Freezing point and melting point are not equal?

[chaser0]

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This idea just took me by surprise and i wanted to confirm here.

When an object is freezing/melting, the temp vs. heat added curve pleateaus. But that plateau is not perfectly slope=0.

Hence the substance begins freezing at a lower temp than when it begins melting~~

 

[chiddler]

ideally they are the same.

due to acceptable experimental/human error, they are different.

 

[Dasypus]

They are the same in completely pure substances completely evenly heated/cooled. Violate one of those, and you'll see the start of melting and the start of freezing seperate by a bit.