How Does a Red Giant Star Produce Energy Through Fusion Processes?

[colloio]

Exercise_C_01
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:

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

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

ε_3α=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 can't see it.

C_01_2 I am totally lost here don't know how to find the tempratur without ε for hydrogen.

 

[mfb]

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 can't see it.

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)?