Why Doesn't the Water Level Decrease When an Ice Cube Melts?

[Sam2847]

Consider a floating ice cube in a glass of water.

I know that the weight of the ice cube is equal to the weight of the water displaced.
This would mean that if the ice cube melted, the volume of water melted would be less than the volume of the ice cube, because ice has a lower density than water. As a result, the volume of water in the glass should decrease.

If this is the case, then why does the water level in the glass remain the same, rather than decreasing?

*Does it have something to do with the part of the the ice cube floating above water, which would account for the greater volume before melting? That way the total volume would still decrease after melting, but the water level would still remain the same.

 

[M Quack]

No, *yes

 

[algebrat]

does the water level change measurably if you submerge the ice with a safety pin?

 

[azizlwl]

Proposition 5 of Archimedes' treatise On Floating Bodies states that:

Any floating object displaces its own weight of fluid.
— Archimedes of Syracuse[2]

Volume displaced = volume submerged.
Volume displaced = ice converted to water. Since the weights are the same.

 

[Nickie]

Yes, you are correct in your understanding that the volume of the ice cube above the water surface plays a role in this phenomenon. When an ice cube is floating in water, it is in equilibrium where the weight of the ice cube is balanced by the upward force of the water, known as buoyancy. This is due to the fact that the density of ice is less than the density of water.

When the ice cube melts, the volume of water added to the glass is equal to the volume of the ice cube below the water surface, which is less than the volume of the entire ice cube. This results in a decrease in the total volume of water in the glass, but the water level remains the same because the ice cube's weight is still being supported by the water.

Therefore, even though the melting of the ice cube does result in a decrease in the total volume of water in the glass, the water level remains unchanged due to the balance of forces acting on the ice cube. This is an example of Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid it displaces.