Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    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


    User Avatar
    Science Advisor
    Homework Helper

    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:


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


    Ok, not too bad.

    Suppose I had:


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


    How about:


    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:


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


    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook