Question:
A cube of ice floats in a glass of water, the entire system at 0°C. Just enough heat is supplied to melt the ice cube without altering the system’s temperature. Does the water level rise, fall or stay the same?
Answer:
The water level remains constant during the melting of the ice cube. This seemingly unaltered state is a result of the unique properties of water and the physics of floating bodies.
Understanding Ice’s Behavior:
- Expansion during Crystallization:
- Density Anomaly: Water exhibits a rare phenomenon where it expands upon freezing, defying the norm observed in most substances. As water molecules arrange into a crystalline structure during freezing, they create a network with more significant volume, resulting in lower density than liquid water.
- Floating Mechanism: The reason an ice cube floats is due to its lower density compared to water. The displaced water volume, equivalent to the weight of the ice, ensures buoyancy.
Conservation of Mass:
- Weight and Volume Relationship:
- Unchanged Weight: The ice cube’s weight remains constant during the melting process because the same amount of water formed it in its frozen state. The melted water from the ice cube contributes the same weight as the water it displaced while floating.
- Displacement Principle: According to Archimedes’ principle, a floating body displaces its own weight of fluid. Therefore, as the ice cube melts, the water level experiences no net change because the melted water precisely matches the volume it displaced when solid.
Visualizing the Process:
- Consistent Water Volume:
- Balanced Changes: As the ice cube transitions from a solid to a liquid state, the volume of water it contributes exactly compensates for the volume it displaced while floating. Consequently, the water level in the glass maintains equilibrium throughout the phase transition.
Conclusion:
In the intriguing dance of phase changes, where solid ice transforms into liquid water, the water level in the glass remains an unyielding constant. This equilibrium is a testament to the fascinating interplay between the unique properties of water, buoyancy principles, and the conservation of mass. Understanding these dynamics provides a glimpse into the intricacies of everyday phenomena, unraveling the secrets hidden within a seemingly simple glass of water and a floating ice cube at 0°C.
