Polytropic Models: Solving Problem at Slide 5

[Giammy85]

Hello, I am studing polytropes and I found something intersting here: http://astronomy.sussex.ac.uk/~pd48/Polytropes.ppt

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

 

[tiny-tim]

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.

Hi Giammy85!

(have a gamma: γ )

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

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

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

What's the problem?

 

[Giammy85]

Hi Giammy85!

(have a gamma: γ )

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

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

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

What's the problem?

are you talking about this? http://astronomy.sussex.ac.uk/~pd48/Polytropes.ppt
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?