Boiling water turns to snow

from Water structure and Science, Martin Chaplin

Samantha Stewart, a Canadian woman, has become an internet hit with her experiment tossing boiling water into the frigid air of Saskatchewan (video)!  This is a popular activity, here being done at Mount Washington in 2007.  These features provide a chance to talk about my very favorite phase diagram!  Which is NOT the pressure-temperature diagram that we all learned in high-school and college (right diagram).

Here's an example of why the P-T diagram isn't helpful: Imagine that you have liquid water at P and T somewhere in the green field on this diagram, and that you lower the pressure while keeping temperature constant.  This would be a vertical path on the P-T diagram--for example, draw a vertical line down the 80 C mark.  The pressure changes continuously and, after the red line is crossed, all of the liquid water has turned to vapor.  But, a lot happens when your path crosses the red line--the liquid water boils.  Initially, just a few bubbles of vapor form, but the pressure and temperature can't change until all of the liquid has turned to vapor.  You are "stuck" on the red line until that happens.

T-S diagram for H2O: Excuse my lack of graphics skills!

In fluid dynamics, it's common to use a plot of temperature vs. entropy (T-S, left graph), which gives much more information about the state of a system for many problems in flow and thermodynamics.  On this diagram, you not only have the solid (ice) =S, liquid=L, and vapor =V) phases that you see on the P-T diagram, but you have the mixed phases: liquid + vapor (= boiling water or an aerosol, depending on the proportions of liquid and vapor) and solid+vapor (bubbly ice or snow). (Be careful, this diagram is only relevant to a pure H2O system, so you can't directly link it to snow in our atmosphere of nitrogen and other gases.) In the mixed phase regions, the horizontal lines are constant pressure, "isobars."

When processes happen very rapidly, they are adiabatic (meaning that no heat is transferred into or out of the system) and reversible.  Reversible processes have constant entropy, and so are represented by a vertical line in the T-S diagram.  I've illustrated two processes with the dashed vertical lines.  The dashed line with an arrow on the right is decompression of a cup of barely boiling water; the one on the left follows the decompression of strongly boiling water.  Both processes start at 212 F and end at -30 F, conditions reported for the Canadian and Mount Washington experiments. They start at 1 bar pressure (the horizontal line) and end at a very low vapor pressure, a fraction of a millibar. The amount of vapor formed is given by the "lever rule": it is the ratio of the dotted segment of the horizontal line to the total length.  You can see that if you approximate the "water tossing" as an adiabatic, isentropic experiment, it ends up as a mixture of cold vapor, and ice crystals (the snow).  There is much more vapor when strongly boiling water is tossed than when weakly boiling (or not even boiling at all) water is tossed, as you can see by the ratios of the arms in the lever rule. Presumably, the vapor that exists in boiling water expands and breaks the liquid water into small drops which crystallize rapidly to snow.  In theory and in equilibrium, vapor is formed even if the water initially has none, but equilibrium conditions may not be obtained in such rapid processes, so this may explain the observations on the video that cold water doesn't work as well as the very hot water.