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The areas on the graph where the lines seem to go flat are areas in which the heat being added to the substance only serves to contribute to the substance's phase change as opposed to increasing the temperature of the substance, whereas areas where the function increases are indicative of temperature increasing relative to the heat added
The flat lines on a heating curve represent the deltaH(fusion) or the deltaH(vaporization) depending on where the horizontal line is. The increasing diagonal lines are representing the q=mcAT as we are heating the substance with a certain heat capacity.
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