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Exact differential problem

  1. Sep 23, 2006 #1
    I have trouble doing a problem involving exact differentials:

    Consider a uniform wire of length L and cross-section area A. A force F is applied to the wire. We can write the relationship:

    dL = (L/YA)dF + (aL)dT

    where Y is the Young's modulus, a the coefficient of thermal expansion, and T the wire temperature. For small deformation and temperature change, we can assume A, Y, and a to be constant. Determine if dL is an exact differential.

    My problem is with L. L is a function of F and T, I'm sure. If dL is an exact differential, I want to check if the partial derivative of (L/YA) w.r.t. T is equal to the partial derivative of of (aL) w.r.t. F. But I'm running into the problem of what the partial derivatives of L w.r.t. to T and F are.

    Thanks in advance.
  2. jcsd
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