Answer to Question #155220 in Molecular Physics | Thermodynamics for Samir khan

Question

A small sample of coal, when completely converted into energy, releases 3.75 * 10 ^ 14 j . What is the initial mass of coal, assuming the final mass 0

Answer 1

We may see that the energy released is quite huge for the really small sample, and the final mass is 0, so it's not the case of combustion, but it is the case of turning mass into energy.

For the combustion the amount of coal needed will be $\dfrac{3.75\cdot10^{14}\,\mathrm{J}}{29.3\cdot10^6\,\mathrm{J/kg}} = 1.3\cdot10^7\,\mathrm{kg}$ and it is a very large amount. So we should determine the mass of coal needed for the energy released:

$E = mc^2, \; \;\; m = \dfrac{E}{c^2} = \dfrac{3.75\cdot10^{14}\,\mathrm{J}}{(3\cdot10^8\,\mathrm{m/s})}^2= 4.17\cdot10^{-3}\,\mathrm{kg} = 4.17\,\mathrm{g}.$