specific enthalpy at state 6 s is h 6 s Write the expression for pump efficiency for process (5-6 s ). η P = h 6 s − h 5 h 6 − h 5 (XIII) Here, specific enthalpy at state 6 s is h 6 s , specific enthalpy at state 5 is h 5 , specific enthalpy at saturated vapor state 6 is h 6 and pump efficiency is η P . Write the expression for the pump work for the process (7-8). W p 2 = − v f ( p 8 − p 7 ) (XIV) Here, pump work is W p 2 , volume at saturated vapor phase is v 3 , pressure at state 7 is p 7 and pressure at state 8 is p 8 . Write the energy equation for the pump work for the process (7-8 s ). h 7 = w p 2 + h 8 s (XV) Here, specific enthalpy at state 7 is h 7 and enthalpy at state 8 s is h 8 s Write the expression for pump efficiency for process (7-8). η P = h 8 s − h 7 h 8 − h 7 (XVI) Here, specific enthalpy at state 8 s is h 6 s , specific enthalpy at state 7 is h 7 , specific enthalpy at saturated vapor state 8 is h 8 and pump efficiency is η P . Write the expression for extraction of steam at state 2. y = ( h 9 − h 8 ) ( h 2 − h 10 ) (XVII) Here, enthalpy at state 9 is h 9 , extraction of steam at state 2 is y and enthalpy at state 10 is h 10 . Write the expression for mass and energy balance to open feed water heater. ( 1 − y − y ′ ) h 6 + y h 11 + y ′ h 3 − h 7 = 0 (XVIII) Write the expression for turbine work output. W T = ( h 1 − h 2 ) + ( 1 − y ) ( h 2 − h 3 ) + ( 1 − y − y ′ ) ( h 3 − h 4 ) (XVIX) Here, extraction of steam at state 3 is y ′ . Write the expression for pump work input. W P = ( 1 − y − y ′ ) ( h 6 − h 5 ) + ( h 8 − h 7 ) (XX) Write the expression for net power developed. W ˙ n e t = m ˙ ( W T + ( − W P ) ) (XXI) Here, mass flow rate is m ˙ . Conclusion: Refer to Table A-4, “Properties of superheated water vapor” to obtain 3465.4 kJ / kg for h 1 , and 6.5132 kJ / kg ⋅ K for s 1 at pressure 16 MPa and inlet temperature 560 ° C for T 1 . Refer to Table A-2, “Properties of superheated water vapor” to obtain 3015.4 kJ / kg for h f , 101.8 kJ / kg for h f g , 6.4553 kJ / kg ⋅ K for s f and 0.16 kJ / kg ⋅ K for s f g at pressure 4 MPa . Substitute 3465.4 kJ / kg for h 1 , 0.85 for η T 1 and 3050.864 kJ / kg for h 2 s in Equation (I). 0.85 = 3465.4 kJ / kg − h 2 3465.4 kJ / kg − 3050.864 kJ / kg h 2 = 3465.4 kJ / kg − 414.536 kJ / kg ( 0.85 ) h 2 = 3113.044 kJ / kg Substitute 3015.4 kJ / kg for h f , 101.8 kJ / kg for h f g , 3113.044 kJ / kg for h 2 , 6.4553 kJ / kg ⋅ K for s f and 0.16 kJ / kg ⋅ K for s f g in Equation (II). s 2 = 6.4553 kJ / kg ⋅ K − ( 0.16 kJ / kg ⋅ K ) ( 3113.044 kJ / kg − 3015.4 kJ / kg 101.8 kJ / kg ) = 6.4553 kJ / kg ⋅ K − ( 0.16 kJ / kg ⋅ K ) ( 97.644 kJ / kg 101.8 kJ / kg ) = 6.61471 kJ / kg Refer to Table A-3, “Properties of superheated water vapor” to obtain, 561.47 kJ / kg for h f , 2163.8 kJ / kg for h f g , 1.6718 kJ / kg ⋅ K for s f , 1.0732 × 10 − 3 m 3 / kg for v f and 5.3201 kJ / kg ⋅ K for s f g at pressure 0.3 MPa . Substitute 6.61471 kJ / kg ⋅ K for s 2 , 1.6718 kJ / kg ⋅ K for s f and 5.3201 kJ / kg ⋅ K for s f g in Equation (III). 6.61471 kJ / kg ⋅ K = 1.6718 kJ / kg ⋅ K + x 3 s ( 5.3201 kJ / kg ⋅ K ) x 3 s = 4.9429 kJ / kg ⋅ K 5.3201 kJ / kg ⋅ K x 3 s = 0.9291 Substitute 561.47 kJ / kg for h f , 2163.8 kJ / kg for h f g and 0.9291 for x 3 s in Equation (IV). h 3 s = 561.47 kJ / kg + 0.9291 ( 2163.8 kJ / kg ) = 561.47 kJ / kg + 2010.38 kJ / kg = 2571.856 kJ / kg Substitute 0.85 for η T 2 , 2571.856 kJ / kg for h 3 s , 3113.044 kJ / kg for h 2 and 2571.856 kJ / kg for h 3 s in Equation (V). 0.85 = 3113.044 kJ / kg − h 3 3113.044 kJ / kg − 2571.856 kJ / kg h 3 = 3113.044 kJ / kg − 541.188 kJ / kg ( 0.85 ) h 3 = 2653.034 kJ / kg Substitute 2653.034 kJ / kg for h 3 , 561.47 kJ / kg for h f and 2163.8 kJ / kg for h f g in Equation (VI). 2653.034 kJ / kg = 561.47 kJ / kg + x 3 2163.8 kJ / kg x 3 = ( 2653.034 kJ / kg − 561.47 kJ / kg ) 2163.8 kJ / kg x 3 = 0.9666 Substitute 0.9666 for x 3 , 1.6718 kJ / kg ⋅ K for s f and 5.3201 kJ / kg ⋅ K for s f g in Equation (VII) s 3 = 1.6718 kJ / kg ⋅ K + 0.9666 ( 5.3201 kJ / kg ⋅ K ) = 1 b) To determine The heat transfer rate to the working fluid passing through the steam generator. (c) To determine The thermal efficiency (d) To determine The mass flow rate of the cooling water passing through the condenser.

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118412930

Author: Michael J. Moran, Howard N. Shapiro, Daisie D. Boettner, Margaret B. Bailey

Publisher: WILEY

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Chapter 8.6, Problem 68P

(a)

To determine

The net power developed.

To determine

The heat transfer rate to the working fluid passing through the steam generator.

(c)

To determine

The thermal efficiency

(d)

To determine

The mass flow rate of the cooling water passing through the condenser.

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Chapter 8.6, Problem 67P

Chapter 8.6, Problem 69P

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Chapter 8 Solutions

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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