# ASTM E1594-16

Designation: E1594 − 16Standard Guide forExpression of Temperature1This standard is issued under the fixed designation E1594; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This guide covers uniform methods for expressingtemperature, temperature values, and temperature differences.1.2 This guide is intended as a supplement to IEEE/ASTMSI-10.2. Referenced Documents2.1 ASTM Standards:2E344 Terminology Relating to Thermometry and Hydrom-etryIEEE/ASTM SI-10 Standard for Use of the InternationalSystem of Units (SI): The Modern Metric System3. Terminology3.1 General—Standard terms used in this guide are definedin Terminology E344 and in IEEE/ASTM SI-10.4. Basic Concepts4.1 Temperature is a fundamental measurable quantity des-ignated by the symbol T or the symbol t (see 5.1).4.2 A temperature value is expressed in terms of a tempera-ture scale. The complete description consists of a numericalvalue designating the magnitude, a unit, and, whereappropriate, a tolerance or uncertainty. Both the numericalvalue and the unit depend upon the scale.4.3 A unit of temperature is understood to mean an intervalon a temperature scale.4.4 A temperature difference, interval, or increment is alsodescribed by a numerical value designating the magnitude, aunit, and, where appropriate, a tolerance or uncertainty.5. Temperature Scales5.1 Thermodynamic Temperature Scales:5.1.1 By international agreement, the theoretical tempera-ture scale to which all temperature values should be ultimatelyreferable is the Kelvin Thermodynamic Temperature Scale(KTTS). A value of temperature expressed on the KTTS isknown as a thermodynamic temperature, symbol T.5.1.2 The unit of thermodynamic temperature is the kelvin,symbol K. The kelvin is a base unit in the International Systemof Units (SI). Note that the symbol for the kelvin is the capitalletter K only; the degree sign (°) is not used.5.1.3 The expression of a value of thermodynamic tempera-ture is written:T 5 nkK (1)where:nk= a numerical value designating the magnitude,K = the symbol for the unit kelvin.The magnitude may also be represented by the notation T/K.5.1.4 A thermodynamic temperature may be expressed as aCelsius temperature. The symbol t is to be used to designate aCelsius temperature, but if this symbol leads to a conflict innotation in a given context, it is acceptable to use the symbolT instead to designate a Celsius temperature.5.1.5 The unit of Celsius temperature is the degree Celsius,symbol °C. The degree Celsius is a derived SI unit. Note thatthe symbol for the degree Celsius consists of the degree sign (°)followed by the capital letter C. Neither the degree sign nor theletter C alone represents the degree Celsius. The Unicode valuefor the degree sign is 176 (00B0 in hexadecimal). The symbolmay be represented by the two separate Unicode characters, thedegree sign (°) followed by the capital letter C. The Unicodecharacter “°C” with the value 8451 (2103 in hexadecimal) mayalso be used as the degree Celsius symbol.5.1.6 The expression of a value of Celsius temperature iswritten:t 5 nc°C (2)where:nc= a numerical value designating the magnitude,°C = the symbol for the unit degree Celsius.The magnitude may also be represented by the notation t/°C.5.1.7 By definition, at any temperature, a temperature incre-ment of one degree Celsius is equal to a temperature incrementof one kelvin.1This guide is under the jurisdiction of ASTM Committee E20 on TemperatureMeasurement and is the direct responsibility of Subcommittee E20.91 on Editorialand Terminology.Current edition approved May 15, 2016. Published May 2016. Originallyapproved in 1994. Last previous edition approved in 2011 as E1594 – 11. DOI:10.1520/E1594-16.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States15.1.8 By definition, the Celsius temperature t = 0 °C is thesame as the thermodynamic temperature T = 273.15 K. Therelation between numerical values associated with both expres-sions of a temperature is therefore given by:nc5 nk2 273.15 (3)where:t = nc°C is the same temperature as T = nkK.5.2 Practical Temperature Scales:5.2.1 Practical temperature scales have been established byinternational agreement for the practice of temperature mea-surement. Practical scales are designed so that a numericalvalue of temperature expressed on the scale is close to thenumerical value of thermodynamic temperature. Because theKTTS is difficult to implement, the vast majority of tempera-ture measurements are based on a practical scale.5.2.2 There are two practical temperature scales now in use,superseding all others. The International Temperature Scale of19903defines temperatures above 0.65 K. The ProvisionalLow-Temperature Scale from 0.9 mK to 1 K4defines tempera-tures between 0.0009 K and 1 K.5.2.3 Examples of previously used practical temperaturescales are the International Practical Temperature Scale of1968, the International Practical Temperature Scale of 1948,and the International Temperature Scale of 1927.55.2.4 A value of temperature on a practical temperaturescale may be expressed either in kelvins or in degrees Celsiususing the designations, symbols, and relations given in 5.1.6. Expression of Values of Temperature6.1 Temperature Scale Identification :6.1.1 In a document containing temperature values, it isimportant that the temperature scale upon which those valuesare expressed be identified. When reference to more than onescale is made in a document, or when critical data arepresented, scale identification is essential.6.1.2 Thermodynamic temperatures may be identified assuch, or with reference to the KTTS. If values of temperatureare expressed on a practical temperature scale, the scale shouldbe identified. The identification may be an abbreviation, asdefined in the text of the scale; for example, the InternationalTemperature Scale of 1990 is abbreviated ITS-90 and theProvisional Low-Temperature Scale from 0.9 mK to1Kisabbreviated PLTS-2000.6.1.3 Scale identification may be placed in text, infootnotes, in table headings, or in figures, as appropriate.6.1.4 A scale may also be identified by a subscript associ-ated with a quantity symbol; for example, TThand tThforthermodynamic temperatures, T90and t90for temperaturevalues on ITS-90, and T2000for temperature values on PLTS-2000.6.2 Numerical Format:6.2.1 Numerical values of temperature should be expressedas decimal numbers.6.3 Unit Symbol Format:6.3.1 The unit symbol should be separated from the numeri-cal value by a single space. There should be no space betweenthe degree sign and the letter C. Punctuation is not part of theunit symbol; only punctuation required by context or grammarshould follow the unit symbol.6.3.2 In an expression of a range of temperature values, thesame unit symbol should be used with each value in the range;for example: “over the temperature range 16 K to 50 K” or“any temperature between 20 °C and 30 °C.” These examplescan also be expressed as “over the temperature range (16 to 50)K” or “any temperature between (20 and 30) °C” respectively.6.3.3 Multiple and submultiple prefixes should not normallybe used with the unit for the expression of values oftemperature, for temperatures above 1 K. For temperaturesbelow 1 K, a submultiple may be used. The preferred submul-tiple is 0.001 (prefix “milli,” symbol m).6.3.4 When a tolerance or uncertainty is associated with avalue of temperature, both the value and the tolerance oruncertainty should be expressed with the same unit. Unitprefixes should not normally be used. The unit symbol shouldfollow each numerical value. For example:t905 60.0 °C61.5 °C (4)T905 273.150 K60.001 K (5)6.3.5 When a tolerance or uncertainty is presented in aformat not directly associated with a value of temperature, aunit prefix may be used. The preferred submultiple is 0.001(prefix “milli,” symbol m). For example, the uncertainty u of atemperature value may be expressed:u~t90! 5 0.7 mK (6)7. Expression of Temperature Differences, Intervals, andIncrements7.1 Temperature differences, intervals, and increments arenormally understood to be expressed with reference to thesame temperature scale as are values of temperature, within agiven context. Where there is a possibility ofmisunderstanding, the temperature scale should be explicitlyidentified.7.2 A small temperature difference, interval, or incrementmay be expressed in terms of a submultiple of the appropriateunit of temperature. The use of unit prefixes to indicatesubmultiples should follow the guidelines in IEEE/ASTMSI-10. The preferred submultiple is 0.001 (prefix “milli,”symbol m).3Preston-Thomas, H., “The International Temperature Scale of 1990 (ITS-90),”Metrologia, Vol 27, No. 1, 1990, pp. 3–10. For errata see ibid, Vol 27, No. 2, 1990,p. 107.4Rusby, R. L., Durieux, M., Reesink, A. L, Hudson, R. P., Schuster, G., Kühne,M., Fogle, W. E., Soulen, R. J., and Adams, E. D., “The Provisional LowTemperature Scale from 0.9 mK to 1 K, PLTS-2000.” J. Low Temp. Physics Vol126, 2002, pp. 633–642.5Evolution of the International Practical Temperature Scale of 1968, ASTM STP565, ASTM, 1974.E1594 − 1627.3 The magnitude of a temperature increment at a particu-lar temperature is sometimes expressed as a relative fraction ora percentage of the numerical value (on a particular tempera-ture scale) of the temperature. Such usage should be carefullyexplained so that the expression is meaningful and unambigu-ous.7.4 When a tolerance or uncertainty is associated with themagnitude of a temperature difference, interval, or increment,both the magnitude and tolerance or uncertainty should beexpressed in the same numerical format and with the same unit.An appropriate unit prefix may be used (see 7.2). The resultingunit symbol should follow each numerical value in the expres-sion. For example:∆t 5 10.00 °C60.01 °C describes a temperature interval of (7)about 10 °C∆T 5 9.8 mK60.2 mK describes a temperature interval of (8)about 9.8 mK7.5 In the expression of derived quantities the unit oftemperature should be the kelvin. For example, the preferredexpression for heat capacity is joules per kelvin, J·K−1or J/K;for temperature gradient, kelvins per metre, K·m−1or K/m.8. Units Other Than SI8.1 Values of temperature are sometimes expressed in de-grees Rankine, symbol °R, instead of kelvins, or in degreesFahrenheit, symbol °F, instead of degrees Celsius. Neither thedegree Rankine nor the degree Fahrenheit are part of the SI.8.2 At any temperature, a temperature increment of onedegree Rankine is equal to a temperature increment of 5/9kelvin. The relation between numerical values associated withboth expressions of a temperature is given by:nr5 9nk/5 (9)where:T = nr°R is the same temperature as T=nkK.8.3 At any temperature, a temperature increment of onedegree Fahrenheit is equal to a temperature increment of 5/9degree Celsius. The relation between numerical values associ-ated with both expressions of a temperature is given by:nf5 9nc/5132 (10)where:t = nf°F is the same temperature as t=nc°C.8.4 From the relations in 5.1, 8.2, and 8.3, it follows that:8.4.1 At any temperature, a temperature increment of onedegree Rankine is equal to a temperature increment of onedegree Fahrenheit.8.4.2 If T=nr°R and t=nf°F are the same temperature,then the relation between the numerical values is given by:nr5 nf1459.67 (11)8.5 Both thermodynamic temperatures and values of tem-perature on a practical temperature scale may be expressed indegrees Rankine or degrees Fahrenheit. In both cases theconsiderations of Section 6 apply.8.6 The use of multiple or submultiple prefixes with thedegree Rankine or the degree Fahrenheit is not recommended.9. Keywords9.1 degree Celsius; degree Fahrenheit; degree Rankine;kelvin; SI; temperature; temperature difference; temperatureincrement; temperature interval; temperature scales; tempera-ture value; thermodynamic temperatureASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the riskof infringement of such rights, are entirely their own responsibility.This standard is subject to revision at any time by the responsible technical committee and must be reviewed every five years andif not revised, either reapproved or withdrawn. Your comments are invited either for revision of this standard or for additional standardsand should be addressed to ASTM International Headquarters. 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