TBR GChem Ex. 7.21

[northpenn]

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The question is if an ice cube floats in a glass of water in such a way that the surface of the water is flush with the brim, and the ice cube sticks out above the level of water, what will occur as the ice cube melts?

The answer was that the water level will remain flush with the top of the glass which makes sense..

But.. I wanted to know if the same answer would result if the ice cube floats in a glass of salt water. Since the densities of the water displaced and the ice cube are different, shouldn't the glass actually overflow then since the density of the pure water < density of the salt water?

 

[vsl5]

I dont think so, the densities are different but the masses would be the same. Buoyant force of a floating object is equal to the mass of fluid displaced which would be equal to the weight of the object if it floats. Imagine the cube floating in salt water, then just replace that volume with water when the cube melts and it would be the same since the weight was the same before.