In trying to understand the Schmidt-Appleman criterion for contrail formation. There is one aspect that I cannot make sense of.

In many papers that describe the criterion they include a plot as shown below:


(image source: https://www.researchgate.net/figure/Schmidt-Appleman-criterion-for-contrail-formation-The-red-line-represents-the-state-of_fig3_244478376)

How can there be a saturation vapor pressure of water (see solid blue line in below plot) at temperatures/pressures below water's triple point (273.16K, ~611.7 Pa). (I thought, perhaps incorrectly, that the "Saturation Vapor Pressure Ice" line is from the phase diagram of water.) To be clear, I can understand the "Saturation Vapor Pressure Water" line was calculated from the Goff-Gratch equation. My confusion is how we can have a saturation vapor pressure above liquid water without having liquid water.


1 Answer 1


Things like a freezing point represent where an equilibrium occurs. Conditions favor the formation in one direction as we move away from that equilibrium. It doesn't prevent the phase from existing entirely.

Bulk water is not stable below the freezing point, instead preferring to form solid ice. But you can still have some liquid around even below freezing, and this liquid still has a defined vapor pressure. This is often called supercooling.

As the wikipedia article you linked to mentions, it's very hard to test this experimentally at very cold temperatures because it is difficult to get water supercooled to that point and very little liquid remains.

The flight altitudes where this study is looking is well above the pressure of water's triple point. I would refer to the conditions above as "below freezing" not "below the triple point".

  • $\begingroup$ Thermodynamically it is easy to calculate the saturation vapor pressure. $\endgroup$
    – Jon Custer
    Feb 18, 2022 at 21:49

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