Answer
We can rank the materials according to heat of fusion:
$2 \gt 3 \gt 1$
Work Step by Step
We can write an expression for the amount of energy a material releases when it changes state:
$Q = L~m$
Then $~~L = \frac{Q}{m}$
It is given in the question that the rate of heat loss is constant.
When the graph shows a horizontal section, this is the time when the material is freezing, that is, changing from liquid state to solid state.
A material with the shortest horizontal section releases the smallest amount of heat $Q$ when it changes state. It follows that the heat of fusion of this material is the smallest.
Since material 1 has the shortest horizontal section, it releases the smallest amount of heat $Q$ when it changes state. It follows that the heat of fusion of material 1 is the smallest.
Since material 2 has the longest horizontal section, it releases the greatest amount of heat $Q$ when it changes state. It follows that the heat of fusion of material 2 is the greatest.
We can rank the materials according to heat of fusion:
$2 \gt 3 \gt 1$
