Two of the samples could be combined and their melting points compared to demonstrate the presence of distinct materials in the test tubes. The two substances are distinct if the melting point is lower than the theoretical melting point. They are the same substance if the melting point of the sample doesn't change.
The melting point is a solid's physical characteristic that can be used to identify a substance. In reality, a solid typically melts over a wide temperature range rather than at a single, set temperature. Because of this, speaking of a melting point range is more useful.
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