8 replies to this topic

[Bogaber]

I have a homwork, and it is required to calculate the volume using Van Der Walls Equatuin, I did some rearrangement in the equation P=(RT/v-β)-(a/V^2), and I got this equation (1/a)V^2-(1/RT)V+((βP+RT)/RTP)=0. I solved for V, but the problem was that I didn't get the answer, because a square root of a minus value doesn't give a solution. Could you please show me what was the mistake ?

Edited by Bogaber, 21 May 2010 - 07:19 PM.

[Art Montemayor]

This is not a contribution to the answer. However, I feel it is important, and I take this opportunity before my good friend Guido reads this post. The correct and accurate identity of the equation you refer to is The van der Waals Equation. It is such an important and critical milestone in the history of engineering that I felt I should make this statement. It is the pioneering Equation Of State, formulated by and derived by a great figure in the history of physics and engineering in 1873: Johannes Diderik van der Waals.

The mere mention of his name should make all process and project engineers stop and contemplate his accomplishments in awe. That's why I make note of the correct spelling of his name and legacy.

[Bogaber]

This is not a contribution to the answer. However, I feel it is important, and I take this opportunity before my good friend Guido reads this post. The correct and accurate identity of the equation you refer to is The van der Waals Equation. It is such an important and critical milestone in the history of engineering that I felt I should make this statement. It is the pioneering Equation Of State, formulated by and derived by a great figure in the history of physics and engineering in 1873: Johannes Diderik van der Waals.

The mere mention of his name should make all process and project engineers stop and contemplate his accomplishments in awe. That's why I make note of the correct spelling of his name and legacy.

I'm sorry for that, I didn't notice the spelling mistake, and I apologize. Thank you for that, and your reply has been considered as a contribution to show how great Johannes Diderik van der Waals is.

[MrShorty]

I haven't got time to thoroughly look over your algebra. One indicator of a mistake is that you ended up with a quadratic equation. The van der Waals equation (and others based on it like the Peng-Robinson and Redlich-Kwong) are cubic in volume. Your final polynomial form should have a V^3 term in it. In your rearrangement, look for a step that will require you to multiply V and V^2.

[latexman]

Personally, I would not solve it algebraicly. I would enter the formula into Excel and use Solver to solve it by trial and error. That way is much faster for me, and then I have a spreadsheet I can use over and over for years to come.

Bogaber, you can use the Edit function and correct your initial post.

Edited by latexman, 21 May 2010 - 01:56 PM.

[kkala]

I have a homework, and it is required to calculate the volume using Van Der Walls Equation, I did some rearangement in the equation P=(RT/v-β)-(a/V^2), and I got this equation (1/a)V^2-(1/RT)V+((βP+RT)/RTP)=0. I solved for V, but the problem was that I didn't get the answer, because a square root of a minus value doesn't give a solution. Could you please show me what was the mistake ?

P=(RT/(v-β))-a/v^2 is correctly written (b was substituted by β to avoid "yellow face"), transformed as below:
a/v^2=RT(v-β)-P
v^2/a=1/(RT(v-β)-P)
v^2/a=(1/RT)/(v-β-P/RT)
v^2/a-(1/RT)/(v-β-P/RT)=0, second term seems different to -(1/RT)v+(βP+RT)/RTP.
Probably easiest way to solve the equation is to transform it into full 3rd degree polynomial of v: Pv3-(Pβ+RT)v2+av-ab=0.

Edited by kkala, 21 May 2010 - 05:12 PM.

[Bogaber]

That was really helpful, I don’t know how to thank you in such a way that I totally pay what you’ve offered.

I spent three days trying to solve this problem alone with no results. Thank you again and again …

[breizh]

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[Bogaber]

Hi Breizh, Thank you, that gave me the confidence to solve this problem, that was nice from you ...