The specific heat capacity of water is 4.18 J/(g*^ C) , while the specific heat of iron is 0.46 J/(g=^ C) . On a hot summer day, which is cooler: pool filled with water, or an iron grate? How is this phenomenon related to their specific heat capacities?

The water will be cooler as it requires more energy to raise its temperature by 1 degree than the iron gate.

The higher the specific heat capacity more cooler it will  be.

Explanation:

The specific heat capacity is defined as the amount of energy required to increase the temperature of the substance by 1 degrees. The energy required to increase the temperature wil be given by the formula:

q = mc ΔT  

From the equation we can see the if specific heat capacity increases the energy of the substance gets increase. If specific heat capacity is lower then it is obvious to have low energy.

On hot summer day the temperature would be high we can see that metal like iron would be much hotter than water because iron has less value of specific heat capacity hence less energy required to heat it by 1 degree.

It is now clear that iron gate with low specific heat capacity value (0.46 J/g °C) gets heat up early in hot summer day while water having higher specific heat capacity (4.186 J/g°C)  will take more time to heat up hence remains cooler compared to iron gate.

sorry, is there a picture? i do not see any arrows.

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