Explanation Calculate the reduced temperature ( T R 1 ) at initial state. T R 1 = T 1 T c r (I) Here, critical temperature is T c r and initial temperature is T 1 . Calculate the reduced pressure ( P R 1 ) at initial state. P R 1 = P 1 P c r (II) Here, critical pressure is P c r and initial pressure is P 1 . Calculate the reduced temperature ( T R 2 ) at final state. T R 2 = T 2 T c r (III) Here, critical temperature is T c r and final temperature is T 2 . Calculate the reduced pressure ( P R 2 ) at final state. P R 2 = P 2 P c r (IV) Here, critical pressure is P c r and final pressure is P 1 . Calculate the change in enthalpy ( h 2 − h 1 ) using generalized chart relation. h 2 − h 1 = R T c r ( Z h 1 − Z h 2 ) + ( h 2 − h 1 ) i d e a l (V) Here, change in enthalpy of ideal gas is ( h 2 − h 1 ) i d e a l and gas constant is R . Calculate the change in entropy ( s 2 − s 1 ) using generalized chart relation. ( s 2 − s 1 ) = R T c r ( Z h 1 − Z h 2 ) + ( s 2 − s 1 ) i d e a l (VI) Here, change in entropy of ideal gas is ( s 2 − s 1 ) i d e a l . Write the formula to calculate the reversible work input to the compressor ( w r e v ) . w r e v = ( h 2 − h 1 ) − T o ( s 2 − s 1 ) (VII) Here, enthalpy at outlet and inlet are h 2 and h 1 , surrounding temperature is T o , entropy at outlet and inlet are s 2 and s 1 . Write the formula to calculate the second law efficiency of the compressor ( η I I ) . η I I = w r e v w a c t u a l (VIII) Here, actual work done of a compressor is w a c t u a l . Conclusion: Substitute 560 R for T 1 and 343.9 R for T c r in Equation (I). T R 1 = 560 R 343.9 R = 1.63 Substitute 50 psia for P 1 and 673 psia for P c r in Equation (II). P R 1 = 50 psia 673 psia = 0.0743 Refer the table A-15E, “Nelson-Obert generalized compressibility chart”, select the compressibility factor Z h 1 and Z s 1 at initial state of reduced pressure and temperature of 1.63 and 0.0743 as 0.03313 and 0.01617 Z h 1 = 0.03313 Z s 1 = 0.01617 Substitute 1560 R for T 2 and 343.9 R for T c r in Equation (III). T R 2 = 1560 R 343 .9 R = 4.54 Substitute 500 psia for P 2 and 673 psia for P c r in Equation (IV)

8th Edition

ISBN: 9781307434316

Author: CENGEL

Publisher: INTER MCG

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Question

Chapter 12.6, Problem 99RP

To determine

The second law efficiency of the compressor.

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Chapter 12 Solutions

THERMODYNAMICS(SI UNITS,INTL.ED)EBOOK>I

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