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Pressure gradient in Jeans Lenght

  1. Jan 30, 2013 #1
    All the demonstrations on Jeans instability start with:

    [itex]\rho g \ge \nabla P[/itex]

    Then they substitute [itex]\nabla P[/itex] with [itex]nkT/R[/itex].

    But from ideal gas law: [itex]PV = nkT[/itex], so [itex]P = nkT/V = nkT/R^3[/itex]
    (I'm not interested in proportionality factors, so let's not bother about [itex]4/3 \pi[/itex], ecc...)

    Now, gradient of [itex]P[/itex], to me, means to derivate with respect to [itex]R[/itex].
    Hence:

    [itex]\nabla P = nkT/R^4[/itex] (again, not interested in proportionality factors)

    So, here's the problem:

    On demonstrations: [itex]\nabla P = nkT/R[/itex]
    To me: [itex]\nabla P = nkT/R^4[/itex]

    Obviously, it's plain i'm missing something, still i can't see what it is.

    (I apologize for my poor scholastic english, i'm not native speaker)
     
    Last edited: Jan 30, 2013
  2. jcsd
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