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Rankine scale

## Summary

The Rankine scale (/ˈræŋkɪn/) is an absolute scale of thermodynamic temperature named after the University of Glasgow engineer and physicist Macquorn Rankine, who proposed it in 1859.[1] Similar to the Kelvin scale, which was first proposed in 1848,[1] zero on the Rankine scale is absolute zero, but a temperature difference of one Rankine degree (°R or °Ra) is defined as equal to one Fahrenheit degree, rather than the Celsius degree used on the Kelvin scale. In converting from kelvin to degrees Rankine, 1 °R = 59 K or 1 K = 1.8 °R . A temperature of 0 K (−273.15 °C; −459.67 °F) is equal to 0 °R.

Rankine
Unit ofTemperature
Symbol°R or °Ra
Named afterMacquorn Rankine
Conversions
x °R in ...... is equal to ...
SI base units   5/9x K
SI units   5/9x − 273.15 °C
Imperial/US units   x − 459.67 °F

The Rankine scale is still used in engineering systems where heat computations are done using degrees Fahrenheit.[citation needed]

The symbol for degrees Rankine is °R[2] (or °Ra if necessary to distinguish it from the Rømer and Réaumur scales). By analogy with the SI unit, the kelvin, some authors term the unit Rankine, omitting the degree symbol.[3][4]

Some important temperatures relating the Rankine scale to other temperature scales are shown in the table below.

Temperature Kelvin Celsius Fahrenheit Rankine
Absolute zero 0 K −273.15 °C −459.67 °F 0 °R
Freezing point of brine[a] 255.37 K −17.78 °C 0 °F 459.67 °R
Freezing point of water[b] 273.15 K 0 °C 32 °F 491.67 °R
Boiling point of water[c] 373.1339 K 99.9839 °C 211.97102 °F 671.64102 °R

## Notes

1. ^ The freezing point of brine was the zero point of the Fahrenheit scale as originally defined.
2. ^ The ice point of purified water has been measured to be 0.000089(10) degrees Celsius – see Magnum 1995
3. ^ 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.

## References

1. ^ a b "Rankine". Merriam-Webster Dictionary. Retrieved 2019-11-07.
2. ^ B.8 Factors for Units Listed Alphabetically from Thompson & Taylor 2008, pp. 45–69
3. ^ Pauken 2011, p. 20
4. ^ Balmer 2011, p. 10

### Sources

• Balmer, Robert (2011). Modern Engineering Thermodynamics. Oxford: Elsevier Inc. ISBN 978-0-12-374996-3.
• 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 2007-03-07. Retrieved 2007-02-11.
• Pauken, Michael (2011). Thermodynamics For Dummies. Indianapolis: Wiley Publishing Inc. ISBN 978-1-118-00291-9.
• Thompson, Ambler; Taylor, Barry N. (2008). "Guide for the use of the International System of Units (SI)" (PDF). doi:10.6028/nist.sp.811e2008. Retrieved 2019-11-07. `{{cite journal}}`: Cite journal requires `|journal=` (help)