(a) Explanation The figure below shows the T - s diagram of the ideal air-standard regenerative cycle. Figure-(1) The process 1-2 is an isentropic expansion process, 2-3 is an isobaric heat addition process, 3-4 is an isentropic compression process and 4-1 is an isobaric heat rejection process. The regeneration takes place in 2- x . Write the expression for the temperature at state 2. T 2 = T 1 ( p 2 p 1 ) k − 1 k (I) Here, the pressure at state 2 is p 2 , the pressure at state 1 is p 1 , the temperature at state 1 is T 1 and the adiabatic constant is k . Write the expression for the temperature at state 4. T 4 = T 3 ( p 4 p 3 ) k − 1 k (II) Here, the pressure at state 4 is p 4 , the pressure at state 3 is p 3 and the temperature at state 3 is T 3 . Write the expression for the net turbine work. W ˙ n e t = m ˙ [ ( h 3 − h 4 ) − ( h 2 − h 1 ) ] (III) Here, the specific enthalpy at state 1 is h 1 , the specific enthalpy at state 2 is h 2 , the specific enthalpy at state 3 is h 3 , the specific enthalpy at state 4 is h 4 and the mass flow rate is m ˙ . Write the expression for the specific enthalpy change in process 1-2. h 2 − h 1 = c p ( T 2 − T 1 ) Write the expression for the specific enthalpy change in process 3-4. h 3 − h 4 = c p ( T 3 − T 4 ) Substitute c p ( T 3 − T 4 ) for h 3 − h 4 and c p ( T 2 − T 1 ) for h 2 − h 1 in the Equation (III). W ˙ n e t = m ˙ [ c p ( T 3 − T 4 ) − c p ( T 2 − T 1 ) ] = m ˙ c p [ T 3 − T 4 − T 2 + T 1 ] W ˙ n e t m ˙ = c p [ T 3 − T 4 − T 2 + T 1 ] (IV) (b) To determine The energy added by heat transfer. (c) To determine The thermal efficiency. (d) To determine The thermal efficiency by using Equation 9.65.

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118832318

Author: MORAN

Publisher: WILEY

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Question

Chapter 9.14, Problem 66P

(a)

To determine

The net work developed in the cycle.

(b)

To determine

The energy added by heat transfer.

(c)

To determine

The thermal efficiency.

(d)

To determine

The thermal efficiency by using Equation 9.65.

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Chapter 9.14, Problem 65P

Chapter 9.14, Problem 67P

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