In the 19th Century one idea of how the Sun produced its ene

In the 19th Century one idea of how the Sun produced its energy assumed it was made of coal that was “burning” (actually the carbon is being oxidized). Assume that the Sun was entirely made of coal (all carbon atoms) and it had somehow an ample source of what ever is needed for the oxidation of carbon, how long could a Sun made of coal produce its luminosity ? Note that the reaction that oxidizes carbon atoms produces approximately 3 eV (or about 5x10­12 ergs) of energy per “burned” or oxidized carbon atom.

Solution

mass of sun is 2*10^33 grams. so, the total energy generated is,

        energy = [5x10­¹² ergs gram] [ 2*10^33 grams] = 1.e+46 ergs

in general, the uses the rate of energy is,

     L = 4*10^33 ergs/s

thus, the required time is calculated as follows:

   t = [1.e+46 ergs] / 4*10^33 ergs/s

     = 2.5e12 s

     = 2.5e12 s [ year / 31 556 926 s]

     = 79221.9 years