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...
For the next level of detail, draw the curves
representing the temperature (for each sample)
as a function of added energy. Colored chalk
may help here.
/
/
/~~~~~~~~~~/
/ /
/----------/
/
/
/
The heat capacity of the two solids is about
the same. The heat capacity of the two liquids
is about the same. The latent heat of melting
is about the same. The big difference is that
the melting occurs at a different temperature.
The plateau corresponds to the physical process
of sucking the entropy out during freezing, and
dumping entropy in during melting.
...
The argument is incomplete at this point, because
we've been measuring the energy, not directly
measuring the entropy. So we must show the
connection.