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 air in process 2- x is preheated through the exhaust air from 4- y . Write the expression for the thermal efficiency of the air standard cycle. η = 1 − c p ( T y − T 1 ) c p ( T 3 − T x ) = 1 − ( T y − T 1 ) ( T 3 − T x ) (I) Here, the temperature at y is T y , the temperature at state 1 is T 1 , the temperature at state 3 is T 3 , the temperature at state x is T x and the specific heat at constant pressure is c p . For an ideal regenerator the temperature of the gases at the states 2 and y as well as states 4 and x should be equal that is T x = T 4 and T y = T 2 . Substitute T 4 for T x and T 2 for T y in the Equation (I). η = 1 − ( T 2 − T 1 ) ( T 3 − T 4 ) = 1 − ( T 2 T 1 − 1 ) T 1 T 3 ( 1 − T 4 T 3 ) = 1 − ( T 1 T 3 ) [ T 2 T 1 − 1 1 − T 4 T 3 ] (II) Write the expression for the pressure ratio at state 2 to 1. p 2 p 1 = r (III) Here, the pressure at state 2 is p 2 and the pressure at state 1 is p 1 and the constant is r . The pressure at state 2 is equal to the pressure at state 3 and the pressure at state 3 is equal to pressure at state 1. Substitute p 3 for p 2 and p 4 for p 2 in Equation (III)

Fundamentals of Engineering Thermodynamics

8th Edition

ISBN: 9781118832301

Author: SHAPIRO

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Chapter 9.14, Problem 65P

To determine

The derivation of the thermal efficiency of an ideal regenerative gas turbine as η=1−(T1T3)(r)(k−1k).

The derivation of the thermal efficiency of an ideal regenerative gas turbine as η=1−T2T3.

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Chapter 9.14, Problem 62P

Chapter 9.14, Problem 66P

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Fundamentals of Engineering Thermodynamics

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The derivation of the thermal efficiency of an ideal regenerative gas turbine as η = 1 − ( T 1 T 3 ) ( r ) ( k − 1 k ) . The derivation of the thermal efficiency of an ideal regenerative gas turbine as η = 1 − T 2 T 3 .

The derivation of the thermal efficiency of an ideal regenerative gas turbine as η=1−(T1T3)(r)(k−1k). The derivation of the thermal efficiency of an ideal regenerative gas turbine as η=1−T2T3.

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Chapter 9 Solutions

The derivation of the thermal efficiency of an ideal regenerative gas turbine as η=1−(T1T3)(r)(k−1k).

The derivation of the thermal efficiency of an ideal regenerative gas turbine as η=1−T2T3.