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When drawing heating curves, the enthalpies of vaporization and fusion guide how long to make the phase change line with slope = 0 relative to the x axis and the heat capacities of solid, liquid, and gas tell you how to sketch the slope. However, how would we know how long to sketch the line corresponding to the increase in temperature as the heat supply increases relative to the x-axis without being told the melting or boiling points?
Without calculation, it is very hard to estimate correctly the exact size of each segment. However, it is known for sure that enthalpy of vaporization is more than enthalpy of fusion because you have to break more intermolecular bonds. So when representing it, make sure that the segment of vaporization is longer than the fusion one.
I think that if they ask for a sketch of the graph, we won't need to label the melting point and boiling point on the graph. They are usually just checking the slopes relative to each other, and how long your lines for enthalpy of fusion and vaporization are relative to each other.
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