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First, let us clarify some terms.
Chemical changes are those that occur when a new substance is formed (whether via decomposition or combination of other substances). This involves re-arrangement of molecules/atoms to produce new species. Physical changes, on the other hand, merely affects the appearance or the form of the substance, without changing its chemical identity.
In the given scenario, we have a candle burning. So now, we have to identify the events happening and classify them as physical or chemical change.
First, when we light the candle, we are burning the candle wick (usually made with cotton which is 90% cellulose). This burning then, which is reaction of the cellulose and other materials in the candle wick, produces carbon dioxide and water vapor (soot, the black smoke). The cellulose, for one, is transformed into other substances such as carbon dioxide and others. This is a chemical reaction.
On the other hand, as the temperature increases, the wax starts to melt. Melting of wax is merely a phase change. It is still the same material except that it assumes a different form due to an increase in temperature. This is also a physical change.
(As other possibilities: for a scented candle, the evaporation of the scents is also a physical change, while degradation of the scented substances due to the flame will be considered chemical changes)
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