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: 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 ε3α=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.