Calculate the hydrogen burning lifetimes of stars near the upper and lower ends

ID: 3900228 • Letter: C

Question

Calculate the hydrogen burning lifetimes of stars near the upper and lower ends of the main sequence using the following information:

Lower end of main sequence constains stars with masses of about 0.07 solar masses and luminosities of about 5*10^-5 solar luminosities.

The upper end of main seuqnece constains stars with masses of about 85 solar masses and luminosities of about 1*10^6 solar luminosities.

Assume that only 10% of the upper main sequence star's hydrogen is present in the core and available for fusion.

Assume that all 100% of lower main sequence star's hydrogen is available for fusion.

If someone could help me solve this, I would be very appreciative.

Mass of hydrogen available in a lower main sequence star=100% of 0.07 solar masses

=1*0.07*2*10^30 kg

=1.4*10^29 kg

Energy from combusting hydrogen E=mc^2=(1.4*10^29)*(3*10^8)^2=12.6*10^45 J

Power dissipated by lower main sequence star = 5*10^-5 solar luminosities = 5*10^-5*3.839*10^26 W

=19.195*10^21 W

Hydrogen burning lifetime=Energy/Power=(12.6*10^45)/(19.195*10^21) seconds

=6.5*10^23 seconds

=20611364789446981.22 years nearly 2*10^16 years

Mass of hydrogen available in a upper main sequence star=10% of 85 solar masses

=0.1*85*2*10^30 kg

=1.7*10^31 kg

Energy from combusting hydrogen E=mc^2=(1.7*10^31)*(3*10^8)^2=15.3*10^47 J

Power dissipated by lower main sequence star = 1*10^6 solar luminosities = 1*10^6*3.839*10^26 W

=3.839*10^32 W

Hydrogen burning lifetime=Energy/Power=(15.3*10^47)/(3.839*10^32) seconds

=3.98*10^15 seconds

=126204972.1 years nearly 1.2*10^8 years

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.