# Thread: Van der Waals equation for arbitrary gas - need HELP!

1. ## Van der Waals equation for arbitrary gas - need HELP!

Hi guys, I've been working on this problem for so long but I cannot figure out how to approach it...what am I supposed to do? Here is the question, and what I have tried...

(Background info is included so you know what's going on...)

What I've done: b) I've taken the derivative of the van der Waals gas equation to get 2a/v^3 - RT/(v-b)^2

Thanks so much to anyone that can help!

2. $\displaystyle p = \frac{RT}{v-b} - \frac{a}{v^2}$

$\displaystyle \frac{dp}{dv} = -\frac{RT}{(v-b)^2} + \frac{2a}{v^3}$

$\displaystyle \frac{d^2p}{dv^2} = \frac{2RT}{(v-b)^3} - \frac{6a}{v^4}$

use the chemists' definition of a critical point.

3. Wait a minute, wouldn't 2RT/(v-b)^3 - 6a/v^4 would be the inflection point for the van der Waals gas? That's actually the next question and what I had done. However, when I get to the last question in that series I have no idea what to do, which is why I was questioning my first two results.

4. Originally Posted by Intrusion
Wait a minute, wouldn't 2RT/(v-b)^3 - 6a/v^4 would be the inflection point for the van der Waals gas? That's actually the next question and what I had done. However, when I get to the last question in that series I have no idea what to do, which is why I was questioning my first two results.

the second derivative expression is not an inflection point ... an inflection point occurs at a defined point on a curve where the second derivative changes sign.

5. Right, where f'' = 0, but I still don't see how that can be used in the last problem....

6. Originally Posted by Intrusion
Right, where f'' = 0, but I still don't see how that can be used in the last problem....
you are looking for points where f' = 0 and f'' = 0 simultaneously.

7. How would I find that? I don't understand what it means by "solve the equations"....

8. I don't mean to "bump" this just for the hell of it because I know how annoying that is to mods, but I am still having trouble with this.

Can anyone help me out? I didn't pick up on the clues skeeter provided.