Put a rock on top of an ice cube in a glass of water, and then fill the water to
ID: 3901138 • Letter: P
Question
Put a rock on top of an ice cube in a glass of water, and then fill the water to the brim of the glass. When the ice cube melts, what will happ en to the water level? One student claims : 'It will clearly overflow the glass, because the rock will then be submersed in the water'
After several minutes, the ice cube melts completely the rock sinks to the bottom of the glass, and the water level decreases!
'What?!' exclaims the student. 'That's crazy! I know that if the ice melts, the water it turns into exactly fills the hole previoulsy filled by the floating ice cube. But the rock was completely out of the water before the cube melted. Now that it is in the water, it is taking up volume previously occupied by water, which cannot possibly fit in the glass anymore! This is deceptive nonsense - it does not obey the laws of physics!'
Explain why the water level in the glass decreases, clearly in accord with the laws of physics. Describe why the student's reasoning is wrong. Use good examples or analogies to emphasize your points. If you think a picture would be helpful, you can include a diagram.
Explanation / Answer
We assign this question all the time to our students. Since the ice, when it floats, displaces exactly its weight in water, when it melts, the water it melts into takes the same volume that the ice cube displaced in the water. So the water level should remain the same.
A small correction to this reasoning comes from the fact that the water cools down as the ice cube melts. Cool water is more dense than warm water, and the water level will go down just a bit as the water shrinks.
A small correction to the small correction comes from the fact that water expands a bit before it freezes. It has a maximum density at around 4 degrees Celsius. If the water has a temperature between 0 and 4 C, and the ice cube melts, the water level should go up because water expands as it cools down in this narrow temperature range
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