Estimate the Hydrogren Burning Lifetimes of Stars

[SHISHKABOB]

Homework Statement

Estimate the hydrogen burning lifetimes of stars on the lower and upper ends of the main sequence.

Lower end: M = 0.085 solar masses; log₁₀(T_eff/K) = 3.438; log₁₀(L/L_solar) = -3.279

Upper end: M = 90 solar masses; log₁₀(T_eff/K) = 4.722; log₁₀(L/L_solar) = 6.045

Assume that the 0.085 solar mass star is entirely convective, so that all of its hydrogen becomes available for burning, while only 10% is available for the high mass star.

Homework Equations

The Attempt at a Solution

So in my book it does an example where it does basically this problem. It takes the sun and assumes that it started off 100% hydrogen. It then assumes that only 10% of the hydrogen is converted into helium via nuclear fusion. It then says that only 0.7% of the mass of hydrogen would be converted to energy when the helium is formed.

So E_nuclear = (0.1)(0.007)*M_solarc² = 1.3*10⁴⁴

then

t_nuclear = E_nuclear/L_solar = ~10¹⁰ years



I would assume that I use the same process for each of the cases given in the problem. But I am hesitating because it gives me the effective temperature of each star. At first I thought perhaps that it wanted me to take into account the energy production rate due to the PP cycle or the CNO cycle, but then of course the effective temperature is not the temperature at the core, so I am a little uncertain of what to do with the temperature.

 

[phyzguy]

Since you're given the luminosity and the amount of hydrogen burned, that is all you need. You don't need the effective temperature - it is probably just there for interest sake.