Stellar structure of stars problem

1. Mar 4, 2014

fu11meta1

1. The problem statement, all variables and given/known data
Consider a star of radius R, with density p that is constant, composed of classical, nonrelativistic, idealg gas of fully ionized hydrogen.
a. Solve the equations of stellar structure for the pressure profile, P(r) with the boundary condition P(R)=0
b. Find the temperature profile T(r)
c. Assume that the nuclear energy production rate depends on temperature as E==T^4. At what radius does E decrease to 0.1 of its central value, and what fraction of the star's volume is included within this radius?

2. Relevant equations
A) dP(r)=-G*M(r)*ρ(r)*dr/r^2
B)dT(r)/dr = -3/4 *( L(r)*k(r)*ρ(r))/(4∏r^24acT(r)^3)
C) I'm not sure about the formulas for C

3. The attempt at a solution
I think I get A part. You have to integrate from r to R of
dP(r)=-G*M(r)*ρ*dr/r^2 ;ρ= M(r)/(4/3)∏r^3, solve for M(r)
=-G*ρ^2*(4/3)*∏*integration of r

b part: I have no idea. Which values will be constant and why?

c part: I'm also not sure which equations to use

2. Mar 4, 2014

SteamKing

Staff Emeritus
For part c, you have to solve part b and figure out the radial distribution of temperature within the star.

3. Mar 4, 2014

fu11meta1

Thanks!
any idea on part b?

4. Mar 4, 2014

SteamKing

Staff Emeritus
You've got a first order ODE to solve here. It's not clear what functions L(r) and k(r) are and how they vary with r, nor what boundary conditions to apply.

5. Mar 4, 2014

fu11meta1

Yeah, that's what I'm trying to figure out. Would the luminosity be constant in this case? or would I need another equation to substitute it with?