Question

After a Melting point determination, why can't you re-use the solidified substance and capllary tube for subsequent determination?

Answers

In reality you probably could, however it is not good science as it has been considered to be contamined or already used and a new substance or solution should be obtained. I know this is wasteful but, that is just how it is.
I don't think it is all that wasteful. Those tiny capillary tubes are IMPOSSIBLE to clean. Even if they could be cleaned who would trust them? You're right. Get a new one.
It is better to get a new one as the used capillary would have residue of the other sample and the residue would act as an impurity causing an alteration in the end product

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