Suppose the Sun is 100 carbon coal for instance and that bur

Suppose the Sun is 100% carbon (coal, for instance) and that burning this can extract 3 eV per carbon nucleus. How long, assuming an inexhaustible supply of oxygen from outside, could burning carbon maintain the Sun’s current luminosity?

Solution

mass pf carbon = 12 amu

amu = 1.67*10^-27 kg

mass of sun = 1.989*10^30 kg

no. of carbon nuclei in sun = weight of sun/(weight of carbon)

= 1.989*10^30/(12*1.67*10^-27) = 9.92*10^55

each carbon molecule generates 3 eV of energy.

total available energy = 3*9.92*10^55 eV = 2.976*10^56 eV = 2.976*1.6*10^56*10^-19 = 4.76*10^37 J

sun\'s liminosity = 3.8*10^26 W

time = total available energy/sun\'s liminosity = 4.76*10^37/(3.8*10^26) = 1.252*10^11 sec = 3967.433 years