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Energy production pr. gram

  1. Oct 2, 2015 #1
    We consider a red giant star. The energy is produced by hydrogen fusion in a shell
    and by helium fusion in the core.
    We assume that the mean density in the hydrogen shell source is 30 g/cm3 and that
    the mean chemical composition is X=0.35, Y=0.63 and Z=0.02.
    The mean density in the core is assumed to be 6000 g/cm3 and the mean
    composition is Y=0.49 and Z=0.51.
    The energy production rates for the relevant processes are:

    εPP_I=9*10^-6*X^2*(ρ/(g*cm^3)*(T/(10^6*T)^4 erg/s/g

    εCNO=1.8*10^-21*X*Z*(ρ/(g*cm^3)*(T/(10^6*T)^18 erg/s/g

    ε=1.7*10^-67*Y^3*(ρ/(g*cm^3)^2*(T/(10^6*T)^30 erg/s/g

    We assume ε3α(centre)= εCNO(shell source) i.e. the energy production per gram
    material is identical for the central triple-alpha fusion and the shell source CNOfusion.
    The relative mass loss for hydrogen fusion is 0.7% and for helium-to-carbon fusion is
    0.07%. We now assume that the star will use 2 million years to transform all the
    helium to carbon in the core. We also assume that the star will have Y=0.98 at the
    beginning of Helium-to-carbon fusion and that the energy production rate is constant
    throughout the helium burning.

    C_01_1: Show that ε3α ≈ 10000 erg/g/s (using the above assumptions).
    C_01_2: Calculate the temperature in the hydrogen shell source and in the
    helium burning core. Show that CNO is dominating the hydrogen fusion and
    that the PP-fusion rate is small.

    I have tryed C_01_1 with E=m*c^2 without luck i get 97 erg/s/g and i have tried every kinda way to get 9700 instead, but no, i cant see it.

    C_01_2 Im totally lost here dont know how to find the tempratur with out ε for hydrogen.
  2. jcsd
  3. Oct 3, 2015 #2


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    Staff: Mentor

    How can we know what went wrong if you don't show your work?

    You should define X, Y and Z, but I can guess that they are the fraction of hydrogen, helium and metals (by number of atoms or by weight?).

    T/(10^6*T) is T/(10^6*K)?
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