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Partial Derivative of Van der Waals Equation

  1. Dec 20, 2011 #1
    Given that the Van Der Waals equation is (p + (an^2)/v^2)(v-nb)=nRT where n,a,R and b are constants...

    How to we find the derivative of p wrt v ?

    How to find the derivative of p wrt T without further differentiation ??

    Can anyone teach me how to do this question ?

    Sincerly thanks~
     
  2. jcsd
  3. Dec 20, 2011 #2

    SammyS

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    What have you tried?

    Where are you stuck ?
     
  4. Dec 21, 2011 #3
    i have no idea on how to solving this...
    please kindly teach me how to start on solving this sort of question...
     
  5. Dec 21, 2011 #4

    dextercioby

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    Do you know the difference between an implicit function and an explicit one ? What do you know about the derivatives for explicit functions ? How about implicit ones ?
     
  6. Dec 21, 2011 #5
    If I had an equation:

    [tex]y(x)+x=k[/tex]

    and I wanted to take the derivative of y with respect to x, I'd get:

    [tex]y'(x)+1=0[/tex]

    Ok, not too bad.

    Suppose I had:

    [tex]y(x)+\frac{1}{x^2}=k[/tex]

    still not too bad if I want the derivative of y with respect to x. That's:

    [tex]y'-2x^{-3}=0[/tex]

    How about:

    [tex](y(x)+\frac{c}{x^2})(x-k)=a[/tex]

    That's still not too bad cus' I'd use the chain rule this time:

    [tex](y(x)+\frac{c}{x^2}) \frac{d}{dx} (x-k)+(x-k)\frac{d}{dx}(y(x)+\frac{c}{x^2})=0[/tex]

    and that's:

    [tex](y(x)+\frac{c}{x^2})(1)+(x-k)(y'(x)-2cx^{-3})=0[/tex]

    ok, now you do one but instead of y(x), I'll say:

    [tex](p(v)+\frac{k}{v^2})(v-c)=a[/tex]

    and I want to take the derivative of p with respect to v. Do that one, then do yours with all the other parameters.
     
    Last edited: Dec 21, 2011
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