Introduction: The Freezing Paradox in a Rigid Vessel

The video begins by stating two intuitive facts: water expands when it freezes, causing ice to float and containers to bulge or even burst in a freezer; conversely, water melts under high pressure. The central thought experiment asks what happens if you try to freeze water while it is compressed inside a vessel that cannot bulge or stretch. If the water remains liquid, below 0 °C it should freeze, but if it freezes, expansion should generate pressure and cause melting, which seems paradoxical.

Phase Diagram as a Guide

To untangle the issue, the presenter turns to water’s phase diagram, which maps the states of matter as a function of temperature and pressure. The diagram shows that at standard atmospheric pressure, cooling water leads to a liquid-to-solid transition, but increasing pressure at subfreezing temperatures can push the solid back toward the liquid state. Following the liquid–solid boundary toward lower temperatures and higher pressures reveals how the system navigates between phases as conditions change, preventing an endless paradox.

Partial Freezing, Pressure Build-Up, and Partial Freezing Dynamics

As the container is cooled, water tends to freeze, yet any portion that freezes expands and pressurizes the container. This pressure rise then halts further freezing of the remaining liquid. The video illustrates this with a graph: the colder the container, the higher the fraction of ice and the higher the pressure becomes, leading to a steady state where both liquid and solid phases coexist.

Non-Binary Phases: Ice I_h and Ice III

Beyond the simple liquid–solid dichotomy, water can form multiple solid phases under different pressures. The phase diagram reveals that, at sufficiently low temperatures and high pressures, the remaining liquid can freeze into a distinct ice phase called I 3 (Ice III). The video notes that Ice III contracts and becomes denser when it freezes, creating more space and enabling the entire container to freeze solid, albeit with a mixture of Ice I_h and Ice III present. This nuanced picture shows there is no paradox after all—the behavior is non-binary and richly structured.

Key Takeaways and Implications

The overarching message is that phase behavior under pressure is more complex than a simple solid-versus-liquid narrative. Water’s phase diagram encodes how pressure and temperature interact to determine which phase dominates and how mixtures of phases can stabilize under constrained conditions. The paradox dissolves when we recognize that phase transitions can proceed through multiple solid states, each with its own density and volume changes, and that compression can dynamically influence freezing.

"There is no paradox. The phase of water, it turns out, can be non-binary." - MinutePhysics

"The colder you make the container, the higher the percentage of ice, and the higher the pressure in the container." - MinutePhysics

"The pressure that causes melting is being generated by expansion that requires being frozen." - MinutePhysics

"the remaining liquid water can freeze into a different phase of ice called I 3" - MinutePhysics

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