# If the thermal expansion coefficient of water was always positive, would ice sink?

I understand that having a negative thermal expansion coefficient means that instead of the material expanding as it heats up it contracts, which is what happens to water, and I know that the coefficient is negative when the temperature is lower than $$4^\circ\text C$$. My textbook asks me to discuss what the process of a body of water freezing over would be if the thermal expansion coefficient of water was always positive.

I think that if this was true then ice wouldn't necessarily float to the top of the lake because water could remain the same density as ice, is this the case?

• The thermal coefficient of expansion of one phase is a different concept than the volume change that accompanies a phase change (and a 1st order phase change must have a volume change). Sep 5 '18 at 20:51

## 3 Answers

When the surrounding temperature decreases, the water in a pond cools down starting from the top.

As long as the temperature of the water at the top is above $4^{\circ}$C, i.e., as long as its thermal expansion coefficient is positive, it becomes denser than the warmer water immediately below it and it sinks. The same process takes place at all levels - all the way to the bottom.

But, at some point, the temperature at the top will drop below $4^{\circ}$C. What happens next? Will the process described above continue?

• It wouldn't continue because the thermal expansion coefficient is negative so it becomes less dense than the warmer water and it would rise to the top, so if it were always positive then no matter what the water in the pond would continuously become colder as you go further down in the pond. Correct? Sep 11 '18 at 15:36
• @Grace When the temperature of the water on the top drops below $4$C, it stops sinking, i.e., it stays on the top and continues getting colder until it freezes. As time goes on, the freezing spreads down, but slowly, since water velow is relatively warm. If the temperature coefficient stayed positive below $4$C, the process of circulation would continue until the temperature of the water at all levels dropped to about zero, at which point the freezing would also start from the top, but it would spread down faster, since the water below is already cold.
– V.F.
Sep 11 '18 at 15:52

Having a positive thermal expansion coefficient would mean that water and ice would have larger interatomic distances, leading to lower densities.

I know V.F.'s answer appears to have solve your problem but think they didn't actually answer your question and you didn't notice. It appears that the question you asked was about ice in the solid form whether it would float, not about how temperature would get distributed in the liquid part. I believe that whether a liquid at its freezing point is denser or less dense than its frozen form at its freezing point does not tell you anything about whether the liquid has positive or negative thermal expansion at its freezing point. In reality, ice is less dense even than boiling water. Suppose that ice at any temperature below its freezing point is less dense than water at any temperature from its freezing point to its boiling point. Then the ice will always float on the water regardless of whether water has positive or negative thermal expansion at its freezing point.

In water above its freezing point at the molecular level, crystals if ice temporarily grow but due to the random motion of the particles but they never keep growing bigger and bigger without bound. In supercooled water, ice crystals will sometimes start growing than shrink again and then after one happens to grow big enough, it will then keep growing bigger easily. When water is only a tiny bit supercooled, it will be a quite inanely long time before an ice crystal reaches the critical size. When we're talking about the density of water, we define the observed density to be the actual density and say water has that density at that temperature. We don't say the water actually has a higher density and it's the nanoparticles of ice in it that lowers the observed density. That's probably because it's normal for those nanoparticles of ice to keep appearing and disappearing all the time. Combining information I learned, I believe that the reason for the negative thermal expansion of water near its freezing point is the higher concentration of nanoparticles of ice in it. However, the frozen state at its of ice at its freezing point is very different from the liquid state at its freezing point. If you have a small particle of ice in freezing water such as an ice pellet and then the air extremely slowly sucks heat out, then it will take a whole lot longer for it to finish freezing than it would have taken for it to get cooled from 20°C to 19°C by air at 0°C assuming there is no radiative diffusion of heat. As more water freezes, heat is actually released in the freezing process. I'm guessing that's because ice at its freezing point stores less thermal energy for its Kelvin temperature than water at its freezing point does. The freezing will only continue if heat continues being sucked out.