Required mass for hydrogen burning in stars

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To calculate the required mass for hydrogen burning in stars at a temperature of 4*10^6K with a mean molecular weight of 0.62, the relevant equations include (R/Rsun)=(M/Msun)^(3/7) and T=(μG)/(2Rr). The energy per nucleon in the proton-proton (PP) chain process is approximately 6.5 MeV, which needs to be factored into the calculations. There is uncertainty about the correct application of the equations, particularly in relation to the energy per nucleon. Additional resources, such as lecture notes from an astronomy course, may provide further clarification on this topic.
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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