A compressor operating isothermally is to compress 2.83 m³/min of ammonium gas at 29.4°C and 102.7kPa to 311.6 kPa.(a) Calculate the power required if the efficiency of the compressor is 75%.(b) Repeat the calculation if the compressor is uncooled and determine the outlet temperature*.(c) What is the percentage of power saved from isothermal operation and can this compressor be safelyoperated without cooling?*Note: y values for NH3 gas: YNH3=1.4.

Given data: Pressure (P1) = 102.7kPa Temperature (T1) = 29.4oC = 302.4K Final pressure (P1)=311.6kPa Volume (V1) = 2.83 m3/mm Efficiency of the compressor,ηc = 0.75a) Isothermal compression: Given that compressor operates isothermally. So, we have formula for work done in isothermally compression. Work done, w = P1V1 ln (P2/P1) w= initial pressure x volume x ln(final pressure/initial pressure) = 102.7×2.83×ln(311.6102.7) = 102.7×2.83×ln[3.0340] = 290.641×1.1098 = 322.553 Ideal power required (P) = w60= 322.5860=5.376kW Actual power required (Pa) Pηc= 5.3760.75=7.168kW b) Let us assuming the compression to be isentropic. We have, formula work done in isentropic compression. Work done=kk-1×P1V1[(P2P1)(k-1k)-1] For ammonium of (k) value is constant=1.312 w=(1.3121.312-1)×102.7×2.83[(311.6102.7)(1.312-11.312)-1] = 1.3120.312×102.7×2.83[(311.6102.7)(0.3121.312)-1]=4.205×102.7×2.83×[(3.03)0.23-1] = 4.205×102.7×2.83×[1.29-1]= 4.205×102.7×2.83×0.29= 354.42 kN-m/mm Ideal power required, P = w60=354.4260 = 5.907kWActual power required Pa=Pηc=5.9070.75 = 7.876kWOutlet temperature, T2 = T1[P2P1](k-1k) T2 = 302.4[311.6102.7](1.312-11.312) T2 = 302.4[(3.03)0.23] = 302.4×1.29 = 390.096K c) % power saving = 8.204-7.1687.168×100 = 1.0367.168×100 = 0.1445×100 = 14.45% T2 = 390.096K < Tcritical 405.5K

Answered: A compressor operating isothermally is…

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

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A compressor operating isothermally is to compress 2.83 m³/min of ammonium gas at 29.4°C and 102.7
kPa to 311.6 kPa.
(a) Calculate the power required if the efficiency of the compressor is 75%.
(b) Repeat the calculation if the compressor is uncooled and determine the outlet temperature*.
(c) What is the percentage of power saved from isothermal operation and can this compressor be safely
operated without cooling?
*Note: y values for NH3 gas: YNH3=1.4.

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