Ice Water

Normally, to cool a pitcher of water quickly, one adds ice. The ice floats at the top. Suppose one could add the same amount of ice so it could be held in the water at the bottom of the pitcher. Which technique would lead to faster cooling of the water?

Answer

The ice at the top brings about faster cooling of the water in the pitcher. As some ice melts, this cold water is more dense than the surrounding water and sinks, cooling the water it passes through. The warmer, less dense water at the bottom is buoyed upward into a cooler region. This mixing helps the water cool faster than when the ice is held at the bottom, because the cold water produced by the ice would remain at the bottom. Thermal conductivity throughout the water would eventually cool the water above, but the convection currents work faster. Of course, vigorous stirring of the ice water eliminates any need for the previous discussion!

One could say that the discussion above is incomplete because in our idealization we have ignored the ice thermal interaction with the ambient air. This interaction can be important, especially on hotter days. The ice does its job when thermally interacting with the water, not with the air! The ice held in the water would be a more efficient direct interaction procedure. So when the ambient air temperature is great enough, they could be competitive.

By the way, this cooling process is exactly the same as the sequence of events that occurs when a pond freezes over in winter. However, in that case, the pond water is prevented from cooling further and from freezing through until all the water reaches 4°C first. This delay in freezing throughout saves the lives of pond organisms through the winter if spring comes soon enough. Evaluated in a different way, there would be no life surviving the worst ice ages on Earth if water did not reach its maximum density at about 4°C!