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What's a circular integral?

  1. Apr 22, 2008 #1
    "
    If we designate the total or internal energy of an isolated or closed system as E, heat as Q and work as W , then the circular integral involving no change in net internal energy is:...
    "

    What is it?
     
  2. jcsd
  3. Apr 23, 2008 #2

    Andy Resnick

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    I think that refers to a path integral- the integral is taken to be along a closed loop, rather than along a segment of a coordinate axis.
     
  4. Apr 23, 2008 #3

    jtbell

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    That's what it must be: integral around a closed path. I've never used the term "circular integral" myself, or seen it in any of my textbooks, but a Google search shows that it does appear in some thermodynamics books.
     
  5. Apr 23, 2008 #4
    Yes, it was in a chapter about thermodynamics.

    My mom said that it was a volume-based integral, or something like that, but it's still a little bit unclear (partially because I only know how to integrate in a straight line)

    And here is what it looks like:

    [tex]\oint[/tex]
     
  6. Apr 23, 2008 #5
    A circular integral is the integration around a closed path or surface. For example, Gauss's law says that
    [tex]{\Phi} = \oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A}
    = {1 \over \varepsilon_0} \int_V \rho\ \mathrm{d}V = \frac{Q_A}{\varepsilon_0}[/tex]
    where you're integrating around a closed surface (such as a sphere, or any other structure else where you can tell at every point whether you're inside or outside).
     
  7. Apr 23, 2008 #6

    Doc Al

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    As others have pointed out, that's usually called a closed path integral (if you are integrating along a line or path).
     
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