Answer
The specific heat for the liquid state is greater than that for the solid state.
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.
Since the magnitude of $\Delta T$ over time is less in the liquid state than in the solid state, the value of $c$ in the liquid state must be greater than the value of $c$ in the solid state.
That is, the specific heat for the liquid state is greater than that for the solid state.
