Van der Waals EOS: Why Pc/Tc, and not Pc/Vc or Vc/Tc?

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SUMMARY

The van der Waals equation of state (EOS) constants can be expressed as functions of critical pressure (Pc) and critical temperature (Tc) due to their fundamental role in defining the behavior of real gases. The constants 'a' and 'b' are derived from these critical parameters rather than volume (Vc) to maintain consistency in thermodynamic relationships. This approach is not merely a preference but is rooted in the physical significance of Pc and Tc in phase transitions and critical phenomena. The discussion emphasizes the importance of these parameters in the formulation of the van der Waals EOS.

PREREQUISITES
  • Understanding of the van der Waals equation of state
  • Knowledge of critical properties of substances (Pc, Tc, Vc)
  • Familiarity with thermodynamic principles and phase behavior
  • Ability to manipulate equations in thermodynamics
NEXT STEPS
  • Study the derivation of the van der Waals equation of state
  • Learn about critical phenomena in thermodynamics
  • Explore dimensionless forms of thermodynamic equations
  • Investigate other equations of state for real gases, such as the Redlich-Kwong EOS
USEFUL FOR

This discussion is beneficial for chemical engineers, thermodynamics students, and researchers focusing on gas behavior and phase transitions in real gases.

maistral
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TL;DR
The title.
As far as I know the van der Waals constants can be expressed as functions of Pc and Tc. Why is it so? Why is it not a function of Vc/Tc, or Pc/Vc?

Say for example, b = Vc/3. Why is this expressed in terms of Pc and Tc instead? Why is a also in terms of Pc and Tc, and not Vc? Is this just a matter of preference?
 
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maistral said:
Summary:: The title.

As far as I know the van der Waals constants can be expressed as functions of Pc and Tc. Why is it so? Why is it not a function of Vc/Tc, or Pc/Vc?

Say for example, b = Vc/3. Why is this expressed in terms of Pc and Tc instead? Why is a also in terms of Pc and Tc, and not Vc? Is this just a matter of preference?
Please show how you would reduce the van der Waals equation to dimensionless form.
 

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