Look at it this way. When you burn coal with oxygen you get carbon dioxide and heat from the exothermic reaction:

C + O2 > CO2 + heat

To make it go the other way (an endothermic reaction)

CO2 + heat > C + O2

requires the same amount of energy as the forward reaction. Even with 100% efficiency you would just be using up all the energy released in burning to put things right back where they started.

__________________
The Devil offered me power. I told him I preferred aperture.