Rankine scale

This article is about the temperature scale. For the idealized thermodynamic cycle for a steam engine, see Rankine cycle. For the scale measuring recovery after stroke, see Modified Rankin Scale.

The Rankine scale (/ˈræŋkɪn/ RANG-kin) is an absolute scale of thermodynamic temperature named after the University of Glasgow engineer and physicist Macquorn Rankine, who proposed it in 1859.^[1]

Rankine
Unit of	Temperature
Symbol	R, °R, °Ra
Named after	Macquorn Rankine
Conversions
491.67 R in ...	... is equal to ...
Kelvin scale	273.15 K
Celsius scale	0 °C
Fahrenheit	32 °F

History

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 K = ⁠9/5⁠ °Ra or 1 K = 1.8 °Ra. A temperature of 0 K (−273.15 °C; −459.67 °F) is equal to 0 °Ra.^[2]

Usage

The Rankine scale is used in engineering systems where heat computations are done using degrees Fahrenheit.^[3]

The symbol for degrees Rankine is °R.^[2] However, historical texts referring to "°R" are much more likely to mean the historically quite common Réaumur scale.^[4] As there is also the Rømer scale, it is better to use °Ra to be unambiguous. By analogy with the SI unit kelvin, some authors term the unit Rankine, omitting the degree symbol.^[5][6]

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

		Scale
		Kelvin	Rankine	Fahrenheit	Celsius	Réaumur
Temperature	Absolute zero	0 K	0 °Ra	−459.67 °F	−273.15 °C	−218.52 °Ré
	Freezing point of brine[a]	255.37 K	459.67 °Ra	0 °F	−17.78 °C	−14.224 °Ré
	Freezing point of water[b]	273.15 K	491.67 °Ra	32 °F	0 °C	0 °Ré
	Boiling point of water[c]	373.1339 K	671.64102 °Ra	211.97102 °F	99.9839 °C	79.98712 °Ré

See also

• Outline of metrology and measurement
• Comparison of temperature scales

Notes

1. The freezing point of brine is the zero point of Fahrenheit scale, old definition, see: Grigull 1986
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.