Explanation Write the expression for the isentropic efficiency of a compressor for an ideal gas ( η C ) . η C = h 2 s − h 1 h 2 − h 1 = c p ( T 2 s − T 1 ) c p ( T 2 − T 1 ) = ( T 2 s − T 1 ) ( T 2 − T 1 ) (I) Here, the specific heat at constant pressure is c p , enthalpy at state 1 is h 1 , enthalpy at state 2 is h 2 and enthalpy on isentropic condition 2 s is h 2 s , temperature at state 1 is T 1 , temperature at state 2 is T 2 and temperature on isentropic condition 2 s is T 2 s . Write the temperature and pressure relation ratio at the compressor exit for the isentropic condition. T 2 s = T 1 ( P 2 P 1 ) ( k − 1 ) / k Here, the specific heat ratio is k , pressure at state 2 is P 2 and pressure at state 1 is P 1 . Write the expression for the isentropic efficiency of a turbine for an ideal gas ( η T ) . η T = h 4 − h 3 h 4 s − h 3 = c p ( T 4 − T 3 ) c p ( T 4 s − T 3 ) = ( T 4 − T 3 ) ( T 4 s − T 3 ) (II) Here, the specific heat at constant pressure is c p , enthalpy at state 3 is h 3 , enthalpy at state 4 is h 4 and enthalpy on isentropic condition 4 s is h 4 s , temperature at state 4 is T 4 , temperature at state 3 is T 3 and temperature on isentropic condition 4 s is T 4 s . Write the temperature and pressure relation ratio at the compressor exit for the isentropic condition. T 4 s = T 3 ( P 4 P 3 ) ( k − 1 ) / k Here, the specific heat ratio is k , pressure at state 3 is P 3 and pressure at state 4 is P 4 . Conclusion: Substitute [ T 1 ( P 2 P 1 ) ( k − 1 ) / k ] for T 2 s in Equation (I)

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Chapter 7.13, Problem 223RP

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The compressor and turbine isentropic efficiencies as (P2P1)(k−1)/k−1(T2T1−1) and T4T3−1(P4P3)(k−1)/k−1.

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Chapter 7.13, Problem 222RP

Chapter 7.13, Problem 224RP

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The compressor and turbine isentropic efficiencies as ( P 2 P 1 ) ( k − 1 ) / k − 1 ( T 2 T 1 − 1 ) and T 4 T 3 − 1 ( P 4 P 3 ) ( k − 1 ) / k − 1 .

Solution Summary: The author explains the isentropic efficiency of a compressor and turbine for an ideal gas.

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The compressor and turbine isentropic efficiencies as (P2P1)(k−1)/k−1(T2T1−1) and T4T3−1(P4P3)(k−1)/k−1.

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