A popular misconception is that "hot water freezes more...

A popular misconception is that "hot water freezes more quickly than cold water." In an experiment, two $100 .-\mathrm{mL}$ samples of water, in identical containers, were placed far apart in a freezer at $-25^{\circ} \mathrm{C}$. One sample had an initial temperature of $78^{\circ} \mathrm{C}$, while the other was at $24^{\circ} \mathrm{C}$. The second sample took 151 minutes to freeze, and the warmer sample took 166 minutes. The warmer sample took more time but not much. How can you explain their taking about the same length of time to freeze?

Key Concepts

Newton’s Law of Cooling

This principle states that the rate at which an object loses heat is proportional to the difference between its temperature and the ambient temperature. In the context of freezing water, although the initially warmer water has more heat to lose, its higher temperature difference from the freezer means it cools faster at the beginning. However, as both samples approach the freezer’s temperature, the rate of cooling diminishes, leading to similar overall freezing times.

Specific Heat Capacity and Latent Heat

Water has a high specific heat capacity, meaning it requires a considerable amount of energy removal to change its temperature. Furthermore, the process of freezing involves removing latent heat, which is independent of the initial temperature. Therefore, despite starting at different temperatures, both water samples must lose nearly the same total amount of energy to transition from liquid to solid, resulting in similar freeze times.

Non-linear Cooling Rate Dynamics

Cooling does not occur at a constant rate; it is faster when there is a larger temperature difference between the object and its surroundings and slows as equilibrium is approached. As both water samples near the freezing point, the cooling rate slows significantly. Thus, even though the warmer water starts with a higher temperature, most of the cooling period for both samples occurs when they are closer to freezing, making the overall times to freeze comparable.

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