Why does water level stay the same when ice melts inside the water?

[starstruck_]

I feel so stupid, intuitively, when we were having this discussion I wanted to say that the level stays the same but when we were discussing with the person beside us, my partner said it would fall because water expands when it freezes, so when it melts, there'll be less displacement, so the water level would drop- this made sense to me so I was like okay alright guess this is it.

Turns out, the water level stays the same- I somewhat understand why but along with clearing that up, I also want to know why the water level couldn't drop, and what was wrong with my partner's reasoning.
This is what I understand though:

If ice is already in the water, the water level would not change. The ice floats which means it is experiencing equilibrium, the ice is submerged as much as it needs to be -displaces as much water as it needs in order to float and be at equilibirum. When it melts, the volume of water the ice displaced to support it self, would be equal to the volume of the water coming from the melting ice cube, hence, the water level will not change (? Not sure if I'm understanding this correctly)

I guess as for my partner being incorrect, it's because they assumed that the volume when the ice melts is less than the displacement, when it's actually the same (?).

I feel so dumb for not understanding this yikes.

 

[andrewkirk]

I feel so dumb for not understanding this yikes.

Don't feel dumb, your initial answer that the water level drops is not wrong.

The trouble is that the question is ambiguous. It depends on what the ice is doing in the water. If the ice is floating freely, the water level will remain constant as the ice melts, but if the ice is fully submerged, eg because it is frozen onto a rock, or held beneath the surface in some way, the water level will drop.

The reason why the water level drops in the second case is that, as you say, the volume decreases when it turns from ice to water. The reason why it stays level in the first case is that the level of the water is determined by the amount of H2O molecules below the surface. Floating ice has some of the H2O molecules (ice) above the surface. As the ice melts, its volume shrinks but so does the amount of H2O molecules above the surface. The movement of H2O molecules from above to below the surface exactly offsets the reduction in volume of the molecules that were already below the surface.

 

[CWatters]

Consider a volume of water (blue). When the smaller volume (dotted) freezes it expands pushing some above the surface. The volume that remains below the surface stays the same because the mass is unchanged. When the ice melts it contracts back to it's original size.

Aside: I know the ice expands in all directions but it's easier to visualise what's going on if you assume it's constrained to expand upwards.

 

[sophiecentaur]

I remember a long discussion with a Science Education tutor (I tried to stay out of it) about the 'proper' answer to this. On the face of it, of course, the level stays the same because the same weight of Water is displaced, whether it's ice or melted water but the very reason that ice floats is due to a change in density due to state change and that change in density also occurs with water below about 4°C so it is quite possible that the melting ice will cool the bath water down while melting (it would depend on the quantities involved. So the volume of the original water could increase measurably, raising the level until the whole system warms up to room temperature.
You can imagine that there is no end to this sort of discussion - especially if you are dealing with educationists who are expecting smartarse students to ask awkward questions.