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Math Help - Van der Waals equation for arbitrary gas - need HELP!

  1. #1
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    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!
    Last edited by Intrusion; April 5th 2010 at 05:43 PM.
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  2. #2
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    p = \frac{RT}{v-b} - \frac{a}{v^2}

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

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

    use the chemists' definition of a critical point.
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    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.

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    Quote Originally Posted by Intrusion View Post
    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.
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    Right, where f'' = 0, but I still don't see how that can be used in the last problem....
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    Quote Originally Posted by Intrusion View Post
    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.
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  7. #7
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    How would I find that? I don't understand what it means by "solve the equations"....
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  8. #8
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    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.
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