As noted in class 07 of the mass of hydrogen is converted to

As noted in class, 0.7% of the mass of hydrogen is converted to energy in nuclear fusion. A main-sequence star has a mass of 0.55 solar masses. Using the mass-luminosity relation L is proportional to M^3, What is the luminosity of the star, in watts (joules per second)? Watts Three-quarters of a star is hydrogen and typically, 10% of the hydrogen in a star is available for fusion during its lifetime. How much energy can be produced during the star\'s lifetime> Joules Estimate the lifetime of the star, in years years

Solution

the luminosity of the star is,

L = [M/Msun]^3*Lsun

= [0.55]^3*4x10²⁶

= 6.66x10²⁵ W

------------------------------------------------------------------------

given that, 0.7% of the mass converted into energy and 10% mass is availabale of mass.

so, total mass is,

m= 0.1*0.07*mass of sun

E = fMc^2 = 5.2x10⁴³ J

here, M is mass of the star. c is the speed of light.

here, f is fraction of mass converted into energy.

---------------------------------------------------------------------

Life time is,

t = 10^10[M/Msun]^-2.5 = 2.47x10^10 years