Answer: The heat capacity of the liquid is greater than the solid for the substance given.
Step-by-step explanation:
The question requires us to compare the heat capacity of a substance in its liquid and solid state, given a graph of heat gained versus temperature where the phase changes of the substance are indicated.
To solve this problem, we need to keep in mind that heat capacity is defined as the amount of heat necessary to produce a temperature change of one unit, and it is usually given in units of energy per unit of temperature (such as J/K or J/°C). Thus, a greater heat capacity means that more energy will be required to cause the same temperature change.
Looking at the graph provided, we can identify the regions where the substance would be in its liquid, solid and gas state, and also the phase changes:
We can see in the graph that the curve where the substance is a solid "grows faster" compared to the curve for the liquid - it means that the curve for the liquid is "less steep". Consider the following example:
In the image above, Δx for the blue curve is greater than Δx for the green curve, considering the same Δy - therefore, the blue curve is less steep than the green one.
Now, going back to the graph provided in the question, we can say that the curve for the liquid is "less steep" than the solid or, in other words, considering the same temperature change (variation in y), the heat required for the liquid would be greater (variation in x). This means that the heat capacity of the liquid is greater than the solid for the substance given.