Question

why charcoal burns without flame

Answer 1

charcoal undergoes complete combustion, hence do not get free atoms to absorb energy and emit light. therefore burns without flame.

Answer 2

Charcoal doesn't burn with flame rather it glows
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This is because charcoal doesn't have any volatile gas.And if there is no volatile gas then there is no vaporization.And if there is no vaporization of the substance then there is no flame.
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In charcoal , there is no vaporization hence it doesn't burn with flame.A complete combustion takes place without leaving any residue.