Thermodynamics Compressibility Factor

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SUMMARY

The discussion focuses on calculating the molar volume of ethylene at 152°F and 126 atm using the compressibility factor (Z) determined by Corresponding States Theory. The relevant equations include Z=PVm/RmT and Zc=(Pcvc)/(R*Tc), with specific values for Rm and molecular weight provided. The participants emphasize the need to determine the reduced temperature and reduced pressure to accurately use the equations, noting that Z is a function of these reduced quantities rather than a constant. The conversation highlights the importance of understanding the relationship between Z, reduced pressure, and reduced temperature in real gas behavior.

PREREQUISITES
  • Understanding of thermodynamic principles, specifically compressibility factors.
  • Familiarity with Corresponding States Theory and its application.
  • Knowledge of molar volume calculations and relevant equations.
  • Basic understanding of reduced temperature and reduced pressure concepts.
NEXT STEPS
  • Study the derivation and application of Corresponding States Theory in thermodynamics.
  • Learn how to calculate reduced temperature and reduced pressure for various substances.
  • Explore the use of compressibility charts and their interpretation for real gases.
  • Investigate the behavior of ethylene under varying temperature and pressure conditions.
USEFUL FOR

Students and professionals in chemical engineering, thermodynamics, and anyone involved in gas behavior analysis, particularly those working with ethylene and compressibility factors.

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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