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Partial derivatives in thermodynamics

  1. Mar 1, 2009 #1
    in basic multivariate calculus, i never learned about differentiating functions of multiple variables which are also functions of each other. i.e.

    [itex] \frac{d}{d x_1} \left[ f(x_1, x_2, x_3) \right] [/itex]

    where [itex] x_1 = g(x_2, x_3) [/itex]

    studying thermodynamics right now, i'm encountering into expressions like

    [itex] \mu = - \left(\frac{\partial U}{\partial S} \right)_{N,V} \left( \frac{\partial S}{\partial N} \right)_{U,V} [/itex]

    where some particular variables are held fixed, but others are not. i'm wondering if there are formal theorems relating to partial derivatives like these or if you guys have any knowledge specifically relating to them.
  2. jcsd
  3. Mar 1, 2009 #2


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    Staff: Mentor

    All the thermodynamics textbooks that I've seen, spend some time discussing them early on.

    If yours doesn't, you might try downloading Chapter 2 from


    which I found by doing a Google search for "partial derivatives in thermodynamics".
  4. Mar 1, 2009 #3
    thank you. that's exactly the kind of thing i was looking for. sorry if that was so easy to find that it didn't warrant asking the forum.
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