1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
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