Answer
We can rank the materials according to specific heat in the solid state:
$1 \gt 2 \gt 3$
Work Step by Step
We can write an expression for a material when it absorbs or releases heat $Q$:
$Q = cm~\Delta T$
It is given in the question that the rate of heat loss is constant.
Thus the value of $c~\Delta T$ is constant over time as the liquid cools or as the solid cools.
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. After the horizontal section, the graph shows the cooling process in the solid state.
Since the magnitude of $\Delta T$ over time in the solid state is greatest for material 3, the value of $c$, the specific heat, in the solid state must be smallest for material 3.
Since the magnitude of $\Delta T$ over time in the solid state is least for material 1, the value of $c$, the specific heat, in the solid state must be greatest for material 1.
We can rank the materials according to specific heat in the solid state:
$1 \gt 2 \gt 3$
