(a) Explanation Write the expression for the saturated temperature at state 2. T 2 s = T 1 ( p 2 p 1 ) k − 1 / k (I) Here, the specific heat ratio is k , the temperature at state 1 is T 1 , the saturated temperature at state 2 is T 2 s , the pressure at inlet of turbine is p 1 and the pressure at exit is p 2 . Write the expression for the temperature at state 2. T 2 = T 1 + ( T 2 s − T 1 η c ) (II) Here, the temperature at state 2 is T 2 and the compressor efficiency is η c . Write the expression for the saturated temperature at state 4. T 4 s = T 3 ( p 4 p 3 ) k − 1 / k (III) Here, the saturated temperature at state 4 is T 4 s , the pressure at state 3 is p 3 and the pressure at state 4 is p 4 . Write the expression for the temperature using turbine efficiency. T 4 = T 3 − η t ( T 3 − T 4 s ) (IV) Here, the thermal efficiency of the turbine is η t , the temperature at state 3 is T 3 , the temperature at state 4 is T 4 . Write the expression for the thermal efficiency of the cycle. η = 1 − ( T 4 − T 1 ) ( T 3 − T 2 ) (V) Here, the thermal efficiency is η Conclusion: Refer to table A-20E “Ideal gas specific heats of some common gases” to obtain the specific heat constant, specific heat ratio at temperature T 1 = 520 °R as 0.240 Btu / lb ⋅ °R and 1.401 respectively. Substitute 520°R for T 1 , 1.401 for k and 14 for p 2 p 1 in Equation (I). T 2 s = ( 520°R ) ( 14 ) 1.401 − 1 1.401 = ( 520°R ) ( 14 ) 0.28622 ≈ 1106.8 °R Substitute 520°R for T 1 , 0 (b) To determine The net power of the cycle. (c) To determine The rate of the entropy production in the turbine. The rate of the entropy production in the compressor.

Fundamentals of Engineering Thermodynamics, Binder Ready Version

8th Edition

ISBN: 9781118820445

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

Publisher: WILEY

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Question

Chapter 9.14, Problem 56P

(a)

To determine

The thermal efficiency for the cycle.

(b)

To determine

The net power of the cycle.

(c)

To determine

The rate of the entropy production in the turbine.

The rate of the entropy production in the compressor.

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Chapter 9.14, Problem 55P

Chapter 9.14, Problem 57P

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Fundamentals of Engineering Thermodynamics, Binder Ready Version

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