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

In summary, the conversation discussed the expression of van der Waals constants in terms of Pc and Tc, rather than Vc/Tc or Pc/Vc. It also questioned why b is expressed in terms of Pc and Tc, and why a is also not in terms of Vc. The conversation then brought up the topic of reducing the van der Waals equation to dimensionless form.
  • #1
maistral
240
17
TL;DR 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?
 
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  • #2
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.
 

1. Why is Pc/Tc used in the Van der Waals equation of state instead of Pc/Vc or Vc/Tc?

The Van der Waals equation of state is used to describe the behavior of real gases, taking into account intermolecular forces and the finite size of gas molecules. The critical temperature (Tc) and critical pressure (Pc) are important parameters in this equation as they represent the temperature and pressure at which a gas can no longer be liquefied, regardless of the applied pressure. Pc/Tc is used because it represents the ratio of the critical pressure to the critical temperature, which is a more accurate measure of the strength of intermolecular forces compared to Pc/Vc or Vc/Tc.

2. How is the critical temperature (Tc) and critical pressure (Pc) determined in the Van der Waals equation of state?

The critical temperature and pressure are experimentally determined by plotting the pressure-volume isotherms of a gas and finding the point at which the isotherm exhibits a horizontal inflection point. This point represents the critical point, where the gas can no longer be liquefied. The corresponding temperature and pressure values at this point are the critical temperature and pressure, respectively.

3. Can the Van der Waals equation of state accurately predict the behavior of all gases?

No, the Van der Waals equation of state is an approximation and does not accurately predict the behavior of all gases. It is most accurate for gases that have low pressures and high temperatures, and it becomes less accurate as the pressure and temperature approach the critical point. Additionally, the equation does not take into account other factors such as non-sphericity of molecules and dipole-dipole interactions.

4. How does the Van der Waals equation of state compare to other equations of state?

The Van der Waals equation of state is a simple and widely used equation that takes into account intermolecular forces and the finite size of gas molecules. However, it is not as accurate as more complex equations of state such as the Redlich-Kwong equation or the Peng-Robinson equation. These equations incorporate additional parameters and factors to improve accuracy, but they also require more experimental data to determine these parameters.

5. Can the Van der Waals equation of state be used for liquids?

No, the Van der Waals equation of state is only applicable to gases. It does not take into account the attractive forces between molecules in liquids, which are much stronger than in gases. For liquids, more complex equations of state such as the Soave-Redlich-Kwong equation or the Patel-Teja equation are used to better describe their behavior.

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