How Does the Conservation of Mass Apply in Stellar Physics?

[GotTrips]

Hi all
I am in deperate, desperate, desperate need of some help. I have this question that I have been working on for hours and have made no progress at all.

Here is the question.

Write down the "conservation of mass" equation for dm(r)/dr, where m(r) is the mass inside radius "r". Assume that the pressure inside a star at radius r is given by

P(r) = Pc/R(R-r)

where Pc is the central pressure and R is the stars outer radius. Combine this and the equation of hydrostatic equlibrium to find an expression for m(r). Hence show that m(r) x r5/2

PLease please help,

any advice on how to solve this or the answer will be great.

Thanks All

 

[Nylex]

The equation for hydrostatic equilibrium is dP/dr = -GM(r)ρ/r^2 and as for your "conservation of mass" equation, if it is the one I think it is, if you don't know it then all you need to do is think about how you would get the mass of a spherical shell. HTH.

 

[thepatientmental]

Hi there,

I can definitely understand your frustration with this question. Conservation of mass is an important concept in physics and can be a bit tricky to understand at first. Let's break down the question and see if we can make some progress.

First, let's define the conservation of mass equation. It states that the total mass of a closed system remains constant, regardless of any physical or chemical changes that may occur within the system. In other words, mass cannot be created or destroyed, only transformed.

Now, let's look at the equation for dm(r)/dr. This represents the change in mass with respect to a change in radius. In other words, it tells us how the mass inside a certain radius changes as we move outward from the center of the star.

Next, we have the equation for pressure inside the star, which is given by P(r) = Pc/R(R-r). This equation tells us that the pressure decreases as we move away from the center of the star, and is dependent on the central pressure (Pc) and the outer radius of the star (R).

To find an expression for m(r), we can combine the conservation of mass equation and the hydrostatic equilibrium equation, which states that the pressure gradient within a star balances the gravitational force. This can be written as:

dP/dr = - (Gm(r)/r^2)

Where G is the gravitational constant and m(r) is the mass inside radius r.

By substituting the equation for pressure (P(r)) into the hydrostatic equilibrium equation, we can solve for m(r). This will give us an expression for the mass inside radius r.

Finally, to show that m(r) x r^(5/2), we can substitute our expression for m(r) into the conservation of mass equation. This will give us an equation in terms of r, which can be simplified to show that m(r) x r^(5/2).

I hope this helps guide you in the right direction. Remember, when solving physics problems, it's important to break down the equations and understand what each variable represents. Good luck!