Required mass for hydrogen burning in stars

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    Hydrogen Mass Stars
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Discussion Overview

The discussion revolves around calculating the required mass for hydrogen burning in stars, specifically focusing on the conditions necessary to ignite the proton-proton (PP) chain reaction at a temperature of 4*10^6 K and a mean molecular weight (μ) of 0.62. Participants explore various equations and concepts related to stellar physics and thermodynamics.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant seeks assistance in calculating the required mass for the PP chain ignition, referencing the relationship (R/Rsun)=(M/Msun)^(3/7) and the energy per nucleon in the PP process as approximately 6.5 MeV.
  • The same participant mentions needing to use the formula T= (μG) /(2Rr) derived from the ideal gas law but expresses uncertainty about incorporating the energy per nucleon into this equation.
  • Another participant questions whether there is an equation that relates the temperature of the gas/plasma to the mass of the object, suggesting it might be helpful.
  • A third participant reiterates the question about the temperature-mass relationship and introduces an equation, F=-((4*a*c)/(3rho*kappa))*T^3*(dT/dr), but doubts its applicability.
  • One participant offers a link to lecture notes that may provide relevant information for the original query, suggesting that they could help answer the question directly.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants express uncertainty and propose different equations without agreeing on a definitive approach to the problem.

Contextual Notes

Participants have not resolved how to incorporate the energy per nucleon into their calculations, and there are uncertainties regarding the applicability of the equations discussed.

ted1986
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Hello all!

I have to calculate the required mass to ignite the PP chain when the given temperature is 4*10^6K and \mu=0.62. (I know the answer is about 8% from the sun's mass)…
I don't know exactly how to do it :-/ I know that (R/Rsun)=(M/Msun)^(3/7), The energy per nucleon in PP process is about 6.5MeV… I guess I need to use the formula: T= (\muG) /(2Rr) when R is the gas constant and r is the radius (This formula was evaluated from the ideal gas law)… I don't know how to consider the energy per nucleon in this equation…
Could someone help me please…
Thanks! :)
 
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Is there an equation that will give you the temperature of the gas/plasma based on the mass of the object? Would that help at all?
 
Drakkith said:
Is there an equation that will give you the temperature of the gas/plasma based on the mass of the object? Would that help at all?



There is the equation F=-((4*a*c)/(3rho*kappa))*T^3*(dT/dr), but I don't think it's the right equation to use...
 
I wish I could help you further. Perhaps someone else will.
 
ted1986 said:
Hello all!

I have to calculate the required mass to ignite the PP chain when the given temperature is 4*10^6K and \mu=0.62. (I know the answer is about 8% from the sun's mass)…
I don't know exactly how to do it :-/ I know that (R/Rsun)=(M/Msun)^(3/7), The energy per nucleon in PP process is about 6.5MeV… I guess I need to use the formula: T= (\muG) /(2Rr) when R is the gas constant and r is the radius (This formula was evaluated from the ideal gas law)… I don't know how to consider the energy per nucleon in this equation…
Could someone help me please…
Thanks! :)

These lecture notes from an astronomy course might be beneficial...

http://www.ucolick.org/~krumholz/courses/fall09_ast112/notes14.pdf"

...answers the exact question. Of course you could just derive them yourself :-)
 
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