If you had an iceberg in a bathtub and it melted, what would happen to the water level in the bathtub, and why?
An iceberg in a bathtub? It depends on whether you are considering a regular sized iceberg or a VERY small one in a normal bathtub. That's because it depends on whether the iceberg is floating or resting on the bottom. If the bathtub is large and deep enough so that the iceberg is floating, the water level won't change.
A floating object displaces an amount of water equal to its own weight. Since water expands when it freezes, one ounce of frozen water has a larger volume than one ounce of liquid water. A completely submerged ice cube weighing one ounce, for example, displaces MORE than one ounce of liquid water. The cube will rise until the volume remaining under the surface displaces only one ounce of water.
If you could remove the ice cube and leave a 'hole' in the water where the cube used to float without disturbing the surrounding water, that hole would take exactly one ounce of liquid water to fill. Let the ice cube melt. Since it is now one ounce of liquid water, putting it back into the 'hole' will exactly fill it and leave the remaining water undisturbed.
If the iceberg is sitting on the bottom of the bathtub and NOT floating, then the water level will rise as the ice melts.
Paul Walorski, B.A., Part-time Physics/Astronomy Instructor
'As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.'