Why does water cool more slowly than the same mass of metal at the same initial temperature?

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Multiple Choice

Why does water cool more slowly than the same mass of metal at the same initial temperature?

Explanation:
The main idea tested is how much energy a substance must lose to change its temperature by a given amount—that is, its specific heat capacity. Water has a much higher specific heat capacity than common metals, meaning it stores a lot more energy per degree of temperature change for the same mass. Because of this, when both a mass of water and an equal mass of metal start at the same temperature and lose heat to their surroundings at the same rate, the water’s temperature drops by a smaller amount. The quantitative relation is ΔT = Q/(m c). With the same amount of heat leaving in a given time (Q) and the same mass (m), a larger specific heat capacity (c) for water yields a smaller temperature change, so water appears to cool more slowly. In numbers, water has about 4.18 J/g°C, while typical metals like copper are around 0.38 J/g°C or iron around 0.45 J/g°C. That makes water roughly ten times more resistant to temperature change per unit mass, which explains why it cools more slowly. Emissivity, while related to radiative heat transfer, isn’t the deciding factor here. Evaporation can actually make water cool faster due to latent heat of vaporization, and better conduction in metals would generally promote faster heat transfer, not slower cooling. The dominant reason in this scenario is water’s much higher specific heat capacity, giving it greater thermal mass.

The main idea tested is how much energy a substance must lose to change its temperature by a given amount—that is, its specific heat capacity. Water has a much higher specific heat capacity than common metals, meaning it stores a lot more energy per degree of temperature change for the same mass.

Because of this, when both a mass of water and an equal mass of metal start at the same temperature and lose heat to their surroundings at the same rate, the water’s temperature drops by a smaller amount. The quantitative relation is ΔT = Q/(m c). With the same amount of heat leaving in a given time (Q) and the same mass (m), a larger specific heat capacity (c) for water yields a smaller temperature change, so water appears to cool more slowly.

In numbers, water has about 4.18 J/g°C, while typical metals like copper are around 0.38 J/g°C or iron around 0.45 J/g°C. That makes water roughly ten times more resistant to temperature change per unit mass, which explains why it cools more slowly.

Emissivity, while related to radiative heat transfer, isn’t the deciding factor here. Evaporation can actually make water cool faster due to latent heat of vaporization, and better conduction in metals would generally promote faster heat transfer, not slower cooling. The dominant reason in this scenario is water’s much higher specific heat capacity, giving it greater thermal mass.

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