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Quick Qns : Partial Derivatives

  1. Sep 11, 2009 #1
    Suppose we are given : PV = nRT, where n and R are constants.

    We are told to find the partial derivative dP/dV.

    Am I allowed to do this :

    P = nRT/V

    Then differentiate this w.r.t. to V.

    I disregarded the fact that V = 0 makes the RHS undefined.

    # This question came from Princeton Review's "Cracking the GRE Math Subject Test" page 160, qns 13.

    The solution given uses the above method but I do not understand why V = 0 is not taken into account.
  2. jcsd
  3. Sep 11, 2009 #2


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    When would the volume of an ideal gas ever be zero?
  4. Sep 11, 2009 #3


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    Doing it that way gives
    [tex]\frac{\partial P}{\partial V}= -nRT/V^2[/tex]
    You don't need to worry about the fact that V= 0 would make nRT/V undefined because it also makes the -nRT/V2 undefined. That is, the formula you got does not give an answer in exactly the situation where there is no answer.

    I would have been inclined to use "implicit" differentiation: from PV= nRT, (dP/dV)V+ P= 0 so dP/dV= -P/V= -(nRT/V)/V= -nRT/V^2.
  5. Sep 11, 2009 #4
    Thanks a lot guys~ That really helped!
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