Why don’t the trees spontaneously catch fire and burn all the time? Why don’t the fires stop immediately as soon as they start?

Both of these phenomena is due to the ignition temperature.

Explanation:

Trees don't spontaneously catch fire because there is a temperature above which materials combust. This is called the "ignition temperature." This temperature must be reached before the trees will ignite, and the external condition does not always harbor such high temperature.

Fires don't stop immediately because, while some parts of the flame has cooled down sufficiently below the ignition temperature, other parts of the flame have not. It takes time for all the part of the flame to cool down below ignition temperature for the burning to stop.

These are all due to the ignition temperature.

The ignition temperature is defined as the temperature at which a substance begins to burn spontaneously.

The ignition temperature of a woody material is about 343 °C (650 °F). This ignition temperature is much higher than ambient temperature hence trees don't spontaneously catch fire and burn all the time.

Also, all the parts of the burning fire are not at the same temperature. Some parts may cool below the ignition temperature quicker than other parts of the flame hence  the fires don't stop immediately as soon as they start.

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