What powers the Sun?


In the 19th century, the most efficient fuel was burning coal. If you assumed that the center of the Sun was all coal (why is this reasonable?), how long could the Sun burn at it's present luminosity?


Each molecule burned, C + O2 -> CO2, releases 1eV of energy


1eV of energy = 1.6 x 10-19 Joules (1 Watt = 1 Joule/second)


How many molecules are there to burn?


12 (carbon) + 2*16 (oxygen) = 44 x 1.67 x 10-27 kg


2 x 1030 kg / 7.34 x 10-26 kg = 2.7 x 1055 molecules


How much energy will be released in the lifetime of the Sun?


2.7 x 1055 molecules x 1.6 x 10-19 Joules/molecule = 4.3 x 1036 Joules


How long will the Sun last if it burns coal in the core?


4.3 x 1036 Joules / 4 x 1026 Joules/second = 1010 seconds = 350 years!




This can be made 10 times longer burning hydrogen (why?), but it is still much to short to explain the existence of Earth for thousands, millions, billions of years.