What melts as you cool it and hardens as you heat it?

Answer 1

Lots of things harden when heated: clay, for instance. But do they melt when cooled? Does clay? Something that melts when cooled, would be a substance whose particles would slip away off each other with lesser average kinetic energy. Something like a soup of magnetic dipoles, or something of the sort. There are no pure substances that melt as you cool them. However, that assumes no simultaneous change in pressure -- if you decrease the pressure a lot as you cool, then you can melt something while cooling. Similarly, no pure substance will harden when you heat it at constant pressure. But again, if you increase the pressure while you heat it, you can solidify something while heating it. But it's important to understand it's the pressure that doing the solidifying or melting in this case, and you are just working against the change in temperature which is effectively doing the opposite. That said, mixtures can often harden when heated. Clay is a good example. Paint, glue, epoxy will also harden when heated. But in all cases that is because you are either removing water (or another solvent) or you are causing a chemical reaction to happen which causes it to harden. In a similar way, there may be mixtures that melt when cooled (due to a chemical reaction for instance), but I don't know of any.