Astrophysics in a Nutshell Problem

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SUMMARY

The discussion focuses on deriving the temperature profile T(r) for a hypothetical star of radius R, composed of a constant density ρ and fully ionized hydrogen gas. The relevant equation is dT(r)/dr = (-3*L(r)*k(r)*ρ(r)) / (4∏*(r^2)*4*a*c*(T(r))^3). Participants express confusion over the integration process and the constants involved, emphasizing the need for clarity in the principles and equations governing the problem. The main goal is to achieve a comprehensive understanding of the temperature distribution within the star.

PREREQUISITES
  • Understanding of classical thermodynamics and ideal gas laws
  • Familiarity with astrophysical concepts such as stellar structure
  • Knowledge of calculus, particularly integration techniques
  • Basic principles of radiation and energy transfer in astrophysics
NEXT STEPS
  • Study the derivation of the ideal gas law in astrophysical contexts
  • Learn about the integration techniques for differential equations in physics
  • Explore the concept of hydrostatic equilibrium in stellar structures
  • Investigate the role of radiation pressure in stellar temperature profiles
USEFUL FOR

Students of astrophysics, educators teaching stellar dynamics, and researchers focusing on stellar structure and thermodynamics will benefit from this discussion.

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Homework Statement



Consider a hypothetical star of radius R, with density ρ that is constant, i.e. independent of radius. The star is composed of a classical, non relativistic, ideal gas of fully ionized hydrogen,
Find the the temperature profile (T(r))

Homework Equations


dT(r)/dr = ( (-3*L(r)*k(r)*ρ(r)) / (4∏*(r^2)*4*a*c*(T(r))^3)
so sorry this is written poorly

The Attempt at a Solution


So what I did is try and assume which of the values on the right side are constant so I could take them outside of the integral, but I'm not sure.Please explain principles and equations fully. I really want to understand this!
 
Last edited:
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Maybe you could state the problem?
 
Oh sorry. I thought I did!
I edited it. I says find the temperature profile (T(r))
 

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