0
$\begingroup$

In my thermodynamics book, I came across the following equation:

$$0=\left[ 1- \left( \dfrac{\partial V(p,T)}{\partial p}\right) \left( \dfrac{\partial p(V,T)}{\partial V}\right) \right] dV +.......$$

Now, is chain rule applicable to this term so that the product of the two partial derivatives is 1 and the whole term is 0?

My book doesn't apply chain rule.

Improve this question
$\endgroup$
4
  • 2
    $\begingroup$ Could you add more details on the nature of your problem? $\endgroup$
    – heaven-of-intensity
    Aug 10, 2017 at 17:54
  • $\begingroup$ I only want to know whether we can apply chain rule to the above partial derivative. $\endgroup$
    – N.G.Tyson
    Aug 10, 2017 at 18:09
  • 1
    $\begingroup$ Yeah, I think that you're right. The same variable is being held constant in both of those partial derivatives (i.e., the temperature T), so those two partial derivatives should be reciprocals of each other. Their product should equal 1 and so that entire dV term should be zero. $\endgroup$
    – user93237
    Aug 10, 2017 at 19:48
  • $\begingroup$ I found the relevant equation in my copy of "Statistical Mechanics" by Franz Mohling. Here's the Google book link ( books.google.com/books/about/… ) and if you type "9.4a" in the "From inside this book" search window, then equation 9.4a will be displayed, which is the equation to use here. $\endgroup$
    – user93237
    Aug 10, 2017 at 20:09

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.