Celsius

The degree Celsius is a unit of temperature on the Celsius scale,[1] a temperature scale originally known as the centigrade scale.[2] 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. It is named after the Swedish astronomer Anders Celsius (1701–1744), who developed a similar temperature scale. 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.

For other uses, see Celsius (disambiguation).

degree Celsius
A thermometer calibrated in degrees Celsius
General information
Unit systemSI derived unit
Unit ofTemperature
Symbol°C 
Named afterAnders Celsius
Conversions
x °C in ...... is equal to ...
   K   x + 273.15
   °F   9/5x + 32

Since 1743 the Celsius scale has been 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 values were reversed (i.e. the boiling point was 0 degrees and the freezing point was 100 degrees). The 1743 scale reversal was proposed by Jean-Pierre Christin.

By international agreement, between 1954 and 2019 the unit degree Celsius and the Celsius scale were defined by absolute zero and the triple point of Vienna Standard Mean Ocean Water (VSMOW), a precisely defined water standard. This definition also precisely related 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. Until 19 May 2019, the temperature of the triple point of water was defined as exactly 273.16 K (0.01 °C).[3] This means that a temperature difference of one degree Celsius and that of one kelvin are exactly the same.[4]

On 20 May 2019, the kelvin was redefined so that its value is now determined by the definition of the Boltzmann constant rather than being defined by the triple point of VSMOW. This means that the triple point is now a measured value, not a defined value. The newly-defined exact value of the Boltzmann constant was selected so that the measured value of the VSMOW triple point is exactly the same as the older defined value to within the limits of accuracy of contemporary metrology. The degree Celsius remains exactly equal to the kelvin, and 0 K remains exactly −273.15 °C.

History
An illustration of Anders Celsius's original thermometer. Note the reversed scale, where 100 is the freezing point of water and 0 is its boiling point.

In 1742, Swedish astronomer Anders Celsius (1701–1744) created a temperature scale that was the reverse of the scale now known as "Celsius": 0 represented the boiling point of water, while 100 represented the freezing point of water.[5] In his paper Observations of two persistent degrees on a thermometer, he recounted his experiments showing that the melting point of ice is essentially unaffected by pressure. He also determined with remarkable precision how the boiling point of water varied as a function of atmospheric pressure. He proposed that the zero point of his temperature scale, being the boiling point, would be calibrated at the mean barometric pressure at mean sea level. This pressure is known as one standard atmosphere. The BIPM's 10th General Conference on Weights and Measures (CGPM) later defined one standard atmosphere to equal precisely 1,013,250 dynes per square centimeter (101.325 kPa).[6]

In 1743, the Lyonnais physicist Jean-Pierre Christin, permanent secretary of the Académie des sciences, belles-lettres et arts de Lyon, working independently of Celsius, developed a scale where zero represented the freezing point of water and 100 represented the boiling point of water.[7][8] On 19 May 1743 he published the design of a mercury thermometer, the "Thermometer of Lyon" built by the craftsman Pierre Casati that used this scale.[9][10][11]

In 1744, coincident with the death of Anders Celsius, the Swedish botanist Carl Linnaeus (1707–1778) reversed Celsius's scale.[12] His custom-made "linnaeus-thermometer", for use in his greenhouses, was made by Daniel Ekström, Sweden's leading maker of scientific instruments at the time, whose workshop was located in the basement of the Stockholm observatory. As often happened in this age before modern communications, numerous physicists, scientists, and instrument makers are credited with having independently developed this same scale;[13] among them were Pehr Elvius, the secretary of the Royal Swedish Academy of Sciences (which had an instrument workshop) and with whom Linnaeus had been corresponding; Daniel Ekström, the instrument maker; and Mårten Strömer (1707–1770) who had studied astronomy under Anders Celsius.

The first known Swedish document[14] reporting temperatures in this modern "forward" Celsius scale is the paper Hortus Upsaliensis dated 16 December 1745 that Linnaeus wrote to a student of his, Samuel Nauclér. In it, Linnaeus recounted the temperatures inside the orangery at the University of Uppsala Botanical Garden:

...since the caldarium (the hot part of the greenhouse) by the angle of the windows, merely from the rays of the sun, obtains such heat that the thermometer often reaches 30 degrees, although the keen gardener usually takes care not to let it rise to more than 20 to 25 degrees, and in winter not under 15 degrees...

Centigrade versus Celsius
  Countries that use Fahrenheit (°F).
  Countries that use both Fahrenheit (°F) and Celsius (°C).
  Countries that use Celsius (°C).

Since the 19th century, the scientific and thermometry communities worldwide have used the phrase "centigrade scale" and temperatures were often reported simply as "degrees" or, when greater specificity was desired, as "degrees centigrade", with the symbol °C.

However, the term centigrade was also used in the Spanish and French language as a unit of angular measurement (1/100 of a right angle), and it had a similar connotation in other languages. The term centesimal degree or gradian ("grad" or "gon": 100ᵍ = 90°, 1ᵍ = 0.9°) was used when unambiguous language was required by international standards bodies such as the BIPM. It would more properly now be called "hectograde".

To eliminate confusion between the unit of temperature and the unit of angular measurement, the 9th meeting of the General Conference on Weights and Measures and the Comité International des Poids et Mesures (CIPM) formally adopted "degree Celsius" in 1948 for the degree of temperature,[15][lower-alpha 1] and keeping the recognized degree symbol (°), rather than adopting the gradian/centesimal degree symbol (ᵍ or gon).

For scientific use, "Celsius" is the term usually used, but in English-speaking countries "centigrade" remains in common use, especially in informal contexts.[16] It was not even until February 1985 that the weather forecasts issued by the BBC switched the term from "centigrade" to "Celsius".[17]

Common temperatures

Some key temperatures relating the Celsius scale to other temperature scales are shown in the table below.

Key scale relations
KelvinCelsiusFahrenheit
Absolute zero (exactly) 0 K −273.15 °C −459.67 °F
Boiling point of liquid nitrogen 77.4 K −195.8 °C[18] −320.4 °F
Sublimation point of dry ice 195.1 K −78 °C −108.4 °F
Intersection of Celsius and Fahrenheit scales 233.15 K −40 °C −40 °F
Melting point of H2O (purified ice)[19] 273.1499 K 0.0001 °C 31.9998 °F
Room temperature (NIST standard)[20] 293.15 K 20.0 °C 68.0 °F
Normal human body temperature (average)[21] 310.15 K 37.0 °C 98.6 °F
Water's boiling point at 1 atm (101.325 kPa)
(approximate: see Boiling point)[lower-alpha 2]		 373.1339 K 99.9839 °C 211.971 °F

Name and symbol typesetting

The "degree Celsius" has been the only SI unit whose full unit name contains an uppercase letter since 1967, when the SI base unit for temperature became the kelvin, replacing the capitalized term degrees Kelvin. The plural form is "degrees Celsius".[22]

The general rule of the International Bureau of Weights and Measures (BIPM) is that the numerical value always precedes the unit, and a space is always used to separate the unit from the number, e.g. "30.2 °C" (not "30.2°C" or "30.2° C").[23] The only exceptions to this rule are for the unit symbols for degree, minute, and second for plane angle (°, ′, and ″, respectively), for which no space is left between the numerical value and the unit symbol.[24] Other languages, and various publishing houses, may follow different typographical rules.

Unicode character

Unicode provides the Celsius symbol at code point U+2103 ℃ DEGREE CELSIUS. However, this is a compatibility character provided for roundtrip compatibility with legacy encodings. It easily allows correct rendering for vertically written East Asian scripts, such as Chinese. The Unicode standard explicitly discourages the use of this character: "In normal use, it is better to represent degrees Celsius "°C" with a sequence of U+00B0 ° DEGREE SIGN + U+0043 C LATIN CAPITAL LETTER C, rather than U+2103 ℃ DEGREE CELSIUS. For searching, treat these two sequences as identical."[25]

Temperatures and intervals

The degree Celsius is subject to the same rules as the kelvin with regard to the use of its unit name and symbol. Thus, besides expressing specific temperatures along its scale (e.g. "Gallium melts at 29.7646 °C" and "The temperature outside is 23 degrees Celsius"), the degree Celsius is also suitable for expressing temperature intervals: differences between temperatures or their uncertainties (e.g. "The output of the heat exchanger is hotter by 40 degrees Celsius", and "Our standard uncertainty is ±3 °C").[26] Because of this dual usage, one must not rely upon the unit name or its symbol to denote that a quantity is a temperature interval; it must be unambiguous through context or explicit statement that the quantity is an interval.[lower-alpha 3] This is sometimes solved by using the symbol °C (pronounced "degrees Celsius") for a temperature, and C° (pronounced "Celsius degrees") for a temperature interval, although this usage is non-standard.[27] Another way to express the same is "40 °C ± 3 K", which can be commonly found in literature.

Celsius measurement follows an interval system but not a ratio system; and it follows a relative scale not an absolute scale. For example, an object at 20 °C does not have twice the energy of when it is 10 °C; and 0 °C is not the lowest Celsius value. Thus, degrees Celsius is a useful interval measurement but does not possess the characteristics of ratio measures like weight or distance.[28]

Coexistence of Kelvin and Celsius scales

In science and in engineering, the Celsius scale and the Kelvin scale are often used in combination in close contexts, e.g. "a measured value was 0.01023 °C with an uncertainty of 70 µK". This practice is permissible because the magnitude of the degree Celsius is equal to that of the kelvin. Notwithstanding the official endorsement provided by decision #3 of Resolution 3 of the 13th CGPM,[29] which stated "a temperature interval may also be expressed in degrees Celsius", the practice of simultaneously using both °C and K remains widespread throughout the scientific world as the use of SI-prefixed forms of the degree Celsius (such as "µ°C" or "microdegrees Celsius") to express a temperature interval has not been well-adopted.

Melting and boiling points of water

The melting and boiling points of water are no longer part of the definition of the Celsius scale. In 1948, the definition was changed to use the triple point of water.[30] In 2005 the definition was further refined to use water with precisely defined isotopic composition (VSMOW) for the triple point. In 2019, the definition was changed to use the Boltzmann constant, completely decoupling the definition of the kelvin from the properties of water. Each of these formal definitions left the numerical values of the Celsius scale identical to the prior definition to within the limits of accuracy of the metrology of the time.

When the melting and boiling points of water ceased being part of the definition, they became measured quantities instead. This is also true of the triple point.

In 1948 when the 9th General Conference on Weights and Measures (CGPM) in Resolution 3 first considered using the triple point of water as a defining point, the triple point was so close to being 0.01 °C greater than water's known melting point, it was simply defined as precisely 0.01 °C. However, later measurements showed that the difference between the triple and melting points of VSMOW is actually very slightly (<0.001 °C) greater than 0.01 °C. Thus, the actual melting point of ice is very slightly (less than a thousandth of a degree) below 0 °C. Also, defining water's triple point at 273.16 K precisely defined the magnitude of each 1 °C increment in terms of the absolute thermodynamic temperature scale (referencing absolute zero). Now decoupled from the actual boiling point of water, the value "100 °C" is hotter than 0 °C – in absolute terms – by a factor of precisely 373.15/273.15 (approximately 36.61% thermodynamically hotter). When adhering strictly to the two-point definition for calibration, the boiling point of VSMOW under one standard atmosphere of pressure was actually 373.1339 K (99.9839 °C). When calibrated to ITS-90 (a calibration standard comprising many definition points and commonly used for high-precision instrumentation), the boiling point of VSMOW was slightly less, about 99.974 °C.[31]

This boiling-point difference of 16.1 millikelvins between the Celsius scale's original definition and the previous one (based on absolute zero and the triple point) has little practical meaning in common daily applications because water's boiling point is very sensitive to variations in barometric pressure. For example, an altitude change of only 28 cm (11 in) causes the boiling point to change by one millikelvin.

Celsius temperature conversion formulae
from Celsius to Celsius
Fahrenheit [°F] = [°C] × ​9⁄5 + 32 [°C] = ([°F] − 32) × ​5⁄9
Kelvin [K] = [°C] + 273.15 [°C] = [K] − 273.15
Rankine [°R] = ([°C] + 273.15) × ​9⁄5 [°C] = ([°R] − 491.67) × ​5⁄9
For temperature intervals rather than specific temperatures,
1 °C = 1 K = ​9⁄5 °F = ​9⁄5 °R
Comparisons among various temperature scales
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See also

Notes
  1. According to The Oxford English Dictionary (OED), the term "Celsius' thermometer" had been used at least as early as 1797. Further, the term "The Celsius or Centigrade thermometer" was again used in reference to a particular type of thermometer at least as early as 1850. The OED also cites this 1928 reporting of a temperature: "My altitude was about 5,800 metres, the temperature was 28° Celsius." However, dictionaries seek to find the earliest use of a word or term and are not a useful resource as regards to the terminology used throughout the history of science. According to several writings of Dr. Terry Quinn CBE FRS, Director of the BIPM (1988–2004), including "Temperature Scales from the early days of thermometry to the 21st century" (PDF). Archived from the original (PDF) on 26 December 2010. Retrieved 31 May 2016. (146 KiB) as well as Temperature (2nd Edition/1990/Academic Press/0125696817), the term Celsius in connection with the centigrade scale was not used whatsoever by the scientific or thermometry communities until after the CIPM and CGPM adopted the term in 1948. The BIPM was not even aware that "degree Celsius" was in sporadic, non-scientific use before that time. It is also noteworthy that the twelve-volume, 1933 edition of OED didn't even have a listing for the word Celsius (but did have listings for both centigrade and centesimal in the context of temperature measurement). The 1948 adoption of Celsius accomplished three objectives:
    1.    All common temperature scales would have their units named after someone closely associated with them; namely, Kelvin, Celsius, Fahrenheit, Réaumur and Rankine.
    2.    Notwithstanding the important contribution of Linnaeus who gave the Celsius scale its modern form, Celsius's name was the obvious choice because it began with the letter C. Thus, the symbol °C that for centuries had been used in association with the name centigrade could remain in use and would simultaneously inherit an intuitive association with the new name.
    3.    The new name eliminated the ambiguity of the term "centigrade", freeing it to refer exclusively to the French-language name for the unit of angular measurement.
  2. For Vienna Standard Mean Ocean Water at one standard atmosphere (101.325 kPa) when calibrated solely per the two-point definition of thermodynamic temperature. Older definitions of the Celsius scale once defined the boiling point of water under one standard atmosphere as being precisely 100 °C. However, the current definition results in a boiling point that is actually 16.1 mK less. For more about the actual boiling point of water, see VSMOW in temperature measurement. A different approximation uses ITS-90, which approximates the temperature to 99.974 °C
  3. In 1948, Resolution 7 of the 9th CGPM stated, "To indicate a temperature interval or difference, rather than a temperature, the word 'degree' in full, or the abbreviation 'deg' must be used." This resolution was abrogated in 1967/1968 by Resolution 3 of the 13th CGPM, which stated that ["The names "degree Kelvin" and "degree", the symbols "°K" and "deg" and the rules for their use given in Resolution 7 of the 9th CGPM (1948),] ...and the designation of the unit to express an interval or a difference of temperatures are abrogated, but the usages which derive from these decisions remain permissible for the time being." Consequently, there is now wide freedom in usage regarding how to indicate a temperature interval. The most important thing is that one's intention must be clear and the basic rule of the SI must be followed; namely that the unit name or its symbol must not be relied upon to indicate the nature of the quantity. Thus, if a temperature interval is, say, 10 K or 10 °C (which may be written 10 kelvins or 10 degrees Celsius), it must be unambiguous through obvious context or explicit statement that the quantity is an interval. Rules governing the expressing of temperatures and intervals are covered in the BIPM's "SI Brochure, 8th edition" (PDF). (1.39 MiB).

References
  1. "Celsius temperature scale". Encyclopædia Britannica. Retrieved 19 February 2012. Celsius temperature scale, also called centigrade temperature scale, scale based on 0 ° for the melting point of water and 100 ° for the boiling point of water at 1 atm pressure.
  2. Helmenstine, Anne Marie (15 December 2014). "What Is the Difference Between Celsius and Centigrade?". Chemistry.about.com. About.com. Retrieved 25 April 2020.
  3. "SI brochure, section 2.1.1.5". International Bureau of Weights and Measures. Archived from the original on 26 September 2007. Retrieved 9 May 2008.
  4. "Essentials of the SI: Base & derived units". Retrieved 9 May 2008.
  5. Celsius, Anders (1742) "Observationer om twänne beständiga grader på en thermometer" (Observations about two stable degrees on a thermometer), Kungliga Svenska Vetenskapsakademiens Handlingar (Proceedings of the Royal Swedish Academy of Sciences), 3 : 171–180 and Fig. 1.
  6. "Resolution 4 of the 10th meeting of the CGPM (1954)".
  7. Don Rittner; Ronald A. Bailey (2005): Encyclopedia of Chemistry. Facts On File, Manhattan, New York City. p. 43.
  8. Smith, Jacqueline (2009). "Appendix I: Chronology". The Facts on File Dictionary of Weather and Climate. Infobase Publishing. p. 246. ISBN 978-1-4381-0951-0. 1743 Jean-Pierre Christin inverts the fixed points on Celsius' scale, to produce the scale used today.
  9. Mercure de France (1743): MEMOIRE sur la dilatation du Mercure dans le Thermométre. Chaubert; Jean de Nully, Pissot, Duchesne, Paris. pp. 1609–1610.
  10. Journal helvétique (1743): LION. Imprimerie des Journalistes, Neuchâtel. pp. 308–310.
  11. Memoires pour L'Histoire des Sciences et des Beaux Arts (1743): DE LYON. Chaubert, París. pp. 2125–2128.
  12. Citation: Uppsala University (Sweden), Linnaeus' thermometer
  13. Citation for Daniel Ekström, Mårten Strömer, Christin of Lyons: The Physics Hypertextbook, Temperature; citation for Christin of Lyons: Le Moyne College, Glossary, (Celsius scale); citation for Linnaeus's connection with Pehr Elvius and Daniel Ekström: Uppsala University (Sweden), Linnaeus' thermometer; general citation: The Uppsala Astronomical Observatory, History of the Celsius temperature scale
  14. Citations: University of Wisconsin–Madison, Linnæus & his Garden and; Uppsala University, Linnaeus' thermometer
  15. "CIPM, 1948 and 9th CGPM, 1948". International Bureau of Weights and Measures. Retrieved 9 May 2008.
  16. "centigrade, adj. and n." Oxford English Dictionary. Oxford University Press. Retrieved 20 November 2011.
  17. 1985 BBC Special: A Change In The Weather on YouTube
  18. Lide, D.R., ed. (1990–1991). Handbook of Chemistry and Physics. 71st ed. CRC Press. p. 4–22.
  19. The ice point of purified water has been measured at 0.000089(10) degrees Celsius – see Magnum, B.W. (June 1995). "Reproducibility of the Temperature of the Ice Point in Routine Measurements" (PDF). Nist Technical Note. 1411. Archived from the original (PDF) on 14 July 2007. Retrieved 11 February 2007.
  20. "SI Units – Temperature". 2010. Retrieved 7 November 2019.
  21. Elert, Glenn (2005). "Temperature of a Healthy Human (Body Temperature)". The Physics Factbook. Retrieved 22 August 2007.
  22. "Unit of thermodynamic temperature (kelvin)". The NIST Reference on Constants, Units, and Uncertainty: Historical context of the SI. National Institute of Standards and Technology (NIST). 2000. Archived from the original on 11 November 2004. Retrieved 16 November 2011.
  23. BIPM, SI Brochure, Section 5.3.3.
  24. For more information on conventions used in technical writing, see the informative SI Unit rules and style conventions by the NIST as well as the BIPM's SI brochure: Subsection 5.3.3, Formatting the value of a quantity. Archived 5 July 2014 at the Wayback Machine
  25. "22.2". The Unicode Standard, Version 9.0 (PDF). Mountain View, CA, USA: The Unicode Consortium. July 2016. ISBN 978-1-936213-13-9. Retrieved 20 April 2017.
  26. Decision No. 3 of Resolution 3 of the 13th CGPM.
  27. H.D. Young, R. A. Freedman (2008). University Physics with Modern Physics (12th ed.). Addison Wesley. p. 573.
  28. This fact is demonstrated in the book Biostatistics: A Guide to Design, Analysis, and Discovery By Ronald N. Forthofer, Eun Sul Lee and Mike Hernandez
  29. http://www.bipm.fr/en/CGPM/db/13/3/
  30. "Resolution 3 of the 9th CGPM (1948)". International Bureau of Weights and Measures. Retrieved 9 May 2008.
  31. Citation: London South Bank University, Water Structure and Behavior, notes c1 and c2

The dictionary definition of Celsius at Wiktionary

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