Triple point

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.^[1] 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 ${p \choose 3}={\tfrac {1}{6}}p(p-1)(p-2)$ triple points.^[1]

The triple point of water is used to define the kelvin, the SI base unit of thermodynamic temperature.^[2] 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

A typical phase diagram. 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 small arbitrary 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 abnegate 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.^[3]

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.

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).^[4]

Substance	T [K]	P [kPa]*
Acetylene	192.4	120
Ammonia	195.40	6.076
Argon	83.81	68.9
Butane^[5]	134.6	7 × 10⁻⁴
Carbon (graphite)	4765	10132
Carbon dioxide	216.55	517
Carbon monoxide	68.10	15.37
Chloroform^[6]	175.43	0.870
Deuterium	18.63	17.1
Ethane	89.89	8 × 10⁻⁴
Ethanol^[7]	150	4.3 × 10⁻⁷
Ethylene	104.0	0.12
Formic acid^[8]	281.40	2.2
Helium-4 (lambda point)	2.19	5.1
Hexafluoroethane^[9]	173.08	26.60
Hydrogen	13.84	7.04
Hydrogen chloride	158.96	13.9
Iodine^[10]	386.65	12.07
Isobutane^[11]	113.55	1.9481 × 10⁻⁵
Mercury	234.2	1.65 × 10⁻⁷
Methane	90.68	11.7
Neon	24.57	43.2
Nitric oxide	109.50	21.92
Nitrogen	63.18	12.6
Nitrous oxide	182.34	87.85
Oxygen	54.36	0.152
Palladium	1825	3.5 × 10⁻³
Platinum	2045	2.0 × 10⁻⁴
Sulfur dioxide	197.69	1.67
Titanium	1941	5.3 × 10⁻³
Uranium hexafluoride	337.17	151.7
Water	273.16	0.6117
Xenon	161.3	81.5
Zinc	692.65	0.065

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

References

^ ^a ^b IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (1994) "Triple point". doi:10.1351/goldbook.T06502
^ Definition of the kelvin at BIPM
^ Carr, Michael H. (2007). The Surface of Mars. Cambridge University Press. p. 5. ISBN 0-521-87201-4.
^ Cengel, Yunus A.; Turner, Robert H. (2004). Fundamentals of thermal-fluid sciences. Boston: McGraw-Hill. p. 78. ISBN 0-07-297675-6.
^ See Butane (data page)
^ See Chloroform (data page)
^ See Ethanol (data page)
^ See Formic acid (data page)
^ See Hexafluoroethane (data page)
^ Walas, S. M. (1990). Chemical Process Equipment – Selection and Design. Amsterdam: Elsevier. p. 639. ISBN 0-7506-7510-1.
^ See Isobutane (data page)

[gold-1] IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (1994) "Triple point". doi:10.1351/goldbook.T06502

[2] Definition of the kelvin at BIPM

[3] Carr, Michael H. (2007). The Surface of Mars. Cambridge University Press. p. 5. ISBN 0-521-87201-4.

[4] Cengel, Yunus A.; Turner, Robert H. (2004). Fundamentals of thermal-fluid sciences. Boston: McGraw-Hill. p. 78. ISBN 0-07-297675-6.

[5] See Butane (data page)

[6] See Chloroform (data page)

[7] See Ethanol (data page)

[8] See Formic acid (data page)

[9] See Hexafluoroethane (data page)

[10] Walas, S. M. (1990). Chemical Process Equipment – Selection and Design. Amsterdam: Elsevier. p. 639. ISBN 0-7506-7510-1.

[11] See Isobutane (data page)

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v t e States of matter (list)
State	Solid Liquid Gas / Vapor Supercritical fluid Plasma
Low energy	Bose–Einstein condensate Fermionic condensate Degenerate matter Quantum Hall Rydberg matter Strange matter Superfluid Supersolid Photonic molecule
High energy	QCD matter Quark–gluon plasma Color-glass condensate
Other states	Colloid Crystal Liquid crystal Time crystal Quantum spin liquid Exotic matter Programmable matter Dark matter Antimatter Magnetically ordered Antiferromagnet Ferrimagnet Ferromagnet String-net liquid Superglass
Phase transitions	Boiling Boiling point Condensation Critical line Critical point Crystallization Deposition Evaporation Flash evaporation Freezing Chemical ionization Ionization Lambda point Melting Melting point Recombination Regelation Saturated fluid Sublimation Supercooling Triple point Vaporization Vitrification
Quantities	Enthalpy of fusion Enthalpy of sublimation Enthalpy of vaporization Latent heat Latent internal energy Trouton's rule Volatility
Concepts	Baryonic matter Binodal Compressed fluid Cooling curve Equation of state Leidenfrost effect Macroscopic quantum phenomena Mpemba effect Order and disorder (physics) Spinodal Superconductivity Superheated vapor Superheating Thermo-dielectric effect