Glass of water

Question:

Consider a glass of water with an ice cube in it and with the water level at the very brim of the glass. What happens to the water level as the ice melts? Will the water level go up and overflow the glass, go down, or remain unchanged. Why? Ignore evaporation and the effects of surface tension.

.

.

C

A

P

T

A

I

N

I

N

T

E

R

V

I

E

W

.

.

Solution: Most of us have encountered this situation before. As ice melts in a full glass, do we find that we need a napkin to mop up the overflow? The answer is no. But the important part of this puzzle is not the answer, but the explanation of why. Here’s one candidate’s response:

Let me think out loud a minute. Ice is less dense than water. That’s why it floats. We also know that ice occupies more volume than water. We know this because a full bottle of water will shatter as it freezes and the ice expands. So the first thought is that the water level will drop. But I know from experience that a glass full of ice doesn’t overflow when the ice melts. Why is that? I think that’s because the ice is floating with a section of the ice sticking up above the water level. Thus, when the ice melts, it shrinks, but this is counterbalanced by the volume of ice that is sticking up out of the water. Thus, there will be no change in the level of the water from the melting ice.

Answer: The water level is unchanged.

Extra credit: Note that if the ice were completely submerged, the water level would fall as the ice melted.

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