Is there a mathematical limit to the difference in the temperatures, a substance acquires before changing states, in this particular case, is there a limit to the difference between the boiling and melting points of an element or a compund?
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1$\begingroup$ You mean an upper bound to the difference? Of course. A million billion kelvin would certainly be an upper bound. The smallest upper bound, however, won't be known since there are plenty of materials we have yet to study/create. $\endgroup$– lemonCommented Apr 9, 2016 at 13:44
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$\begingroup$ No, for instance the 100 K gap for water the near 2000 K gap for gallium, how far does this difference proceed? Is there any sort of symmetry to this? $\endgroup$– AbhinavCommented Apr 9, 2016 at 13:47
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Since the melting point and especially the boiling point of a substance depend on the pressure you had to specify a pressure. Also not all substances do have a melting or boiling point. Some, e.g. carbon at standard pressure sublimate.
A good canditate for the substance with the highest difference at standard pressure is neptunium with a value above 3200 K.