A fire is a reaction that needs 3 things: a fuel, an oxidising agent and heat. The fuel (paper for example) is what gets oxidised, very often by oxygen. Heat is what gets the reaction started by activating the fuel (heat from a match for example). Heat is also what gets released during the reaction so even without the starting match it will keep going.
If you want to stop a fire all you need to do is remove one of the 3 components (sounds easier than it sometimes is!).
Comments