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If something has a higher heat capacity that means it can absorb more energy before it increases in temperature. Therefore, it should have a smaller slope because the temperature is increasing at a lower rate due to the higher heat capacity of the liquid.
Think of the heat capacity as the amount of heat something can absorb. The larger the value, the more heat it will be able to absorb before it transitions to the next phase. If it can absorb more heat,it will take longer for this process to happen and will thus have a less steep slope.
The slope corresponds with the coinciding heat capacity of that specific liquid. The higher the heat capacity, the more heat is require to raise its temperature so it will take longer for the temperature to rise thus leasing to a smaller slope and less steep curve.
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