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Math Help - Partial derivation issue

  1. #1
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    Partial derivation issue

    I got this problem with a simple partial derivation that is driving me crazy, since the solution I obtain is different from the one published in the article, in which I believe.
    Basically I got this equation:

    P=\frac{RT}{v-b}-\frac{a(T)}{v(v+b)+b(v-b)}

    Where:
    P= pressure
    R=Gas constant
    T= temperature
    V= molar volume

    And
    a(T) = a(Tc)*( 1+ k( 1-Tr^(1/2) ) )^2
    a(Tc) = 0.45724 * R^2 * Tc^2 / Pc
    Tc & Pc are the critical temperature & pressure respectively
    k = 0.37464 + 1.54226*w - 0.26992*w^2
    b=0.0778*R * Tc / Pc
    Tr = T / Tc
    w is the acentric factor.

    Now I need to make this partial derivation:

    pi = internal pressure = T*/frac{dP}{dT}v -P
    Guy sorry first time I'm using latex, with this frac{dP} {dT}v (if some one can show me the code please) I mean the partial derivation of P respect to T at constant volume.


    The solution on the article is:

    pi=\frac{a(T)}{v(v+b)+b(v-b)}(1+kTr^(^1^/^2^))



    Could you please help me to understand how to arrive there.
    Thanks
    Last edited by Giuseppe; April 11th 2011 at 11:58 PM.
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  2. #2
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    pickslides's Avatar
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    Might be worth posting this one again, seems a little tricky to follow

    under the "math" tags a fraction has the code \frac{RT}{v-b} giving, \frac{RT}{v-b}

    Click on the code to see how!
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  3. #3
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    Thanks pickslides,

    but i do really do not succede to write the partial derivetion correctely. Do you have any tips for this.
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