Solving Stellar Structure: Pressure & Temperature Stratification

In summary, the problem at hand is finding the temperature stratification using the given density expression p = pc(1-r/R). The Equilibrium equation and Continuity equation may be used to find the pressure distribution, and the ideal gas law can be rewritten in terms of density to find a relation between temperature and density.
  • #1
atomqwerty
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0

Homework Statement



Let be the density given by the expression p = pc(1-r/R) where R is tha radius of the star. Find the stratification for pressure and temperature.

Homework Equations



Equilibrium eq. dP/dr = -Gm(r)p/r2

Continuity eq. dm/dr = 4*Pi*r2p

PS.: p == rho (sorry for not using TeX)

The Attempt at a Solution



The main problem is how to find the temperature stratification... maybe using the ideal gas equation PV =nRT?

Thanks!
 
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  • #2
Have you already found the pressure distribution? If so, try rewriting the ideal gas law in terms of density, by multiplying both sides of PV=nRT by molar mass.
 
  • #3
ideasrule said:
Have you already found the pressure distribution? If so, try rewriting the ideal gas law in terms of density, by multiplying both sides of PV=nRT by molar mass.

Yes, I've found P(r) using Equilibrium equation, now if I write P=puRT (p:density; u:molar mass) and p=pc(1-r/R). Then I Have a relation between T and p, is that right?

thnk
 

1. What is stellar structure?

Stellar structure refers to the internal composition and layers of a star, including its temperature and pressure stratification. It is important for understanding how stars form, evolve, and eventually die.

2. How do pressure and temperature stratification affect stellar structure?

The pressure and temperature stratification within a star are crucial for maintaining its equilibrium and enabling nuclear fusion to occur. As a star's core produces energy through fusion, the pressure and temperature increase, leading to different layers with varying densities and temperatures.

3. How is stellar structure determined?

Scientists use a combination of observational data, theoretical models, and simulations to determine the structure of stars. This includes measuring a star's luminosity, surface temperature, and spectral lines to infer its internal properties.

4. What role does gravity play in stellar structure?

Gravity is the force that holds a star together and determines its overall shape and size. It is also responsible for the inward pressure that balances out the outward pressure from nuclear fusion, maintaining the star's stability.

5. How does the size and mass of a star affect its structure?

The size and mass of a star are directly related to its structure. More massive stars have stronger gravitational forces, leading to higher internal pressures and temperatures. This results in larger and more complex structures, such as multiple layers of fusion reactions. Smaller stars have lower internal pressures and temperatures, resulting in simpler structures and longer lifespans.

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