Assume there is an ice cube in a glass of water. When the ice cube melts, will the water level have risen, fallen, or remained the same? Why?
Lets see now. Some intuitive center in my brain is screaming 'it will remain
the same', but we will try to think it over.
In the first state, we have an ice cube of mass m floating in the water. If it
is floating (in equilibrium), it will have to displace enough water to support its
weight. How much is that? It is just Volume = m/d , where m is the mass of the ice cube,
and d is the density of water.
In the second state, where the ice has melted, it turns into water of
volume.... Volume = m/d! exactly the same volume as it displaced before. So the added
volume is the same, so the level of the water will not change.
As a matter of fact, as long as objects are floating (i.e. they don't rest on
the bottom) they displace enough water to support their mass. Since by turning from
solid to liquid, the mass of water does not change (well, maybe it does, due to
mass-energy equivalence, but that's _really_ negligible) it will keep displacing
the same amount of water.
However, note that this may not apply to everything. If you had solid alcohol
floating in water, when it melts, the level would drop, because water and alcohol
mix at the molecular level; i.e. water filling spaces among alcohol molecules.
Yasar Safkan, Ph.D., Sofware Engineer, Noktalar A.S., Istanbul, Turkey
The water level remains the same when the ice cube melts.
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.
Paul Walorski, Part Time Physics Instructor
'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'