If an ice cube floating in a glass of water melts, won't the water level decrease?

In summary, a floating ice cube in a glass of water has a weight equal to the weight of water it displaces. When the ice cube melts, the volume of water melted is less than the volume of the ice cube due to ice having a lower density. This would result in a decrease in the volume of water in the glass. However, the water level in the glass remains the same because the part of the ice cube above water accounts for the greater volume before melting. Submerging the ice cube with a safety pin does not significantly change the water level due to Archimedes' principle that a floating object displaces its own weight of fluid.
  • #1
Sam2847
1
0
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.
 
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  • #2


No, *yes
 
  • #3


does the water level change measurably if you submerge the ice with a safety pin?
 
  • #4


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.
 
  • #5


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.
 

1. Why does the water level decrease when an ice cube melts?

When an ice cube melts, it changes from a solid state to a liquid state. This means that the molecules in the ice cube are now moving more freely and taking up more space. As a result, the water level decreases because the liquid water takes up less space than the solid ice cube.

2. Does the water level decrease in all cases when an ice cube melts in water?

No, the water level only decreases if the ice cube is floating in the water. If the ice cube is completely submerged in the water, the water level will not change because the volume of the ice cube is already accounted for in the volume of water.

3. How does the displacement of water by the floating ice cube affect the water level?

When an object, such as an ice cube, is placed in water, it will displace a volume of water equal to its own volume. This displaced water will cause the water level to rise slightly. However, when the ice cube melts, it will no longer displace water and the water level will decrease back to its original level.

4. Why does the water level not change when an ice cube melts in a completely filled glass of water?

In this case, the water level does not change because the volume of the ice cube is already accounted for in the volume of water. Since the glass is completely filled, there is no additional space for the water level to decrease when the ice cube melts.

5. Will the water level continue to decrease as more ice cubes melt in the same glass of water?

No, the water level will not continue to decrease as more ice cubes melt. This is because the volume of water displaced by the ice cubes will be equal to the volume of water created by the melted ice cubes. Therefore, the water level will remain constant after all the ice cubes have melted.

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