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Polytropic Models

  1. Oct 22, 2008 #1
    Hello, I am studing polytropes and I found something intersting here: http://astronomy.sussex.ac.uk/~pd48/Polytropes.ppt [Broken]

    I got a problem at slide 5 where she says that the polytropic index n is equal to 0 for a homogenous gas sphere.

    I am not able to figure out why. From the polytropic equation P=K*ro^(gamma) we can write: dP/dr=k(gamma)ro^(gamma-1)d(ro)/dr
    and since ro=const we can say that dP/dr=0 for any value of gamma and moreover we can say that there is no equilibrium.

    thanks for help
    Last edited by a moderator: May 3, 2017
  2. jcsd
  3. Oct 23, 2008 #2


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    Hi Giammy85! :smile:

    (have a gamma: γ :smile:)

    I can't see the equations in your slide … the background is too dark.

    But if dP/dr = k γ roγ-1 d(ro)/dr, and if ro = constant,

    then dro/dr = 0 and dP/dr = 0.

    What's the problem? :confused:
  4. Oct 23, 2008 #3
    are you talking about this? http://astronomy.sussex.ac.uk/~pd48/Polytropes.ppt [Broken]
    I can clearly see them in every pc I used

    The problem is that according to the author of this ppt for a homogenous gas sphere the polytropic index n has to be equal to 0 and so γ=1+1/n=infinite.

    Instead I found that for ro=const there is no equilibrium for any value of γ. So if that author is right, how to demonstrate n=0?
    Last edited by a moderator: May 3, 2017
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