Let's imagine that I have a match in hand and nugget of coal on my desk. Then I light up the match and place it for few seconds near the coal so a tiny piece of nugget catches fire. Then another piece catches fire, then another and soon all the nugget is burnt down.
How did it happen? I gave the nugget just enough heat to burn the first piece. Where does come energy to burn the rest of nugget from?
It is called combustion, and it happens in materials which have a lower energy content when their component molecules join with the oxygen in the atmosphere, than when in a solid/liquid structure. When energy is given to start the fire the piece of coal burns and releases energy with excess enough to sustain the reaction and leave heat energy for use.
Combustion is a high-temperature exothermic chemical reaction between a fuel and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke.
Burning/combustion involves chemical reactions that transform the molecules of the initial compounds into molecules with lower (i.e., bigger) binding energy. In the case of burning coal we are mainly speaking about breaking the crabon bonds of the hydrocarbons in coal (see here for an example) and those in the atmospheric oxygen, $O_2$, whereas the final compounds are mainly $CO$ and $CO_2$.
The difference in the binding energies is the heat released, and can be quite significant. However, the initial carbon and oxygen bonds are already rather strong and do not spontaneously break at room temperature. Therefore one needs to heat the carbon and the oxygen, to break the bonds and initiate the reaction. Once the reaction is launched, the heat released through it breaks additional bonds and thus the reaction continues.
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