When a drink is filled with ice to the brim, a common question is whether the melting ice will cause an overflow. If the ice is freely floating in liquid water, the water level remains precisely the same once the ice has fully melted. This seemingly counterintuitive result is due to two interconnected scientific principles involving how water behaves in its liquid and solid forms. The process demonstrates the precise mass and volume balance that occurs during the phase change from ice back to water.
The Physics of Floating Ice
A floating object, such as an ice cube, displaces a volume of fluid exactly equal to its own weight. This principle dictates that the buoyant force supporting the ice is equivalent to the downward force of its mass. Since the mass of the ice remains constant during melting, the mass of the water it displaces while floating equals the mass of the liquid water the ice will become. For instance, a 10-gram ice cube displaces 10 grams of water, and the resulting meltwater will also weigh 10 grams.
Because mass is conserved, the volume of the resulting liquid water is exactly the same as the volume of water the ice cube was submerging while floating. The space previously occupied by the submerged portion of the ice cube is precisely filled by the newly melted water. The volume of the ice sticking up above the surface is the “excess” volume due to freezing, which disappears when the ice converts back to liquid. This volumetric swap ensures that the water level remains constant.
Water’s Unique Expansion Property
Ice floats because of a unique molecular property of water. Unlike most substances, water in its solid form is less dense than its liquid form. This occurs because water molecules are polar, leading to the formation of hydrogen bonds. As liquid water cools and freezes, these hydrogen bonds force the molecules into a highly organized, open hexagonal lattice structure.
This crystalline arrangement spaces the molecules farther apart than they are in the liquid state. The open lattice structure causes a volume expansion of about nine percent when water turns into ice. This increase in volume means the ice is less dense, which is why it floats with approximately 90% of its volume submerged. When the ice melts, the lattice collapses, and the molecules pack closer together, causing the volume to decrease back to the original liquid volume, perfectly balancing the initial displacement.
When the Rules Change
The “no overflow” rule strictly applies only when the ice is floating in its own meltwater. If the ice is placed in a liquid that is denser than water, the rule is violated, and the cup may overflow slightly. For example, if ice melts in salt water, the ice displaces a volume of the denser salt water equal to its weight. The meltwater, however, is pure, less dense fresh water. The volume of the fresh meltwater is greater than the volume of the salt water that was displaced, causing a small rise in the liquid level.
Another exception occurs if the ice is not fully floating in the liquid. If ice cubes are resting on the bottom or are supported by the rim, they are displacing less water than their weight requires. When this non-floating ice melts, the added volume of water is not fully accounted for by the initial displacement, which can lead to the cup overflowing. The principle of equal volume replacement only works when the object is fully buoyant in the fluid.