Thermodynamics Compressibility Factor

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Discussion Overview

The discussion revolves around the calculation of the molar volume of ethylene at specific conditions (152°F and 126 atm) using the compressibility factor (Z) as determined by Corresponding States Theory. The scope includes theoretical application and mathematical reasoning related to thermodynamics.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant seeks to determine the molar volume using the equation Z=PVm/RmT, noting uncertainty about the value of Z at the given conditions.
  • Another participant asks for the reduced temperature and reduced pressure, suggesting the need for a graph of Z as a function of these variables.
  • Some participants propose that if Z is determined by Corresponding States Theory, it may imply that Z is constant under certain conditions.
  • It is noted that Z is a function of reduced pressure and reduced temperature, prompting a question about the definitions of these quantities.
  • One participant mentions that for an ideal gas, Z is constant as a function of pressure, but acknowledges that closer to the critical point, Z may vary with pressure, raising questions about its critical value in this context.
  • Areas of Agreement / Disagreement

    Participants express differing views on the constancy of Z and its dependence on reduced variables, indicating that multiple competing perspectives remain without a clear consensus.

    Contextual Notes

    There are unresolved aspects regarding the specific values of reduced temperature and pressure, as well as the implications of Corresponding States Theory on the behavior of Z at the given conditions.

Logan McEntire
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Homework Statement


Please consider ethylene at 152oF and 126 atm. Please determine the molar volume (ft3/lbmole) if Z is determined by Corresponding States Theory.

Homework Equations


Z=PVm/RmT
Vm= Molar volume
R=Rm/M
M= molecular weight
Rm=1545(ft*lbf)/(lbmol*oR)
Zc=(Pcvc)/(R*Tc)
Tc=283 K
Pc=51.2 Bar
M=28.05 Kg/Kmol
PR=P/Pc

The Attempt at a Solution


I can find Vc but that's not 152 oF and 126 atm.
I don't know Z at these conditions either so I can't use the other equation.
 
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What is the reduced temperature and the reduced pressure? Do you have a copy of the graph of z as a function of reduced pressure and reduced temperature?
 
I'd imagine that if they say "Z is determined by Corresponding States Theory", that implies it's constant.
 
John Park said:
I'd imagine that if they say "Z is determined by Corresponding States Theory", that implies it's constant.
What does this mean? Actually, z is a function of reduced pressure and reduced temperature. Do you know the definition of these quantities?
 
For an ideal gas (admittedly a long way from the critical point) z is constant as a function of pressure. Closer to the critical point in general it varies with pressure, but that doesn't seem to rule out the possibility that it takes its critical value here. How would you use the statement about Corresponding States Theory?
 

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