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Think about what processes are occurring in the heating curves. Fusion and vaporization are physical processes, not chemical processes. They occur when energy is invested into the resulting physical change, not into changes in temperature. Thus, (d) is incorrect. The deltaH values represent how much energy must be invested to convert a mole of the substance from one phase to the next. Thus, the heating curve will indicate a longer line for higher deltaH values. Because deltaH_vap > deltaH_fus, (a) is incorrect. Now, we have to think about the heat capacities. Since the x-axis represents the amount of heat supplied, given a fixed amount of heat, what would change temperature faster: solid or liquid? Since the heat capacity for solid is lower than heat capacity for liquid, it is easier to raise the temperature of solid vs. that of liquid. Thus, the slope for the solid state must be more steep than the slope for liquid state, since it should reach the next higher state faster given a equivalent magnitude of temperature change. From there, you should get the right answer.