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This is only how i explained it to myself after i did the experiment, so it might not be right. Burning is the result of a combustion reaction, and combustion reactions require a certain amount of activation energy to start. When the paper is in contact with water, the energy from the open flame that would usually start the combustion reaction is transferred to the water before the paper can ignite. This raises the temperature of the water and it will eventually reach boiling point. Now when all the water has evaporated, then the cup burns because there is nowhere left for the heat to be transferred to.

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Q: You can boil water in a paper cup over a direct flame without burning it How can you explain that?
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