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1. The problem statement, all variables and given/known data

Establish the relationship between the critical constants and the parameters of Dieterici equation of state.

Show that [tex]Z_c[/tex][tex]=2e^{-2}[/tex] and deduce the reduced Dieterici equation of state.

Compare the predicted [tex]Z_c[/tex] from both Dieterici's and Van der Waals' equations. Which best approximates reality?

2. Relevant equations

http://img299.imageshack.us/i/dieterici.png/

3. The attempt at a solution

I have substituted p with [tex]p_c[/tex] and then tried to work my way around proving that the first and second partial derivatives relative to p evaluate to 0.

I have failed.

I know that at the critical point, any pair of first and second derivatives will evaluate to 0, since the critical point is an inflexion point. But other than that... I'm pretty much powerless.

Therefore, my question is: would someone please direct me so that I can establish the relationship between the critical constants ([tex]p_c, V_c, T_c[/tex]) and the parameters (a,b) of the Dieterici equation of state please?

Thank you.

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# Dieterici equation of state

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