Exploring the Rankine Scale: Understanding the Basics and Applications

We explain what the Rankine scale is and its history. In addition, we give examples of conversions to Celsius, Fahrenheit, and Kelvin.

What is the Rankine scale?

The Rankine scale is an absolute scale of thermodynamic temperature in which all its values are positive, since they are referred to absolute zero, the lowest theoretical temperature that a body can reach, but which is experimentally and thermodynamically impossible to achieve.

It was proposed in 1859 by the Scottish engineer William John MacQuorn Rankine, eleven years after William Thomson (Lord Kelvin, 1848) published his absolute temperature scale based on degrees Celsius, °C.

Absolute zero on the kelvin scale has a value of -273.15 °C. The rest of the temperatures on this scale are obtained by adding 273.15 to the value of the temperatures in degrees Celsius (or better known as centigrade).

The Rankine scale is related to degrees Fahrenheit. Therefore, the absolute zero value for this scale is expressed in degrees Fahrenheit, which is -459.67 °F. Thus, to obtain the other temperatures, it is enough to add 459.67 to the value of the temperatures (°R = °F + 459.67).

Rankine degrees came to be used in engineering pursuits in the United States and England. However, today its use has practically died out.

Rankine and other temperature scales

Celsius

Celsius (symbol: °C) is a unit of measurement for temperature. It is named after the Swedish astronomer Anders Celsius. In the Celsius scale, the freezing point of water is defined as 0 degrees Celsius (°C) and the boiling point of water is defined as 100 degrees Celsius (°C) at standard atmospheric pressure. The Celsius scale is widely used in most countries around the world, except for the United States, where the Fahrenheit scale is more commonly used.

Fahrenheit

Fahrenheit is a temperature scale that was proposed by a German physicist named Daniel Gabriel Fahrenheit in 1724. On the Fahrenheit scale, the freezing point of water is 32 degrees and the boiling point of water is 212 degrees, with a difference of 180 degrees between the two.

In the United States, Fahrenheit is still commonly used for weather forecasts, baking, and other everyday temperature measurements. However, most other countries use the Celsius scale, which is based on the freezing and boiling points of water at 0 and 100 degrees, respectively.

Rankine

Rankine temperature scale: The Rankine temperature scale is a temperature scale that uses degrees Fahrenheit as its unit. It was also developed by William John Macquorn Rankine, and is used primarily in engineering applications in the United States. On the Rankine scale, absolute zero is 0 Rankine, and the freezing point of water is 491.67 Rankine.

Furthermore, the National Institute of Standards and Technology recommends against using the degree symbol when using the Rankine temperature scale in NIST publications.

Radiation heat transfer, entropy change, the thermal efficiency of the Carnot heat engine, and the coefficient of performance of the heat pump, all require the use of absolute temperature in Rankine degrees when working in the American Engineering System. .

Some engineering fields in the United States measure thermodynamic temperature using the Rankine temperature scale. However, throughout the scientific world, thermodynamic temperature is measured using the Kelvin scale.

It has even been pointed out that the Rankine temperature scale is used mainly because of its relationship with the Fahrenheit temperature scale.

Absolute zero

The Kelvin and Rankine temperature scales have absolute zero as their starting point. But what is absolute zero?

Absolute zero is the lowest temperature that can possibly be reached. It is said that the internal energy of the system reaches its lowest level, lacking the motion particles: all their vibrations and displacements would be frozen.

According to the third law of thermodynamics, absolute zero is an unreachable limit.

The closest temperature to absolute zero is 5∙10-10 K above absolute zero, obtained in an MIT laboratory in 2003, by cooling a gas in a magnetic field.

William John Macquorn Rankine

William John Macquorn Rankine (1820-1872) was one of the pioneers in the study of thermodynamics. He developed a complete theory on the steam engine and thermal engines, as well as on thermal energy.

Born in Edinburgh, Rankine was educated at the university in that city. He worked as a civil engineer and published articles on practical engineering topics, and later on molecular physics, as well as thermodynamics.

In 1855 he was appointed chairman of the chair of mechanical and civil engineering at the University of Glasgow.

He wrote more than 150 scientific articles and manuals, as well as books for the use of his students. He was elected a Fellow of the Royal Society in 1853 and was the first President of the Scottish Institution of Engineers.

In addition to his immense scientific and academic activity, Rankine was very fond of music, both as a performer and as a composer. Thus, he composed a song called “The Three Foot Rule”, where he defends the British tradition of its measures threatened by the invasion of the centesimal system.

Rankine scale temperature conversion

From Rankine to Celsius, Fahrenheit and Kelvin to Celsius

[°C] = ([ºR] – 491.67) ∙ 5/9

The value 491.67 equals 459.67 (Rankine absolute zero) plus 32°F (freezing temperature of water). And 5/9 is a conversion factor from degrees Celsius to degrees Rankine or Fahrenheit, since, on these temperature scales, 100 °C equals 180 °R or °F.

to Fahrenheit

[°F] = [°R] – 459.67

to Kelvin

[K] = [°R] ∙ 5/9

From Celsius, Fahrenheit and Kelvin to Rankine

[°R] = ([°C] + 273.15) ∙ 9/5

The value 273.15 is absolute zero on the Kelvin temperature scale. And 9/5 is a conversion factor, since 180 °F or ºR equals 100 °C.

[ºR] = [°F] + 459.67

[ºR] = [K] ∙ 9/5

Examples of comparing various temperatures with different scales

Absolute zero

Kelvin 0 (by definition).

Celsius -273.15°C.

Fahrenheit -459.67°F.

Rankine 0 ºR (by definition).

Freezing point of brine

(Zero point of the Fahrenheit Scale)

Kelvin: 255.37K

Celsius: -17.78°C.

Fahrenheit: 0°F.

Rankine: 459.67 ºR.

Freezing point of water

Kelvin: 273.15K

Celsius: 0°C.

Fahrenheit: 32°F.

Rankine: 459.67 ºR.

Triple point of water

Kelvin: 273.16K

Celsius: 0.01°C.

Fahrenheit: 32.018°F.

Rankine: 491.688 ºR.

Boiling point of water

Kelvin: 373.1339K.

Celsius: 99.9839°C.

Fahrenheit: 211.97102°F.

Rankine: 671.64102 ºR.

Human body temperature

Kelvin: 310K

Celsius: 37°C.

Fahrenheit: 98°F.

Rankine: 558ºR.