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Originally Posted by Theodoric
I know that at first sight it seems like it should, but in actual fact, the changes in density don't make any difference. The ice contains exactly enough water, when it melts, to fill the space that the ice occupies in the water; no more, no less.
Even if the ice has drifted south to warmer water before it started melting it still wouldn't make any difference. Consider the ice at 0C and the water at 20C. The ice contains the same weight of water as that that was in the "hole" it makes. Assume it now melts very rapidly. Initially, as the melt water is at 0C, it will be a little smaller in volume than the hole. However, when it warms up to 20C it will expand exactly enough to fill the "hole", so the water level will remain the same.
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Density of ice = 0.931 gcm^-3
Density of water = 1 gcm^-3
Let's say there was 1 mol of water molecules, that's 6.02x10(23) water molecules, and has a mass of 18g.
Density = mass / volume so the volume in the solid state will be 18/0.931 = 19.33 ml
In the liquid state the same water will have a volume of 18 ml.
The density of the water will remain constant whilst the water remains in one state.
So your argument that the water somehow expands to fill the space is fundamentally flawed. How would it happen?