# Pressure gradient in Jeans Lenght

1. Jan 30, 2013

### Daaavde

$\rho g \ge \nabla P$

Then they substitute $\nabla P$ with $nkT/R$.

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

Now, gradient of $P$, to me, means to derivate with respect to $R$.
Hence:

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

So, here's the problem:

On demonstrations: $\nabla P = nkT/R$
To me: $\nabla P = nkT/R^4$

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