# The Triple Point

One of the most familiar things in science is that water freezes at 32o Fahrenheit and boils at 212oF. Indeed, the Celsius (or Centigrade) scale of temperature is based on this phenomenon, with freezing at 0oCelsius and boiling at 100oC. Celsius was the temperature scale used in the original metric system of measurement; but now the Système International d'Unités (SI) actually uses degrees Kelvin, or just Kelvins, although the intervals in the Kelvin scale are the same as the Celsius, so that Celsius temperatures can be converted to Kelvin just by adding 273.15. So water freezes at 273.15 K and boils at 373.15 K. The Kelvin scale begins at Absolute Zero, where there is no molecular motion (although there is still random quantum motion).

The idea that there is something natural or mathematically helpful about the "centigrade" Celsius scale, however, was silly; and the fact that a Celsius degree is almost twice (9/5) as large as a Fahrenheit degree means that Celsius thermometers give one a scale that is less fine for the identification of temperatures in ordinary life than the Fahrenheit scale. Thus, 100oF is a temperature that one unfortunately will see with some regularity in hot climates; but 100oC is a temperature one would only see in the laboratory, the kitchen, industry, geological hot springs, or volcanoes. Also, the Fahrenheit scale has positive degrees well below the freezing point of water, which means that most winter temperatures in the temperate zones will not involve negative numbers. Both scales curiously coincide at exactly -40o, which can simplify the mathematics of conversion.

However, a more germane issue than the scale as such is something familiar to people living at higher elevations than Sea Level:  Water boils at a lower temperature. Because of this, it makes a difference in how long one must cook certain things. So this physical difference in the boiling point isn't just a phenomenon of science; it is a reality of the kitchen, known to millions of people. If you are going to cook in Denver or Albuquerque, where water boils at 203oF (95oC) -- about 1oF lower for each 500 feet of altitude -- you better be aware of it.

Well, for all substances, when they freeze and when they boil is a function not of one but of two variables:  temperature and also pressure. Boiling water in Denver is just a small clue about this. As it happens, if the pressure is low enough, a substance may not exist in a liquid state at all. With water, if the pressure is less than 611.657 Pascals, water does not exist in liquid form. The Pascal (Pa) is the SI unit of pressure, defined as Newtons/meter2 (N/m2). On the table, we also see alternative units of pressure, the "atmosphere" and the "bar," which are based on the average atmospheric pressure at Sea Level. One atmosphere of pressure is 101 kiloPascals (kPa). So liquid water does not exist below 1/165 of an atmosphere. There is not a place on the Earth where the pressure is this low. You must go up to the edge of Space.

From the table, we see that there is a key point in the relation between solid, liquid, and gaseous states. This is where the curves all come together, at the "Triple Point" -- 273.16 K and 611.657 Pa. Physically, solid, liquid, and gas exist equally at that temperature and pressure. The temperature actually only differs by a hair from the freezing temperature at atmospheric pressure. But below that, the freezing point drops; and we see a domain where water as a gas abuts directly on water as ice. At those pressures, as ice heats up, it goes directly from the solid to the gaseous state. This phenomenon has the interesting name of sublimation, and ice that turns directly into water vapor is said to sublime. The thought seems to be that this is a loftier and more noble event than ice merely becoming water. Hence, it is sublime.

The phenomenon of sublimation is familar with "dry ice," which is solid carbon dioxide (CO2). Carbon dioxide will occur as a liquid only at pressures above 5.1 atmospheres (518 kPa). The Triple Point for carbon dioxide is 5.1 atm at a temperature of -56.6oC (-69.8oF). At one atmosphere pressure, carbon dioxide freezes, or sublimes, at -78.5oC (-109.2oF). So dry ice is pretty cold, which is what it is useful for. Indeed, because the temperature is not as extreme as other frozen gasses, it is for most ordinary purposes more convenient. Thus, Nitrogen freezes at -210oC (-346oF), Oxygen at -218.8oC (-361.8oF), and Helium at -272.2oC (-458oF). Remember that Absolute Zero is -273.15oC. These liquids can be fun in the lab, and there are some practical uses for them, but they are rather more difficult, dangerous, and expensive to deal with than carbon dioxide. So the -78.5oC of dry ice may be quite enough for your purposes. Or fun.

Water also turns to a gas by evaporation, at temperatues far below boiling. Molecules on the surface are simply lost into the air. Similarly, snow also sublimes and turns directly into a gas, at temperatures that can remain below freezing. Evaporation is a familiar phenomenon and becomes a matter of concern at farms and reservoirs. It is still surprising to me, however, to see snow disappear even when the thermometer says it should remain in place. What is more familiar is when a great deal of snow does remain even after the thermometer has gone well above freezing.

Off the chart for water but on the chart for carbon dioxide is the "Critical Point." This is where the pressure and temperature are so high that the distinction between liquid and gas seems to be lost. For carbon dioxide, the critical point temperature is only 31.1oC, which is not much above room temperature (88.0oF), but the pressure is 7.38 MPa, which is something like 73 atmospheres. So these are not conditions we'll find on the surface of the Earth.

At different temperatures and pressures, ice crystals assume different forms. Mostly, these are at pressures that are off the diagram above. What are visible are two forms of Ice I, Ice III, and Ice XI. Below is the continuation of the table at higher pressures.

There is a novel by Kurt Vonnegut, Cat's Cradle [1963], where we find "ice-nine," which in the story had a property of converting all other forms of ice, and water also, to its structure. So, when introduced out of the lab, it froze all the water on Earth, rendering life impossible. This was before Vonnegut discovered that there were medications for his depression.

There is an actual Ice IX (q.v.), but it is one of the high pressure crystaline structures (of tetragonal geometry) and does not exist outside temperatures above 140 K (-133oC) and pressures between 200 and 400 MPa. It does not turn all ice and water into Ice IX.

When we are so familiar with a linear scale of one variable, the Triple Point, which involves two variables and two dimensions, throws a very different light on matters -- much like the use of both personal and economic freedom in the "diamond quiz" for political viewpoints. Where the precise conditions that allow for liquid water may become a great practical concern is in space. Water could be stored at low pressure, but not at such low pressure that it will not exist as a liquid. Similarly, living things, which largely consist of water, cannot exist where liquid water cannot. We may not need to worry about this right now, but in the future it may be of daily concern.

Units of Measurement