Science Puzzle
Melting Iceberg Stasis
An ice cube is floating in a glass of water. You mark the water level on the side of the glass. The ice melts completely.
Does the water level rise, fall, or stay exactly the same?
The Answer
Stays exactly the same. This is a direct consequence of Archimedes' principle.
A floating object displaces water equal to its own weight. The ice cube is less dense than water, so it floats with most of its volume submerged and a small portion above the waterline. The mass of water it displaces equals the mass of the ice cube.
When the ice melts, it turns into liquid water with the same mass it had as ice. Because water and ice have different densities, the ice occupied more volume as a solid than the liquid it produces. But the liquid water produced fits exactly into the space that was previously occupied by the submerged portion of the ice.
The water level is unchanged. This is why climate scientists note that melting sea ice (which is floating) does not directly raise sea levels, unlike melting glaciers and ice sheets on land, which do add new water to the ocean.
The principle: Archimedes' principle and phase change. A floating object displaces its own weight in water. When it melts, the resulting liquid occupies exactly the volume previously displaced, so the water level is unchanged.