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What the FAQ are Kelvin, Rankine et al?

There are many ways of measuring and representing temperature, such as the relationship between air temperature and the rate at which certain crickets chirp.

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In my previous column – What the FAQ are Celsius and Fahrenheit? – we introduced the German physicist Daniel Gabriel Fahrenheit (1686–1736) and the Swedish astronomer Anders Celsius (1701–1744). We also became acquainted with the temperature scales that were named after Celsius and Fahrenheit, but that they didn’t actually invent (it really is a funny old world when you come to think about it). Even though that column was posted only a couple of days ago, I’ve already received numerous emails saying things like, “You forgot to mention the Kelvin scale!” What? Do I look like the sort of man who would forget to mention the Kelvin scale? Of course I didn’t forget, it’s just that I didn’t want to confuse the issue. In fact, as Piotr Małek and Álvaro Díez say on OmniCalculator.com: “…there are many more units of temperature, some arguably as useless as unknown.” In addition to Celsius (a.k.a. Centigrade) (°C) and Fahrenheit (°F), there are a variety of other temperature scales, including Kelvin (K), Rankine (R or Ra), Delisle (°De), Newton (°N), Réaumur (°Ré), and Rømer (°Rø). We will consider all of these shortly, but first…  

Why K and R not °K and °R?

Did you notice anything funny about the previous paragraph? I’m talking about the fact that most of the temperature scale units are indicated using a degree symbol (°), except for Kelvin (K) and Rankine (R), but why should this be?
Comparison of the Celsius, Fahrenheit, Kelvin, and Rankine temperature scales (Click image to see a larger version — Image source: Max Maxfield)
Well, the term “degree” carries an implication of qualitative comparison. Temperature scales like Celsius and Fahrenheit have arbitrary zero points. This means that, even though they are linear, they aren’t proportional, so we use the degree symbol (°). By comparison, temperature scales like Kelvin and Rankine are referred to as absolute or thermodynamic scales because they have absolute zero as their zero point. This means that, in addition to being linear, these scales are also proportional. Another way to think of this is that, in the case of absolute scales, the value 0 indicates that there is none of the associated quantity (which would be temperature, in this case). As a result of all this, on the Kelvin and Rankine scales, degrees are called kelvins (K) and rankines (R), respectively, and no degree symbols (°) are used. For example, 100 on the Kelvin scale is spoken as “one hundred kelvins” and written as 100 K; similarly, 100 on the Rankine scale is spoken as “one hundred rankines” and written as 100 R. But wait, there’s more, because — in SI units — C is used for coulomb (the derived unit of electrical charge) and F is used for farad (the unit of electrical capacitance). Since we can’t have two units represented by the same letter, we are obliged to use the degree symbol in °C and °F to differentiate Celsius and Fahrenheit from coulomb and farad, respectively. Happily, the only SI unit that uses K is Kelvin, but this is where we run into a little problem, because R is a pseudo SI unit representing the universal gas constant. Nonetheless, the National Institute of Standards and Technology (NIST) recommends saying “rankines” without the “degree” prefix and using R without the degree symbol (°). We will return to consider the Kelvin and Rankine scales in more detail in a moment, but first…  

Cricket Chirps Thermometer

Another thing I discovered on OmniCalculator.com is the concept of the Cricket Chirps Thermometer. It seems that, towards the end of the 1800s, American physicist and inventor Amos Emerson Dolbear (1837–1910) observed that crickets of a certain type were all chirping at the same time. After performing some experiments, Dolbear derived a formula describing the relationship between air temperature and the rate at which crickets chirp:  
temperature = 50 + ((chirps-per-minute – 40) / 4)
Crickets Chirping Thermometer
Unfortunately, Dolbear didn’t specify which species of crickets he used for his experiments, which seems to be a bit of an oversight. But turn that frown upside down into a smile, because the OmniCalculator above is based on field crickets, which is the most common species in the US.  

The Kelvin Scale (K)

The “gas laws” (Boyle’s law, Charles’s law, Gay-Lussac’s law, Avogadro’s law, etc.) were developed in the 1600s, 1700s, and early 1800s as scientists began to realize that relationships between the pressure, volume, and temperature associated with a sample of gas could be obtained that would hold to approximation for all gases. As part of this, in the early 1800s, scientists theorized that the volume of a gas should become zero at a temperature of –273.15 °C (this was subsequently refined to its current value of –273.16 °C). In 1848, the Irish-Scottish mathematical physicist and engineer William Thomson (1824–1907) wrote in his paper, On an Absolute Thermometric Scale, of the need for a scale whereby “infinite cold” (absolute zero) was the scale’s null point. Since dividing the difference between the freezing and boiling points of water into 100 units (as in the Celsius scale) made sense to him, Thomson decided to use the degree Celsius as the unit increment in his own scale. In 1892, in recognition of his achievements in thermodynamics (and of his opposition to Irish Home Rule), Thomson was ennobled with the title 1st Baron Kelvin, which is why his temperature scale is now known as the Kelvin scale. The Kelvin scale has 0 K (i.e., –273.16 °C) as absolute zero, 273.16 K (0 °C) as the freezing point of water, and 373.16 K (0 °C) as the boiling point of water. Since you can’t get any colder than absolute zero, there are no negative numbers on the Kelvin scale.  

The Rankine Scale (R or Ra)

Professor William John Macquorn Rankine (1820–1872) was a Scottish mechanical engineer who also contributed to civil engineering, physics, and mathematics. He was also an enthusiastic amateur singer, pianist, and cellist who composed his own humorous songs and sang them to anyone who couldn’t get out of the way in time. Along with Rudolf Clausius and William Thomson, Rankine was a founding contributor to the science of thermodynamics. Not wanting his chum Thomson (later Lord Kelvin) to have all the fun, Rankine proposed his own temperature scale in 1859. The Rankine scale is to Fahrenheit what the Kelvin scale is to Celsius. As for the Kelvin scale, 0 on the Rankine scale corresponds to absolute zero, but the unit increment corresponds to one Fahrenheit degree. For this reason, the Rankine scale may be used in engineering systems where heat computations are performed using degrees Fahrenheit. The Rankine scale has 0 R (i.e., 0 K, −459.67 °F) as absolute zero, 491.67 R (32 °F) as the freezing point of water, and 671.67 R (212 °F) as the boiling point of water. As for the Kelvin scale, since you can’t get any colder than absolute zero, there are no negative numbers on the Rankine scale.  

The Newton Scale (°N)

The English mathematician, physicist, astronomer, and theologian Sir Isaac Newton (1642–1726) is widely recognized as one of the most influential scientists of all time. Newton devised his own temperature scale in 1702 but — although he called his device a thermometer — he didn’t use the term “temperature,” speaking instead of gradus caloris (“degrees of heat”). Newton set as 0 on his scale to be Calor aeris hyberni ubi aqua incipit gelu rigescere (“the heat of air in winter at which water begins to freeze”), which is reminiscent of the modern Celsius scale (i.e., 0 °N = 0 °C). The problem is that Newton didn’t provide a second definitive reference point; instead, he provided 18 subjective reference points, along the lines of: “the heat at midday about the month of July,” “the greatest heat which a thermometer takes up when in contact with the human body”, and “the greatest heat of a bath which one can endure for some time when the hand is dipped in and is kept in constant movement.” Can you imagine if someone came to you and said, “Here’s a pile of money, can you build me a thermometer based on the Newton temperature scale, but I’m short-sighted so can you use a large font?”  

The Rømer Scale (°Rø)

Ole Christensen Rømer (1644–1710) was a Danish astronomer who, in 1676, made the first quantitative measurements of the speed of light. In 1701, Rømer proposed a temperature scale based on having the freezing point of water being 7.5 °Rø and the boiling point of water being 60 °Rø. Although the Rømer scale is no longer in use, it is of some historical importance, because it was one of the first calibrated scales. Previous devices, called thermoscopes, gave only an indication as to whether the temperature was rising or falling, or else were infuriatingly inaccurate. Using two fiduciary points with equally spaced calibration marks between them — as proposed by Rømer — was a completely new concept at that time. Furthermore, as we discussed in my previous column – What the FAQ are Celsius and Fahrenheit? – Rømer introduced his scale to Daniel Gabriel Fahrenheit, leading to the Fahrenheit scale we know and love today.  

The Delisle Scale (°De)

This scale was invented in 1732 by the French astronomer Joseph-Nicolas Delisle (1688–1768). Delisle decided to use the boiling point of water as the 0 point on his scale. Rather enthusiastically, he then divided things up into 2,400 (sometimes 2,700) degrees. In 1738, Josias Weitbrecht (1702–1747) recalibrated the Delisle thermometer, keeping 0 degrees as the boiling point of water and adding 150 degrees as the freezing point of water. Weitbrecht sent copies of his calibrated thermometers to various scholars, including Anders Celsius, which may explain why Celsius originally decided to use 0 as the boiling point of water in his thermometer.  

The Réaumur Scale (°Ré)

The French entomologist and writer René Antoine Ferchault de Réaumur (1683–1757) contributed to many different fields, especially the study of insects. In 1730, Réaumur proposed a temperature scale based on a principle known as the “octogesimal division,” resulting in the freezing and boiling points of water being defined as 0 and 80 °Ré respectively. The reasons why Réaumur chose the 80 degree value are long and complicated. Somewhat surprisingly (at least to me), the Réaumur scale was used widely in Europe, particularly in France, Germany, and Russia. It was also referenced in the works of Dostoyevsky, Flaubert, Tolstoy, and Nabokov. For example, at the beginning of Book X of The Brothers Karamazov by Dostoyevsky, the narrator says, “We had eleven degrees of frost” (i.e., –11 °Ré, which would be equivalent to 7 °F or –14 °C). I’m sure that Réaumur was a nice chap who selected the values on his temperature scale for the best of reasons, but I cannot help but think of the skit in Monty Python and the Holy Grail where the “Insulting Frenchman” proclaims: “Your mother was a hamster and your father smelt of elderberries, now go away or I shall taunt you a second time!”  

Conversion Rates and Converter

Fahrenheit to Celsius: Subtract 32, then multiply by 5, then divide by 9 Celsius to Fahrenheit: Multiply by 9, divide by 5, then add 32 Kelvin to Celsius: Add 273.16 Celsius to Kelvin: Subtract 273.16 Fahrenheit to Kelvin: Subtract 32, multiply by 5, divide by 9, then add 273.16. Kelvin to Fahrenheit: Subtract 273.16, multiply by 1.8, then add 32. If you get a moment, you really should visit the OmniCalculator.com website, which offers a treasure trove of information. In addition to 895 calculators (the number goes up day-by-day), they provide all sorts of additional information that I love to read (see A Calculator for All Seasons). Of particular interest in the context of this column is the fact that they provide a handy-dandy Temperature Conversion Calculator that addresses all of the temperature scales we’ve discussed in my columns (apart from the Cricket Chirp scale, which is served by its own calculator).  
Temperature Conversion
Phew! When I first started my quest to introduce the various temperature scales, I had no idea how much there was going to be (in reality, of course, we’ve only scratched the surface of this teasingly tricky topic). On the bright side, I’ve learned lots on nuggets of knowledge and tidbits of trivia that I will be using for years to come. I hope you’ve enjoyed reading all this, and I also hope you will share your thoughts, along with any other thought-provoking morsels, in the comments below.

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Aubrey Kagan

It seems totally illogical to me that anyone could conceive the going from freezing to boiling should be a decreMental process. Shows how much we (or at least I) have been conditioned.

Do you suppose there are other scales which are measured as decrement when logically increases? I still find conductivity a little disconcerting.

Aubrey Kagan

Is anyone else having speed issues writing comments on this web site and scrolling . Each keystroke takes about 10 seconds. I an using Chrome on my iPad.

Aubrey Kagan

No VPN or anything like that. Typing this now, using Windows and Chrome at work has no issue at all.

Yes, I know- I should stop using my iPad then. But the desire to contribute arises more often when the work day has slowed down and I have a chance to ruminate as I lounge around when I get home. Also you tend to post towards eventide.

Charles Pfeil

This reminds me of a poster that I saw on the wall in the Intergraph office back in the early 90s. It said “The nice thing about standards is that there are so many to choose from – Andrew S. Tanenbaum.”

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