Register to reply

Dieterici equation of state

by Aeon
Tags: dieterici, equation, gas, gases, state
Share this thread:
Oct5-10, 07:43 PM
P: 21
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

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.
Phys.Org News Partner Science news on
Climate change increases risk of crop slowdown in next 20 years
Researcher part of team studying ways to better predict intensity of hurricanes
New molecule puts scientists a step closer to understanding hydrogen storage
Oct6-10, 01:38 PM
P: 21
I got it.

The Dieterici equation of state can be differentiated as it is, but it's more convenient to change its form before differentiating it. To help with differentiation, I used the natural logarithm of both sides.

I differentiated the log() form of the equation, twice. At the critical point (point of inflexion), [tex]\frac{\partial ln(p)}{\partial V_m} = 0[/tex] and [tex]\frac{\partial^2 ln(p)}{\partial V_m^2} = 0[/tex]. You can then divide the first partial derivative by the second and everything clears up. Simple transformations then enable you to isolate [tex]V_c[/tex] (not [tex]V_m[/tex] since you're evaluating at the critical point).

Register to reply

Related Discussions
Equation of state Cosmology 8
Equation of State of an Ideal Gas Advanced Physics Homework 3
Dieterici Equation Calculus & Beyond Homework 0
Equation of state for an ideal gas Introductory Physics Homework 6
The equation of state Cosmology 2