1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Education Advisor

    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


    User Avatar

    Staff: Mentor

    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:

  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

    User Avatar

    Staff: Mentor

    As others have pointed out, that's usually called a closed path integral (if you are integrating along a line or path).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook