# 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] It is that temperature and pressure at which the sublimation curve, fusion curve and the vaporisation curve meet. For example, the triple point of mercury occurs at a temperature of −38.83440 °C and a pressure of 0.2 mPa.

In addition to the triple point for solid, liquid, and gas phases, a triple point may involve 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 (lambda point).[1]

The triple point of water was used to define the kelvin, the base unit of thermodynamic temperature in the International System of Units (SI).[2] The value of the triple point of water was fixed by definition, rather than measured, but that changed with the 2019 redefinition of SI base units. 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, 0.01 °C, or 32.018 °F).

The term "triple point" was coined in 1873 by James Thomson, brother of Lord Kelvin.[3]

## Triple point of water

### Gas–liquid–solid triple point

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

The single combination of pressure and temperature at which liquid water, solid ice, and water vapor can coexist in a stable equilibrium occurs at exactly 273.1600 K (0.0100 °C; 32.0180 °F) and a partial vapor pressure of 611.657 pascals (6.11657 mbar; 0.00603659 atm).[4][5] 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 the triple point of water, provided that the partial pressure of the water vapor is 611.657 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 tension.

The gas–liquid–solid triple point of water corresponds to the minimal 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 vapor 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 minimal 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 dashed 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.[6]

### High-pressure phases

At high pressures, water has a complex phase diagram with 15 known phases of ice and several triple points, including 10 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.
The various triple points of water
Phases in stable equilibrium Pressure Temperature
liquid water, ice Ih, and water vapor 611.657 Pa[7] 273.16 K (0.01 °C)
liquid water, ice Ih, and ice III 209.9 MPa 251 K (−22 °C)
liquid water, ice III, and ice V 350.1 MPa −17.0 °C
liquid water, ice V, and ice VI 632.4 MPa 0.16 °C
ice Ih, Ice II, and ice III 213 MPa −35 °C
ice II, ice III, and ice V 344 MPa −24 °C
ice II, ice V, and ice VI 626 MPa −70 °C

## 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, 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, that 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 several substances. Unless otherwise noted, the data come from the U.S. National Bureau of Standards (now NIST, National Institute of Standards and Technology).[8]

Substance T [K] (°C) p [kPa]* (atm)
Acetylene 192.4 K (−80.7 °C) 120 kPa (1.2 atm)
Ammonia 195.40 K (−77.75 °C) 6.060 kPa (0.05981 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[9] 134.6 K (−138.6 °C) 7×10−4 kPa (6.9×10−6 atm)
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[10] 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 (7.9×10−6 atm)
Ethanol[11] 150 K (−123 °C) 4.3×10−7 kPa (4.2×10−9 atm)
Ethylene 104.0 K (−169.2 °C) 0.12 kPa (0.0012 atm)
Formic acid[12] 281.40 K (8.25 °C) 2.2 kPa (0.022 atm)
Helium-4 (lambda point)[13] 2.1768 K (−270.9732 °C) 5.048 kPa (0.04982 atm)
Helium-4 (hcpbcc−He-II)[14] 1.463 K (−271.687 °C) 26.036 kPa (0.25696 atm)
Helium-4 (bcc−He-I−He-II)[14] 1.762 K (−271.388 °C) 29.725 kPa (0.29336 atm)
Helium-4 (hcp−bcc−He-I)[14] 1.772 K (−271.378 °C) 30.016 kPa (0.29623 atm)
Hexafluoroethane[15] 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[16] 386.65 K (113.50 °C) 12.07 kPa (0.1191 atm)
Isobutane[17] 113.55 K (−159.60 °C) 1.9481×10−5 kPa (1.9226×10−7 atm)
Krypton 115.76 K (−157.39 °C) 74.12 kPa (0.7315 atm)
Mercury 234.2 K (−39.0 °C) 1.65×10−7 kPa (1.63×10−9 atm)
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 (3.5×10−5 atm)
Platinum 2,045 K (1,772 °C) 2×10−4 kPa (2.0×10−6 atm)
Radon 202 K (−71 °C) 70 kPa (0.69 atm)
(mono)Silane[18] 88.48 K (−184.67 °C) 0.019644 kPa (0.00019387 atm)
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 (5.2×10−5 atm)
Uranium hexafluoride 337.17 K (64.02 °C) 151.7 kPa (1.497 atm)
Water[4][5] 273.16 K (0.01 °C) 0.611657 kPa (0.00603659 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". doi:10.1351/goldbook.T06502.
2. ^ Definition of the kelvin at BIPM.
3. ^ James Thomson (1873) "A quantitative investigation of certain relations between the gaseous, the liquid, and the solid states of water-substance", Proceedings of the Royal Society, 22 : 27–36. From a footnote on page 28: " … the three curves would meet or cross each other in one point, which I have called the triple point".
4. ^ a b International Equations for the Pressure along the Melting and along the Sublimation Curve of Ordinary Water Substance. W. Wagner, A. Saul and A. Pruss (1994), J. Phys. Chem. Ref. Data, 23, 515.
5. ^ a b Murphy, D. M. (2005). "Review of the vapour pressures of ice and supercooled water for atmospheric applications". Quarterly Journal of the Royal Meteorological Society. 131 (608): 1539–1565. Bibcode:2005QJRMS.131.1539M. doi:10.1256/qj.04.94.
6. ^ Carr, Michael H. (2007). The Surface of Mars. Cambridge University Press. p. 5. ISBN 0-521-87201-4.
7. ^ Murphy, D. M. (2005). "Review of the vapour pressures of ice and supercooled water for atmospheric applications". Quarterly Journal of the Royal Meteorological Society. 131: 1539–1565. Bibcode:2005QJRMS.131.1539M. doi:10.1256/qj.04.94.
8. ^ Cengel, Yunus A.; Turner, Robert H. (2004). Fundamentals of thermal-fluid sciences. Boston: McGraw-Hill. p. 78. ISBN 0-07-297675-6.
9. ^
10. ^
11. ^
12. ^
13. ^ Donnelly, Russell J.; Barenghi, Carlo F. (1998). "The Observed Properties of Liquid Helium at the Saturated Vapor Pressure". Journal of Physical and Chemical Reference Data. 27 (6): 1217–1274. Bibcode:1998JPCRD..27.1217D. doi:10.1063/1.556028.
14. ^ a b c Hoffer, J. K.; Gardner, W. R.; Waterfield, C. G.; Phillips, N. E. (April 1976). "Thermodynamic properties of 4He. II. The bcc phase and the P-T and VT phase diagrams below 2 K". Journal of Low Temperature Physics. 23 (1): 63–102. Bibcode:1976JLTP...23...63H. doi:10.1007/BF00117245.
15. ^
16. ^ Walas, S. M. (1990). Chemical Process Equipment – Selection and Design. Amsterdam: Elsevier. p. 639. ISBN 0-7506-7510-1.
17. ^
18. ^ "Silane-Gas Encyclopedia". Gas Encyclopedia. Air Liquide. Retrieved 22 May 2019.
Aluminosilicate

Aluminosilicate minerals are minerals composed of aluminium, silicon, and oxygen, plus countercations. They are a major component of kaolin and other clay minerals.

Andalusite, kyanite, and sillimanite are naturally occurring aluminosilicate minerals that have the composition Al2SiO5. The triple point of the three polymorphs is located at a temperature of 500 °C and a pressure of 0.4 GPa. These three minerals are commonly used as index minerals in metamorphic rocks.

Hydrated aluminosilicate minerals are referred to as zeolites and are porous structures that are naturally occurring materials.

The catalyst silica-alumina is an amorphous substance which is not an aluminosilicate compound.

Argon

Argon is a chemical element with the symbol Ar and atomic number 18. It is in group 18 of the periodic table and is a noble gas. Argon is the third-most abundant gas in the Earth's atmosphere, at 0.934% (9340 ppmv). It is more than twice as abundant as water vapor (which averages about 4000 ppmv, but varies greatly), 23 times as abundant as carbon dioxide (400 ppmv), and more than 500 times as abundant as neon (18 ppmv). Argon is the most abundant noble gas in Earth's crust, comprising 0.00015% of the crust.

Nearly all of the argon in the Earth's atmosphere is radiogenic argon-40, derived from the decay of potassium-40 in the Earth's crust. In the universe, argon-36 is by far the most common argon isotope, as it is the most easily produced by stellar nucleosynthesis in supernovas.

The name "argon" is derived from the Greek word ἀργόν, neuter singular form of ἀργός meaning "lazy" or "inactive", as a reference to the fact that the element undergoes almost no chemical reactions. The complete octet (eight electrons) in the outer atomic shell makes argon stable and resistant to bonding with other elements. Its triple point temperature of 83.8058 K is a defining fixed point in the International Temperature Scale of 1990.

Argon is produced industrially by the fractional distillation of liquid air. Argon is mostly used as an inert shielding gas in welding and other high-temperature industrial processes where ordinarily unreactive substances become reactive; for example, an argon atmosphere is used in graphite electric furnaces to prevent the graphite from burning. Argon is also used in incandescent, fluorescent lighting, and other gas-discharge tubes. Argon makes a distinctive blue-green gas laser. Argon is also used in fluorescent glow starters.

Boiling point

The boiling point of a substance is the temperature at which the vapor pressure of a liquid equals the pressure surrounding the liquid and the liquid changes into a vapor.

The boiling point of a liquid varies depending upon the surrounding environmental pressure. A liquid in a partial vacuum has a lower boiling point than when that liquid is at atmospheric pressure. A liquid at high pressure has a higher boiling point than when that liquid is at atmospheric pressure. For example, water boils at 100 °C (212 °F) at sea level, but at 93.4 °C (200.1 °F) at 1,905 metres (6,250 ft) altitude. For a given pressure, different liquids will boil at different temperatures.

The normal boiling point (also called the atmospheric boiling point or the atmospheric pressure boiling point) of a liquid is the special case in which the vapor pressure of the liquid equals the defined atmospheric pressure at sea level, 1 atmosphere. At that temperature, the vapor pressure of the liquid becomes sufficient to overcome atmospheric pressure and allow bubbles of vapor to form inside the bulk of the liquid. The standard boiling point has been defined by IUPAC since 1982 as the temperature at which boiling occurs under a pressure of 1 bar.The heat of vaporization is the energy required to transform a given quantity (a mol, kg, pound, etc.) of a substance from a liquid into a gas at a given pressure (often atmospheric pressure).

Liquids may change to a vapor at temperatures below their boiling points through the process of evaporation. Evaporation is a surface phenomenon in which molecules located near the liquid's edge, not contained by enough liquid pressure on that side, escape into the surroundings as vapor. On the other hand, boiling is a process in which molecules anywhere in the liquid escape, resulting in the formation of vapor bubbles within the liquid.

Celsius

The Celsius scale, also known as the centigrade scale, is a temperature scale used by the International System of Units (SI). As an SI derived unit, it is used by all countries except the United States, the Bahamas, Belize, the Cayman Islands and Liberia. It is named after the Swedish astronomer Anders Celsius (1701–1744), who developed a similar temperature scale. The degree Celsius (symbol: °C) can refer to a specific temperature on the Celsius scale or a unit to indicate a difference between two temperatures or an uncertainty. Before being renamed to honor Anders Celsius in 1948, the unit was called centigrade, from the Latin centum, which means 100, and gradus, which means steps.

From 1743, the Celsius scale is based on 0 °C for the freezing point of water and 100 °C for the boiling point of water at 1 atm pressure. Prior to 1743, the scale was also based on the boiling and melting points of water, but the values were reversed (i.e. the boiling point was at 0 degrees and the melting point was at 100 degrees). The 1743 scale reversal was proposed by Jean-Pierre Christin.

By international agreement, since 1954 the unit degree Celsius and the Celsius scale are defined by absolute zero and the triple point of Vienna Standard Mean Ocean Water (VSMOW), a specially purified water. This definition also precisely relates the Celsius scale to the Kelvin scale, which defines the SI base unit of thermodynamic temperature with symbol K. Absolute zero, the lowest temperature possible, is defined as being exactly 0 K and −273.15 °C. The temperature of the triple point of water is defined as exactly 273.16 K (0.01 °C). This means that a temperature difference of one degree Celsius and that of one kelvin are exactly the same.On 20 May 2019, the kelvin, along with degree Celsius, was redefined so that its value is now determined by definition of the Boltzmann constant.

Chile Rise

The Chile Rise or Chile Ridge is an oceanic ridge, a tectonic divergent plate boundary between the Nazca and Antarctic plates. Its eastern end is the Chile Triple Junction where the Chile Rise is being subducted below the South American Plate in the Peru–Chile Trench. It runs westward to a triple point south of the Juan Fernández Microplate where it intersects the East Pacific Rise.

The Chile Rise subducts near Taitao Peninsula where Taitao ophiolite and other geolical features are associated to the interactions at the triple junction.

Condensation

Condensation is the change of the physical state of matter from the gas phase into the liquid phase, and is the reverse of vaporisation. The word most often refers to the water cycle. It can also be defined as the change in the state of water vapour to liquid water when in contact with a liquid or solid surface or cloud condensation nuclei within the atmosphere. When the transition happens from the gaseous phase into the solid phase directly, the change is called deposition.

Eastern Continental Divide

The Eastern Continental Divide or Eastern Divide or Appalachian Divide is a hydrographic divide in eastern North America that separates the easterly Atlantic Seaboard watershed from the westerly Gulf of Mexico watershed. The divide nearly spans the United States from south of Lake Ontario through the Florida peninsula, and consists of raised terrain including the Appalachian Mountains to the north, the southern Piedmont Plateau and lowland ridges in the Atlantic Coastal Plain to the south. Water including rainfall and snowfall, lakes, streams and rivers on the eastern/southern side of the divide drains to the Atlantic Ocean; water on the western/northern side of the divide drains to the Gulf of Mexico. The ECD is one of six continental hydrographic divides of North America which define several drainage basins, each of which drains to a particular body of water.

The divide originates at the Eastern Triple Divide(see sidebar) near the middle of the northern border of Pennsylvania then runs generally south-by-southwest following the crest of the Appalachian Mountains through Pennsylvania, western Maryland, West Virginia, Virginia and North Carolina to its high point on Grandfather Mountain (Though Mount Mitchell is the highest point in the Appalachian Mountains, it is not on the ECD, but 4 miles west of the ECD), then descends to the city of Atlanta in northwestern Georgia, where it doglegs southeasterly across the Georgia plateau and through the lowlands of Northern Florida to its terminus in central Florida at the northern boundary of the Lake Okeechobee Basin(see sidebar).

Though the divide is often associated with high elevation, at its southern terminus at the northern Kissimmee River watershed in Florida, the elevation is only 70ft. above sea level. Nor does the divide always coincide with the highest point or ridgeline, because streams can flow through passes or gaps in the ridge, so that terrain on one side of the ridge drains to the other side and therefore to the other watershed. This occurs in several places. The ECD is not completely fixed, but can shift due to erosion, tectonic shift and also anthropogenic activity such as tunnel excavation, damming of rivers and road construction.

In colonial times, except for Spanish Florida, the ECD served as the boundary between English colonies on the Atlantic seaboard and Indian lands to the interior.

Garbolc

Garbolc is a settlement (village) in Szabolcs-Szatmár-Bereg county, Hungary. Garbolc is located near to the eastern geographical point (the Romanian-Ukrainian-Hungarian triple border point, see the photo; the triple point is 1 km eastward from the leg) of Hungary.

International Temperature Scale of 1990

The International Temperature Scale of 1990 (ITS-90) published by the Consultative Committee for Thermometry (CCT) of the International Committee for Weights and Measures (CIPM) is an equipment calibration standard for making measurements on the Kelvin and Celsius temperature scales.

ITS-90 is an approximation of the thermodynamic temperature scale that facilitates the comparability and compatibility of temperature measurements internationally.

It specifies fourteen calibration points ranging from 0.65±0 K to 1357.77±0 K (−272.50±0 °C to 1084.62±0 °C)

and is subdivided into multiple temperature ranges which overlap in some instances.

ITS-90 is the latest (as of 2014) of a series of International Temperature Scales adopted by CIPM since 1927.

Adopted at the 1989 General Conference on Weights and Measures, it supersedes the International Practical Temperature Scale of 1968 (amended edition of 1975) and the 1976 "Provisional 0.5 K to 30 K Temperature Scale". CCT has also adopted a mise en pratique (practical instructions) in 2011.

The lowest temperature covered by ITS-90 is 0.65 K. In 2000, the temperature scale was extended further, to 0.9 mK, by the adoption of a supplemental scale, known as the Provisional Low Temperature Scale of 2000 (PLTS-2000).

Kelvin

The Kelvin scale is an absolute thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics. The kelvin (symbol: K) is the base unit of temperature in the International System of Units (SI).

Until 2018, the kelvin was defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water (exactly 0.01 °C or 32.018 °F). In other words, it was defined such that the triple point of water is exactly 273.16 K.

On 16 November 2018, a new definition was adopted, in terms of a fixed value of the Boltzmann constant. For legal metrology purposes, the new definition officially came into force on 20 May 2019 (the 144th anniversary of the Metre Convention).The Kelvin scale is named after the Belfast-born, Glasgow University engineer and physicist William Thomson, 1st Baron Kelvin (1824–1907), who wrote of the need for an "absolute thermometric scale". Unlike the degree Fahrenheit and degree Celsius, the kelvin is not referred to or written as a degree. The kelvin is the primary unit of temperature measurement in the physical sciences, but is often used in conjunction with the degree Celsius, which has the same magnitude. The definition implies that absolute zero (0 K) is equivalent to −273.15 °C (−459.67 °F).

Lambda point

The Lambda point is the temperature at which normal fluid helium (helium I) makes the transition to superfluid helium II (approximately 2.17 K at 1 atmosphere). The lowest pressure at which He-I and He-II can coexist is the vapor−He-I−He-II triple point at 2.1768 K (−270.9732 °C) and 5.048 kPa (0.04982 atm), which is the "saturated vapor pressure" at that temperature (pure helium gas in thermal equilibrium over the liquid surface, in a hermetic container). The highest pressure at which He-I and He-II can coexist is the bcc−He-I−He-II triple point with a helium solid at 1.762 K (−271.388 °C), 29.725 atm (3,011.9 kPa).The point's name derives from the graph (pictured) that results from plotting the specific heat capacity as a function of temperature (for a given pressure in the above range, in the example shown, at 1 atmosphere), which resembles the Greek letter lambda. The specific heat capacity tends towards infinity as the temperature approaches the lambda point. The tip of the peak is so sharp that a critical exponent characterizing the divergence of the heat capacity can be measured precisely only in zero gravity, to provide a uniform density over a substantial volume of fluid. Hence the heat capacity was measured within 2 nK below the transition in an experiment included in a Space Shuttle payload in 1992.

Occluded front

In meteorology, an occluded front is a weather front formed during the process of cyclogenesis, when a cold front overtakes a warm front. When this occurs, the warm air is separated (occluded) from the cyclone center at the Earth's surface. The point where the warm front and the occluded front meet (and consequently the nearest location of warm air to the center of the cyclone) is called the triple point.The trowal (short for TROugh of Warm air ALoft) is the projection on the Earth's surface of the trough of warm air aloft formed during the occlusion process of the depression.

Quartz thermometer

The quartz thermometer is a high-precision, high accuracy temperature sensor. It measures temperature by measuring the frequency of a quartz crystal oscillator. The oscillator contains a specially cut crystal that results in a linear temperature coefficient of frequency, so the measurement of the temperature is essentially reduced to measurement of the oscillator frequency. Resolutions of .0001 °C, and accuracy of .02 °C from 0-100 °C are achievable. The high linearity makes it possible to achieve high accuracy over an important temperature range that contains only one convenient temperature reference point for calibration, the triple point of water.

Introduced by Hewlett-Packard in 1965, the successor company, Agilent, has discontinued the Model 2804A Quartz Thermometer.

Other manufacturers make nearly linear-in-temperature quartz crystals that may be used to construct thermometers of similar performance.

Rodrigues Triple Junction

The Rodrigues Triple Junction (RTJ), also known as the Central Indian [Ocean] Triple Junction (CITJ) is a geologic triple junction in the southern Indian Ocean where three tectonic plates meet: the African Plate, the Indo-Australian Plate, and the Antarctic Plate. The triple junction is named for the island of Rodrigues which lies 1,000 km (620 mi) north-west of it.

The RTJ was first recognized in 1971, then described as a stable R-R-R (ridge-ridge-ridge) triple junction based on coarse ship data.

Sierra Crest

The Sierra Crest is a ~500 mi (800 km) generally north-to-south ridgeline that demarcates the broad west and narrow east slopes of the Sierra Nevada (U.S.) and that extends as far east as the Sierra's topographic front (e.g., Diamond Mountains and Sierran escarpment). The northern and central Sierra Crest sections coincide with over 300 mi (480 km) of the Great Basin Divide, and the southern crest demarcates Tulare and Inyo counties and extends through Kern County to meet the Tehachapi crest. The Sierra Crest also forms two paths (bifurcates) around endorheic cirques (e.g., Cup Lake) between the west and east Sierra slopes.

Theodore Solomons made the first attempt to map a crest route along the Sierras. He was instrumental in envisioning, exploring, and establishing the route of what became the John Muir Trail from Yosemite Valley along the crest of the Sierra Nevada to Mount Whitney.

Sublimation (phase transition)

Sublimation is the transition of a substance directly from the solid to the gas phase, without passing through the intermediate liquid phase. Sublimation is an endothermic process that occurs at temperatures and pressures below a substance's triple point in its phase diagram, which corresponds to the lowest pressure at which the substance can exist as a liquid. The reverse process of sublimation is deposition or desublimation, in which a substance passes directly from a gas to a solid phase. Sublimation has also been used as a generic term to describe a solid-to-gas transition (sublimation) followed by a gas-to-solid transition (deposition). While a transition from liquid to gas is described as evaporation if it occurs below the boiling point of the liquid, and as boiling if it occurs at the boiling point, there is no such distinction within the solid-to-gas transition, which is always described as sublimation.

At normal pressures, most chemical compounds and elements possess three different states at different temperatures. In these cases, the transition from the solid to the gaseous state requires an intermediate liquid state. The pressure referred to is the partial pressure of the substance, not the total (e.g. atmospheric) pressure of the entire system. So, all solids that possess an appreciable vapour pressure at a certain temperature usually can sublimate in air (e.g. water ice just below 0 °C). For some substances, such as carbon and arsenic, sublimation is much easier than evaporation from the melt, because the pressure of their triple point is very high, and it is difficult to obtain them as liquids.

The term sublimation refers to a physical change of state and is not used to describe the transformation of a solid to a gas in a chemical reaction. For example, the dissociation on heating of solid ammonium chloride into hydrogen chloride and ammonia is not sublimation but a chemical reaction. Similarly the combustion of candles, containing paraffin wax, to carbon dioxide and water vapor is not sublimation but a chemical reaction with oxygen.

Sublimation is caused by the absorption of heat which provides enough energy for some molecules to overcome the attractive forces of their neighbors and escape into the vapor phase. Since the process requires additional energy, it is an endothermic change. The enthalpy of sublimation (also called heat of sublimation) can be calculated by adding the enthalpy of fusion and the enthalpy of vaporization.

Thermodynamic temperature

Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics.

Thermodynamic temperature is defined by the third law of thermodynamics in which the theoretically lowest temperature is the null or zero point. At this point, absolute zero, the particle constituents of matter have minimal motion and can become no colder. In the quantum-mechanical description, matter at absolute zero is in its ground state, which is its state of lowest energy. Thermodynamic temperature is often also called absolute temperature, for two reasons: one, proposed by Kelvin, that it does not depend on the properties of a particular material; two that it refers to an absolute zero according to the properties of the ideal gas.

The International System of Units specifies a particular scale for thermodynamic temperature. It uses the kelvin scale for measurement and selects the triple point of water at 273.16 K as the fundamental fixing point. Other scales have been in use historically. The Rankine scale, using the degree Fahrenheit as its unit interval, is still in use as part of the English Engineering Units in the United States in some engineering fields. ITS-90 gives a practical means of estimating the thermodynamic temperature to a very high degree of accuracy.

Roughly, the temperature of a body at rest is a measure of the mean of the energy of the translational, vibrational and rotational motions of matter's particle constituents, such as molecules, atoms, and subatomic particles. The full variety of these kinetic motions, along with potential energies of particles, and also occasionally certain other types of particle energy in equilibrium with these, make up the total internal energy of a substance. Internal energy is loosely called the heat energy or thermal energy in conditions when no work is done upon the substance by its surroundings, or by the substance upon the surroundings. Internal energy may be stored in a number of ways within a substance, each way constituting a "degree of freedom". At equilibrium, each degree of freedom will have on average the same energy: ${\displaystyle k_{B}T/2}$ where ${\displaystyle k_{B}}$ is the Boltzmann constant, unless that degree of freedom is in the quantum regime. The internal degrees of freedom (rotation, vibration, etc.) may be in the quantum regime at room temperature, but the translational degrees of freedom will be in the classical regime except at extremely low temperatures (fractions of kelvins) and it may be said that, for most situations, the thermodynamic temperature is specified by the average translational kinetic energy of the particles.

Three Waters Mountain

Three Waters Mountain (11,685 ft (3,562 m)) is located in the northern Wind River Range in the U.S. state of Wyoming. Three Waters Mountain straddles the Continental Divide and is in both Bridger-Teton and Shoshone National Forests. The mountain receives its name from being the triple point between the watersheds of the Colorado, Columbia, and Mississippi Rivers.

Tripoint

A tripoint, trijunction, triple point, or tri-border area is a geographical point at which the boundaries of three countries or subnational entities meet.

There are approximately 176 international tripoints. Nearly half are situated in rivers, lakes or seas. On dry land, the exact tripoints are usually indicated by markers or pillars, and occasionally by larger monuments.

Usually, the more neighbours a country has, the more international tripoints that country has. China with 16 tripoints and Russia with 11 to 14 lead the list of states by number of tripoints. Within Europe, landlocked Austria has nine tripoints, among them two with Switzerland and Liechtenstein. Island countries such as Japan have no country tripoints (some, like Bahrain and Singapore, have tripoints in the territorial waters), and the same goes for states with only one neighbour state, like Portugal or Denmark. Likewise, the United States with two neighbour states has no country tripoints; it has a number of tristate points as well as one point where four states meet. Canada, as well, has five tripoints on land where the boundaries of provinces and territories meet, including one quadripoint where four provinces and territories meet.

Border junctions (or "multiple points" or "multipoints" as they are also sometimes called) are most commonly threefold. There are also a number of quadripoints, and a handful of fivefold points, as well as probably unique examples of a sixfold, sevenfold, and eightfold point. No more than eight borders meet at a single multipoint anywhere on earth, but the territorial claims of six countries converge at the south pole in a point of elevenfold complexity.

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