Triple point

For other uses, see Tripoint (disambiguation) and tripoint.

In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium. For example, the triple point of mercury occurs at a temperature of −38.8344 °C and a pressure of 0.2 mPa.

In addition to the triple point between solid, liquid, and gas, there can be triple points involving more than one solid phase, for substances with multiple polymorphs. Helium-4 is a special case that presents a triple point involving two different fluid phases (see lambda point). In general, for a system with p possible phases, there are ${p\choose 3} = \tfrac16p(p-1)(p-2)$ triple points.

The triple point of water is used to define the kelvin, the SI base unit of thermodynamic temperature. The number given for the temperature of the triple point of water is an exact definition rather than a measured quantity. The triple points of several substances are used to define points in the ITS-90 international temperature scale, ranging from the triple point of hydrogen (13.8033 K) to the triple point of water (273.16 K).

Triple points of water

Gas–liquid–solid triple point

Main article: Water (molecule)#Triple point

A typical phase diagram. The solid green line applies to most substances; the dotted green line gives the anomalous behaviour of water

The single combination of pressure and temperature at which liquid water, solid ice, and water vapour can coexist in a stable equilibrium occurs at exactly 273.16 K (0.01 °C) and a partial vapour pressure of 611.73 pascals (ca. 6.1173 millibars, 0.0060373 atm). At that point, it is possible to change all of the substance to ice, water, or vapor by making arbitrarily small changes in pressure and temperature. Even if the total pressure of a system is well above triple point of water, provided the partial pressure of the water vapour is 611.73 pascals then the system can still be brought to the triple point of water. Strictly speaking, the surfaces separating the different phases should also be perfectly flat, to negate the effects of surface tensions.

The gas–liquid–solid triple point of water corresponds to the minimum pressure at which liquid water can exist. At pressures below the triple point (as in outer space), solid ice when heated at constant pressure is converted directly into water vapour in a process known as sublimation. Above the triple point, solid ice when heated at constant pressure first melts to form liquid water, and then evaporates or boils to form vapor at a higher temperature.

For most substances the gas–liquid–solid triple point is also the minimum temperature at which the liquid can exist. For water, however, this is not true because the melting point of ordinary ice decreases as a function of pressure, as shown by the dotted green line in the phase diagram. At temperatures just below the triple point, compression at constant temperature transforms water vapor first to solid and then to liquid.

The triple point pressure of water was used during the Mariner 9 mission to Mars as a reference point to define "sea level". More recent missions use laser altimetry and gravity measurements instead of pressure to define elevation on Mars.

Other triple points of water at high pressure

At high pressures water has a complex phase diagram with 15 known phases of ice and a number of triple points including ten whose coordinates are shown in the diagram. For example, the triple point at 251 K (−22 °C) and 210 MPa (2070 atm) corresponds to the conditions for the coexistence of ice Ih (ordinary ice), ice III and liquid water, all at equilibrium. There are also triple points for the coexistence of three solid phases, for example ice II, ice V and ice VI at 218 K (−55 °C) and 620 MPa (6120 atm).

For those high-pressure forms of ice which can exist in equilibrium with liquid, the diagram shows that melting points increase with ice. At temperatures above 273 K (0 °C), increasing the pressure on water vapor results first in liquid water and then a high-pressure form of ice. In the range 251–273 K, ice I is formed first, followed by liquid water and then ice III or ice V, followed by other still denser high-pressure forms.

Phase diagram of water including high-pressure forms ice II, ice III, etc. The pressure axis is logarithmic. For detailed descriptions of these phases, see Ice#Phases.

Triple point cells

Triple point cells are used in the calibration of thermometers. For exacting work, triple point cells are typically filled with a highly pure chemical substance such as hydrogen, argon, mercury, or water (depending on the desired temperature). The purity of these substances can be such that only one part in a million is a contaminant; what is called "six-nines" because it is 99.9999% pure. When it is a water-based cell, a special isotopic composition called VSMOW is used because it is very pure and produces temperatures that are more comparable from lab to lab. Triple point cells are so effective at achieving highly precise, reproducible temperatures, an international calibration standard for thermometers called ITS–90 relies upon triple point cells of hydrogen, neon, oxygen, argon, mercury, and water for delineating six of its defined temperature points.

Table of triple points

This table lists the gas–liquid–solid triple points of common substances. Unless otherwise noted, the data comes from the U.S. National Bureau of Standards (now NIST, National Institute of Standards and Technology).

Substance	T [K]	p [kPa]*
Acetylene	192.4	7002120000000000000 120
Ammonia	195.40	7000607590000000000 6.076
Argon	83.81	7001689000000000000 68.9
Arsenic	1090	7003362800000000000 3628
Butane	134.6	6996700000000000000 7 × 10−4
Carbon (graphite)	4765	7004101320000000000 10132
Carbon dioxide	216.55	7002517000000000000 517
Carbon monoxide	68.10	7001153700000000000 15.37
Chloroform	175.43	6999870000000000000 0.870
Deuterium	18.63	7001171000000000000 17.1
Ethane	89.89	6996800000000000000 8 × 10−4
Ethanol	150	6993429990000099999 4.3 × 10−7
Ethylene	104.0	6999120000000000000 0.12
Formic acid	281.40	7000220000000000000 2.2
Helium-4 (lambda point)	2.19	7000510000000099999 5.1
Hexafluoroethane	173.08	7001266000000000000 26.60
Hydrogen	13.84	7000704000000000000 7.04
Hydrogen chloride	158.96	7001139000000000000 13.9
Iodine	386.65	7001120700000000000 12.07
Isobutane	113.55	6995194810000000000 1.9481 × 10−5
Mercury	234.2	6993165009999999999 1.65 × 10−7
Methane	90.68	7001117000000000000 11.7
Neon	24.57	7001432000000000000 43.2
Nitric oxide	109.50	7001219200000000000 21.92
Nitrogen	63.18	7001126000000000000 12.6
Nitrous oxide	182.34	7001878500000000000 87.85
Oxygen	54.36	6999152000000000000 0.152
Palladium	1825	6997350000000000000 3.5 × 10−3
Platinum	2045	6996200000000000000 2.0 × 10−4
Sulfur dioxide	197.69	7000167000000000000 1.67
Titanium	1941	6997530000000000000 5.3 × 10−3
Uranium hexafluoride	337.17	7002151690000000000 151.7
Water	273.16	6999611700000000000 0.6117
Xenon	161.3	7001815000000000000 81.5
Zinc	692.65	6998650000000000000 0.065

* Note: for comparison, typical atmospheric pressure is 101.325 kPa (1 atm).

See also

• Critical point
• Gibbs' phase rule