# 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 ${p\choose 3} = \tfrac16p(p-1)(p-2)$ 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, or 0.01 °C).

## Triple points of water

### Gas–liquid–solid 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 vapour 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 (water ice has lower density than liquid water, so increasing pressure leads to a liquefaction).

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 pressure. 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).[4]

Substance T [K] (°C) p [kPa]*
Acetylene 192.4 K (−80.7 °C) 120 kPa (1.2 atm)
Ammonia 195.40 K (−77.75 °C) 6.076 kPa (0.05997 atm)
Argon 83.81 K (−189.34 °C) 68.9 kPa (0.680 atm)
Arsenic 1,090 K (820 °C) 3,628 kPa (35.81 atm)
Butane[5] 134.6 K (−138.6 °C) 7× 10−4 kPa
Carbon (graphite) 4,765 K (4,492 °C) 10,132 kPa (100.00 atm)
Carbon dioxide 216.55 K (−56.60 °C) 517 kPa (5.10 atm)
Carbon monoxide 68.10 K (−205.05 °C) 15.37 kPa (0.1517 atm)
Chloroform[6] 175.43 K (−97.72 °C) 0.870 kPa (0.00859 atm)
Deuterium 18.63 K (−254.52 °C) 17.1 kPa (0.169 atm)
Ethane 89.89 K (−183.26 °C) 8 × 10−4 kPa
Ethanol[7] 150 K (−123 °C) 4.3 × 10−7 kPa
Ethylene 104.0 K (−169.2 °C) 0.12 kPa (0.0012 atm)
Formic acid[8] 281.40 K (8.25 °C) 2.2 kPa (0.022 atm)
Helium-4 (lambda point) 2.19 K (−270.96 °C) 5.1 kPa (0.050 atm)
Hexafluoroethane[9] 173.08 K (−100.07 °C) 26.60 kPa (0.2625 atm)
Hydrogen 13.84 K (−259.31 °C) 7.04 kPa (0.0695 atm)
Hydrogen chloride 158.96 K (−114.19 °C) 13.9 kPa (0.137 atm)
Iodine[10] 386.65 K (113.50 °C) 12.07 kPa (0.1191 atm)
Isobutane[11] 113.55 K (−159.60 °C) 1.9481 × 10−5 kPa
Mercury 234.2 K (−39.0 °C) 1.65 × 10−7 kPa
Methane 90.68 K (−182.47 °C) 11.7 kPa (0.115 atm)
Neon 24.57 K (−248.58 °C) 43.2 kPa (0.426 atm)
Nitric oxide 109.50 K (−163.65 °C) 21.92 kPa (0.2163 atm)
Nitrogen 63.18 K (−209.97 °C) 12.6 kPa (0.124 atm)
Nitrous oxide 182.34 K (−90.81 °C) 87.85 kPa (0.8670 atm)
Oxygen 54.36 K (−218.79 °C) 0.152 kPa (0.00150 atm)
Palladium 1,825 K (1,552 °C) 3.5 × 10−3 kPa
Platinum 2,045 K (1,772 °C) 2.0 × 10−4 kPa
Sulfur dioxide 197.69 K (−75.46 °C) 1.67 kPa (0.0165 atm)
Titanium 1,941 K (1,668 °C) 5.3 × 10−3 kPa
Uranium hexafluoride 337.17 K (64.02 °C) 151.7 kPa (1.497 atm)
Water 273.16 K (0.01 °C) 0.6117 kPa (0.006037 atm)
Xenon 161.3 K (−111.8 °C) 81.5 kPa (0.804 atm)
Zinc 692.65 K (419.50 °C) 0.065 kPa (0.00064 atm)

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

## References

1. ^ a b IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (1994) "Triple point".
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. ^
6. ^
7. ^
8. ^
9. ^
10. ^ Walas, S. M. (1990). Chemical Process Equipment – Selection and Design. Amsterdam: Elsevier. p. 639. ISBN 0-7506-7510-1.
11. ^