Post a Comment On: Backreaction

Matter comes in different forms, we learn at school: solid, liquid, and as gas. December days in Canada give us plenty of occasions to experience these different forms of matter - phases, as they are called in physics and chemistry - in the case of water: ice and snow, the both annoying and beautiful appearances of solid water, the liquid form in rain and fog, and if the Sun succeeds to disperse the fog, tiny water droplets have evaporated, and the water has been transformed into invisible gas.

Ice melts at a temperature of 0°C (or 273.15 Kelvin), and water boils at 100°C (or 373.15 Kelvin). However, to be precise, these melting and boiling temperatures are not fixed - they depend on the ambient pressure. On top of a mountain, say the Puy de Dôme, air pressure is lower than in the lowlands, and as consequence, water boils at temperatures below 100°C.

To get a better overview how the occurrence of the different phases of water - solid ice, liquid water, gaseous vapour - depends on temperature and pressure, it's a good idea to plot in a diagram the transition lines between the different phases as a function of these two parameters. Such a diagram is called a phase diagram. And a simplified version of the phase diagram of water looks like this:

[Image]

The x-axis of the diagram shows the temperature T in units of Kelvin (K). Keep in mind that 0°C = 273.15 K and 100°C = 373.15 K - both temperatures are marked by the grey vertical lines. The y-axis shows the pressure p in units of Megapascal (MPa), where 0.1 MPa = 1000 hPa = 1000 mbar and the standard atmospheric pressure is 1013 mbar. Since pressure covers a huge range of values from the very small to the very large, a convenient way to represent this is the usage of a logarithmic scale. Thus, the phase diagram manages to represent pressure from 1/100.000 of ambient pressure to 1 million times ambient pressure. Ambient pressure is marked by the horizontal grey line.

The blue line in the diagram is the melting line - it separates ice from liquid water - and the light-blue line the boiling line, which divides liquid and gaseous water. The green line is the so-called sublimation line, across which ice transforms directly to the gaseous states, without the intermediate step of liquid water. All three lines meet at one point (marked by the black dot) which is called the triple point - at this value of temperature and pressure, all three forms of water can coexist. At sufficiently high pressure, water solidifies even at temperatures well above room temperature: these transitions to different sorts of ice (distinct by the respective crystal structures) are shown as the red and orange line. Trying to understand these different phases of ice is a topic still under investigation, both by experiment and by theory.

One feature of the diagram might seem strange at first sight: The boiling line separating liquid and gaseous water ends at one point. This is a very generic feature of all liquid matter: At high enough pressure, the distinction between liquid and gas gets lost - essentially, the difference in density between gas and liquid becomes zero, and the latent heat of condensation/evaporation vanishes. The end point of the boiling line, marked by the grey dot, is called the critical point. If temperature and pressure can be chosen such that the fluid is very close to the critical point, it will develop bubbles of gas containing small droplets of liquid containing small bubbles of gas... and as a result of bubbles and droplets of many different sizes, covering the range of wavelengths of visible light, the system becomes opaque. This quite spectacular effect is called critical opalescence.

But of course, we can also recover our mundane everyday experience with water in the diagram: If we increase temperature at constant ambient pressure, following the horizontal grey line, we cross the blue melting line at 0°C, and the light-blue boiling line at 100°C - that's the melting of ice and the boiling of water as we know it. And we see that if ambient pressure is reduced, for example during stormy weather or on top of a mountain, the crossing of the horizontal line and the boiling line shifts to lower temperature: Water will boil at temperatures below 100°C. At a height of 2000 m above sea level, for example, water boils at about 94°C - things to keep in mind if boiling an egg on a mountain.

If you look closely, you can note that the blue melting line is slightly inclined, meaning that with increasing pressure, the melting temperature drops slightly. This effect is often invoked as an explanation for the low friction of skates on ice: The pressure applied by the weight of the skater reduces the melting temperature of ice, causing a thin film of liquid water, on which the blade of the skate glides nearly without friction, or so goes the story. This, however, is not the whole truth: the small, pressure-induced reduction of the melting temperature is not sufficient to produce this effect. While it's correct that the reduction of friction is caused by a slippery film of water on the surface of the ice, this film is created by complicated mechanisms whose details are still under debate.

So, an elementary plot such as the phase diagram of water can still hide some surprises and riddles for us.


Phase diagram data via www.chemicalogic.com. Source for the sublimation and melting lines: W. Wagner, A. Saul, A. Pru&szlig: International Equations for the Pressure along the Melting and along the Sublimation Curve for Ordinary Water Substance, J. Phys. Chem. Ref. Data 23, No 3 (1994) 515 (PDF file from NIST). Source for the saturation line: IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam (IAPWS-IF97).

You can find much more about the phase diagram of water - and about the properties of water in general - at Water Structure and Science by Martin Chaplin.

The physics behind the slickness of ice has been discussed by Robert Rosenberg in Why Is Ice Slippery?, Physics Today, December 2005, pages 50-55 (doi 10.1063/1.2169444, subscription required).



This post is part of our 2007 advent calendar A Plottl A Day.