- #1

Daaavde

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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)

[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)

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