Required mass for hydrogen burning in stars

[ted1986]

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! :)

[Drakkith]

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?

[ted1986]

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...

[Drakkith]

I wish I could help you further. Perhaps someone else will.

[qraal]

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 :-)