Complete Question:
Problem 8 Determine the horsepower required to compress 1 lbm/min of ethylene oxide from 70 °F and 1 atm to 250 psia. The compressor has an efficiency of 75%. The molar heat capacity of ethylene oxide is given by
C_p=10.03+0.0184T C_p[=]Btu/lbmole- "F ; T[=] °F C,
Answer:
[tex]P'=0.377hp[/tex]
Explanation:
From the question we are told that:
Initial Temperature T_1=70 F
Final Temperature [tex]T_2=250pisa =114.94F[/tex]
Efficiency [tex]E=75\%=0.75[/tex]
Generally the equation for Work-done is mathematically given by
[tex]W=\int C_pT[/tex]
[tex]W=10.03(114.94-70 )+0.0184((114.94)^2-70^2 )[/tex]
[tex]W=527.21btu/ibmole[/tex]
[tex]W=11.982btu/ibm[/tex]
Generally the equation for Efficiency is mathematically given by
[tex]E=\frac{isotropic Power}{Actual P'}[/tex]
[tex]E=\frac{P}{P'}[/tex]
Since
Isotropic Power
[tex]P=0.0167*11.982btu/ibm[/tex]
[tex]P=0.2btu/s[/tex]
Therefore
[tex]P'=\frac{0.2}{0.75}[/tex]
[tex]P'=0266btu/s[/tex]
Since
[tex]1btu/s=1.4148hp[/tex]
Therefore
[tex]P'=0.377hp[/tex]
