## Saturday, January 2, 2010

### A Cube of Ice

You pour yourself a glass of water, drop a cube of ice and see that water edge is only a few millimeters away from the top of the glass. Will it overflow when the ice melts?

Here is a relevant story about golden wreath, Archimedes and Eureka moments of our households.

Enter your answer on our Family Puzzle Marathon page. Solve three and get a prize!

Alin Grin said...
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Alin Grin said...
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Alin Grin said...

The glass will not overflow. The volume of water will decrease. One of the water anomalies is that it expands when cooled to 4°C or below. When the ice melts, its temperature gradually rises from 0°C or below towards the ambiance temperature. The ice will decrease in volume once it gets warmer than 4°C.

Maria said...

The glass will not overflow, but will the water level decrease? Let's try it out with our next glass of water. A picture is added to this puzzle to help you in explanations.

Maria said...

Well, it is indeed a very tricky puzzle!
There is a complex answer, and a more complex one :)
If we ignore changes in the temperature of the water, then it turns out that when the above water part A and below water part B of the ice cube will melt, in a liquid state they together will fill the same volume as currently is taken by B. Therefore water will not rise or descend.

Why volume of A+B in ice state is equal to the volume B in water state? This comes from Archimedes' Principle:
Since the ice cube is floating, it is displacing a volume of water (equal to the volume of B) that has a weight equal to that of the ice cube. So, we know that water of volume equal B weights the same as (A+B) in ice. After the ice has melted, it still weights the same = A+B. And A+B in water state gives us volume B. The level stays the same for all practical purposes.

Reading more about this puzzle and knowing Alin's expertise, I saw that there is actually more to it if we consider water temperature changes. Water contracts as it cools until it reaches 4 degrees C at which it reaches its maximum density. As it cools below 4 degrees it expands until it freezes. Our water is likely above 4 degrees C and therefore will contract a bit. So, Alin was right!

aron said...

The compound H2O is one of the few coumpounds that are bigger when turned into a solid