Effect of Melting Ice on Water Level in a Vessel at 4°C

When a block of ice at 0°C is placed in water at 4°C, the ice eventually melts. This phenomenon can be analyzed using the principles of buoyancy and density. In this article, we will delve into the detailed process of how the water level changes when the ice melts in water at 4°C.

Initial Condition

Assume a container filled with water at 4°C. This is the densest point of water, with a density of 999.9720 kg/m3. A piece of ice at 0°C has a density of 999.8395 kg/m3. When the ice is floating, it displaces an amount of water equal to its own weight according to Archimedes' principle. As a result, the displaced water and the floating ice are in a state of equilibrium.

Melting of Ice

When the ice melts, it turns into water at 0°C. The volume of water produced by the melting ice is equal to the volume of water displaced by the ice while it was floating. However, the density of water at 0°C is slightly different from the densest state at 4°C.

Final Condition

Consider the volume of ice that has melted into water. Although the mass remains constant, the volume will decrease due to the change in density. For example, one cubic meter of ice at 0°C (999.8395 kg/m3) will melt into one cubic meter of water at 0°C, which has a higher density at 4°C (999.9720 kg/m3).

Since the mass of the melted ice is 999.8395 kg, and we need 999.9720 kg to fill one cubic meter, we find that we are short by 0.1325 kg of water. This means that the volume of the melted ice is a bit less than one cubic meter of water at 4°C.

Conclusion

Therefore, the water level in the vessel will drop when the ice at 0°C melts, due to the difference in density. The decrease in volume corresponds to a reduction in the water level for every cubic meter of ice that melts.

Explanation of Weight and Mass

In the discussion above, the terms 'weight' and 'mass' have been used. Mass is the amount of matter in an object, while weight is the force exerted on that mass due to gravity. In scientific discussions, it is important to distinguish between the two concepts. When we talk about the displacement of water, we are dealing with mass, but the force exerted by the displaced water when it overflows is what we refer to as weight.

To summarize, when a block of ice at 0°C is placed in water at 4°C, the water level in the vessel will initially rise to the brim. It will then drop slightly after the ice has fully melted due to the difference in density between the water and the melted ice.