Editing 3001: Temperature Scales

{{comic
| number    = 3001
| date      = October 21, 2024
| title     = Temperature Scales
| image     = temperature_scales_2x.png
| imagesize = 740x535px
| noexpand  = true
| titletext = In my new scale, °X, 0 is Earths' record lowest surface temperature, 50 is the global average, and 100 is the record highest, with a linear scale between each point and adjustment every year as needed.
}}

==Explanation==

Since the invention of the {{w|thermometer}}, a number of different {{w|temperature}} scales have been proposed. In modern times, most of the world uses the 1745 {{w|Celsius}} scale for everyday temperature measurements. A small number of countries (the USA and {{w|Territories of the United States|its territories}}, the Bahamas, Belize, the Cayman Islands, Liberia, and Palau) retain the {{w|Imperial units|imperial system}} (or the related {{w|United States customary units|US customary system}}), which uses the 1724 {{w|Fahrenheit}} scale. The other widely used temperature scale is the 1848 {{w|Kelvin}} scale, which uses the same degrees as Celsius, but is rooted at {{w|absolute zero}}, making it both useful in scientific calculations and easy to convert to and from Celsius (which, along with degrees Fahrenheit, is now defined relative to kelvins.) The Kelvin scale has been part of the widely adopted official {{w|metric system}} since 1954. Even in countries that use Fahrenheit, scientific measurements are usually made in degrees Celsius or kelvins.

The comic compares these scales, and a number of others, on [[Randall]]'s scale of "cursedness." The joke is highlighting how different the temperature scales are, and how impractical most of them are. All of the listed scales (except Randall's new °X scale defined in the title text) are real, but most are obsolete. See also [[1923: Felsius]].

{| class=wikitable
! scope="col" | Unit
! scope="col" | Water freezes
! scope="col" | Water boils
! scope="col" | Notes
! scope="col" | Cursedness
! scope="col" | Explanation
|-
| {{w|Celsius}} || 0 || 100 || Used in most of the world || 2/10 || The Celsius (°C) scale, also known as "centigrade", was devised by Swedish astronomer {{w|Anders Celsius}} in 1742 and revised in 1745, a year after his death. 0°C represents the freezing point of water and 100°C represents the boiling point, both under {{w|standard atmospheric pressure}}. The Celsius scale is now defined in terms of kelvin. By the given "cursedness," it is regarded as one of the least problematic temperature scales.
|-
| {{w|Kelvin}} || 273.15 || 373.15 || 0K is absolute zero || 2/10 || Kelvins (plural with a lowercase 'k' as a temperature unit, like meters, ohms, watts, and amps; or as the symbol 'K', without the degrees symbol '°', unlike most other such units) are a unit of temperature devised by {{w|Lord Kelvin}} in 1848. They use the same degrees as Celsius do, but shifted by 273.15 to set absolute zero at 0K (based on the {{w|Boltzmann constant}}.)
<center>Celsius = kelvin – 273.15</center>
<center>kelvin = Celsius + 273.15</center>
While kelvins are very useful for calculations in {{w|thermodynamics}} and material physics, they can be unintuitive to laypersons.
|-
| {{w|Fahrenheit}} || 32 || 212 || Outdoors in most places is between 0–100 || 3/10 || Fahrenheit (°F) is officially used in a few countries and informally in several others. It originated in a time when factors of 360 (amount of ''degrees'' in a circle) were favored in science over powers of 10, which is why the freezing and boiling points of water are set 180° apart. Devised around 1724, {{w|Daniel Fahrenheit}} chose to base 0° on the coldest temperature he could achieve: the freezing point of an {{w|ammonium chloride}} {{w|brine}} solution.
<center>Celsius = (Fahrenheit – 32) × 5/9</center>
<center>Fahrenheit = Celsius × 9/5 + 32</center>
Although those reference points are now considered arbitrary and outdated by modern scholars, the scale gained popularity in Anglophone countries, and - as Randall notes - some retroactive justification coined that claims 0°F to 100°F as covering the entire range of temperatures humans would encounter in daily life. 100°F is {{w|Human body temperature#Historical understanding|close to normal human body temperature}} (the original intent was to set 90°F as exactly this, 90 being a quarter of 360). The Fahrenheit scale remains officially used only in the U.S., its territories, the Bahamas, Belize, the Cayman Islands, Liberia and Palau.
|-
| {{w|Réaumur scale|Réaumur}} || 0 || 80 || Like Celsius, but with 80 instead of 100 || 3/8 || Abbreviated as °Ré, this system devised by {{w|René Antoine Ferchault de Réaumur}} in 1730 was used in some places until the early 20th century, mostly for cheese-making.
<center>Celsius = Réaumur / 0.8</center>
<center>Réaumur = Celsius × 0.8</center>
The rating (3/8) is a joke on the boiling point of water in this system being 80 instead of 100 as it is in the Celsius scale; converting this to an out-of-ten scale would give 3.75/10, labeling it as more cursed than Fahrenheit but less so than Rømer.
|-
| {{w|Rømer scale|Rømer}} || 7.5 || 60 || Fahrenheit precursor with similarly random design || 4/10 || Abbreviated as °Rø, this scale was created by the Danish astronomer {{w|Ole Rømer}} around 1702. Much like Fahrenheit, it originally used the freezing point of ammonium chloride brine as the benchmark for 0°, and the scale is built with factors of 360 in mind with the boiling point of pure water at 60°. Like the Fahrenheit scale, the freezing point of pure water was not originally considered significant by Rømer, but the scale was later updated to give the value of 7.5 at this point.
<center>Celsius = (Rømer – 7.5) × 40/21</center>
<center>Rømer = Celsius × 21/40 + 7.5</center>
The Rømer scale is considered the predecessor of both the Celsius and Fahrenheit scales, because Réaumur was inspired by Rømer's scale, Celsius based his work on Réaumur and Fahrenheit specifically designed his scale with more divisions than Rømer's to reduce the necessity for fractions.
|-
| {{w|Rankine scale|Rankine}} || 491.7 || 671.7 || Fahrenheit, but with 0°F [''sic''; should be 0°Ra] set to absolute zero  || 6/10 || The Rankine scale (°R or °Ra), created by {{w|William Rankine}} in 1859, is to Fahrenheit what the Kelvin scale is to Celsius: an absolute temperature scale. The scale is mostly obsolete, but is still occasionally used in legacy industrial operations where absolute temperature scales are required. It is described as more cursed than the otherwise identical Fahrenheit scale, despite being rooted at a more universal zero point.
<center>Celsius = (Rankine – 491.67) × 5/9</center>
<center>Rankine = (Celsius + 273.15) × 9/5</center>
<center>Rankine = Fahrenheit – 491.67</center>
[[2292: Thermometer]] expresses disdain for this scale.
|-
| {{w|Newton scale|Newton}} || 0 || 33-ish || Poorly defined, with reference points like "the hottest water you can hold your hand in" || 7-ish/10 || The famous scientist and mathematician {{w|Isaac Newton}} published this scale in 1701, which was referred to by the °N symbol. Unfortunately, the degrees of temperature specified do not correlate exactly with amounts of {{w|heat}} because his scale is nonlinear. His scale used three fixed-points: 0ºN, the temperature of air when water begins to freeze, 12ºN, the heat of blood in the human body, and 34ºN, rapidly boiling water.<ref>https://www.whipplemuseum.cam.ac.uk/explore-whipple-collections/meteorology/early-thermometers-and-temperature-scales</ref> Therefore:
<center>Celsius = 37 × Newton / 12 if Newton ≤ 12;<br/>63 × (Newton – 12) / 22 + 37 if Newton > 12</center>
<center>Newton = 12 × Celsius / 37 if Celsius ≤ 37;<br/>22 × (Celsius – 37) / 63 + 12 if Celsius > 37</center>
Very few other than Newton ever used this scale, but it did appear on commercial thermometers around 1758.<ref>https://www.scienceandsociety.co.uk/results.asp?image=10413117&wwwflag=&imagepos=43</ref> The cursedness rating (7-ish/10) jokes about the vagueness of the scale's definition.
|-
| {{w|Wedgwood scale|Wedgwood}} || –8 || –6.7 || Intended for comparing the melting points of metals, all of which it was very wrong about || 9/10 || Created by the potter {{w|Josiah Wedgwood}} in 1782, the '°W' scale was based on the shrinking of clay when heated above red heat, but was found to be very inconsistent.
<center>Celsius = (Wedgwood + 8) × 100/1.3</center>
<center>Wedgwood = (Celsius × 1.3/100) – 8</center>
The comic has a typo, as the scale is actually called Wedgwood, without the second 'e', but is spelled in the comic as "Wedgewood". 
|-
| Galen || –4? || 4?? || Runs from –4 (cold) to 4 (hot). 0 is "normal"(?) || 4/–4 || The Greek physician {{w|Galen}} suggested a "neutral" temperature around 180 AD<ref>https://www.loebclassics.com/view/galen-temperaments/2020/pb_LCL546.3.xml</ref> when he was a prominent physician in the {{w|Roman Empire}}. Created by mixing equal parts of boiling water and ice, on either side of this neutral point he described four degrees of heat and four degrees of cold. Assuming his extremes were those points, Galen's scale is also nonlinear:
<center>Celsius = 22 × (Galen + 4) / 4 if Galen ≤ 0;<br/>78 × Galen / 4 + 22 if Galen > 0</center>
<center>Galen = 4 × Celsius / 22 – 4 if Celsius ≤ 22;<br/>4 × (Celsius – 22) / 78 if Celsius > 22</center>
This range from +4 to –4 is humorously used as its rating, implying –100% cursedness. Technically this makes it the least cursed of all the listed scales, but the idea of negative cursedness, and cursedness itself, is not clear. There is no standard modern abbreviation for Galen's scale.
|-
| {{w|Celsius#History|''Real'' Celsius}} || 100 || 0 || In Anders Celsius's original 1742 specification, bigger numbers are ''colder''; others later flipped it || 10/0 || Most scales' temperatures can be indefinitely large, but have an absolute minimum temperature. By starting at a maximum value and counting down, this scale is indeed cursed, as nearly all possible temperatures through 1.42×10<sup>32</sup>K, the maximum attainable physical temperature,<ref>https://doi.org/10.4236/jamp.2024.1210198</ref> will be negative on this scale. The cursedness rating (10/0) is a joke on the scale "flipping" the fixed points of modern Celsius. Division by zero is strictly undefined (see [[2295: Garbage Math]]) and may be interpreted in a number of counter-intuitive ways.
<center>Celsius = 100 – ''Real'' Celsius</center>
<center>''Real'' Celsius = 100 – Celsius</center>
The original logic was that zero could be easily calibrated to the height of a {{w|Millimetre of mercury|column of mercury}} at the temperature of boiling water, and further measurements then made of the amount it ''reduced'' in height under cooler conditions. This orientation survives in the historic {{w|Delisle scale}} devised in 1732 by French astronomer {{w|Joseph-Nicolas Delisle}}, which arguably inspired the Celsius scale. The scale originally used by Professor Celsius was changed, to more or less the form already described above, after his death in 1745. Delisle's scale was never reversed.
|-
| [https://physics.stackexchange.com/questions/459851/john-daltons-temperature-scale#459863 Dalton] || 0 || 100 || A nonlinear scale; 0°C and 100°C are 0 and 100 Dalton, but 50°C is 53.9 Dalton || 53.9/50 || {{w|John Dalton}} proposed a logarithmic temperature scale in 1802 during his work on what became {{w|Charles's Law}}. The scale is defined so that absolute zero is at negative infinity, with the exponent chosen to match the Celsius scale at 0 and 100:
<center>Celsius = 273.15 × ''e''<sup>(Dalton / 320.55)</sup> – 273.15</center>
<center>Dalton = 320.55 × {{w|Natural logarithm|''ln''(}} (Celsius + 273.15) / 273.15 )</center>
There is no standard abbreviation for Dalton's scale. While Dalton temperature is defined for all positive and negative numbers, the nonlinear scale is difficult to work with since the amount of heat represented by a change of one degree Dalton is not constant. Degrees Dalton differ from Celsius ones by as much as 3.9 degrees between 0 and 100, but diverge much more for more extreme temperatures. The rating (53.9/50) is a joke about the unit, as 53.9 Dalton equates to 50 degrees Celsius — i.e., it could be said to be 107.8% (even more than entirely) cursed.
|-
| °X || 42.9 || 151.4 || '''Title text:''' "In my new scale, °X, 0 is Earths' [''sic''] record lowest surface temperature, 50 is the global average, and 100 is the record highest, with a linear scale between each point and adjustment every year as needed." || Randall has not stated the cursedness of his new scale. || The {{w|Lowest temperature recorded on Earth|record lowest surface temperature on Earth}} as of 2024 is –89.2°C (–128.6°F), recorded at the {{w|Vostok Station|Vostok Research Station}} in Antarctica on July 21, 1983.<ref>https://wmo.asu.edu/content/world-lowest-temperature</ref> The average surface temperature as of 2023, the most recent available, is 14.8°C (58.6°F.)<ref>https://climate.copernicus.eu/climate-indicators/temperature</ref> The {{w|Highest temperature recorded on Earth|record highest temperature}} is 56.7°C (134.1°F), recorded on July 10, 1913 at {{w|Furnace Creek, California|Furnace Creek Ranch}} in Death Valley, California.<ref>https://wmo.asu.edu/content/world-highest-temperature</ref>

{{cot|Derivation and graph}}
To break the scale into two linear parts (below and above 14.8°C), we define two separate equations for each range:

1. Below 14.8°C (from –89.2°C to 14.8°C):
* 0 °X corresponds to –89.2°C
* 50 °X corresponds to 14.8°C

We calculate the slope m₁:

<center>m₁ = (50 – 0) / (14.8 – (–89.2)) = 50 / (14.8 + 89.2) = 50 / 104 ≈ 0.48</center>

Now, using the point (14.8°C, 50 °X), we calculate the intercept b₁:

<center>50 = 0.48 × 14.8 + b₁</center>

<center>50 = 7.1 + b₁</center>

<center>b₁ = 50 – 7.1 = 42.9</center>

Thus, the equation for temperatures '''below 14.8°C''' is:

<center>'''X = 0.48 × C + 42.9'''</center>

2. Above 14.8°C (from 14.8°C to 56.7°C):
* 50 °X corresponds to 14.8°C
* 100 °X corresponds to 56.7°C

We calculate the slope m₂:

<center>m₂ = (100 – 50) / (56.7 – 14.8) = 50 / 41.9 ≈ 1.19</center>

Now, using the point (14.8°C, 50 °X), we calculate the intercept b₂:

<center>50 = 1.19 × 14.8 + b₂</center>

<center>50 = 17.6 + b₂</center>

<center>b₂ = 50 – 17.6 = 32.4</center>

Thus, the equation for temperatures '''above 14.8°C''' is:

<center>'''X = 1.19 × C + 32.4'''</center>

;Freezing and boiling points of water

Freezing point of water (0°C): Since 0°C is below 14.8°C, we use the equation X = 0.48 × C + 42.9:

<center>X = 0.48 × 0 + 42.9 = 42.9</center>

So, '''the freezing point is 42.9 °X.'''

Boiling point of water (100°C): Since 100°C is above 14.8°C, we use the equation X = 1.19 × C + 32.4:

<center>X = 1.19 × 100 + 32.4 = 119 + 32.4 = 151.4</center>

So, '''the boiling point is 151.4 °X.'''

[[File:XvsC.png|400px|center]]

See also [[2701: Change in Slope]] for a general discussion of separate linear scales between three points.
{{cob}}
<center>Celsius = (°X – 42.9) / 0.48 if °X < 50;<br/>or (°X – 32.4) / 1.19 if °X ≥ 50.</center>
<center>°X = 0.48 × Celsius + 42.9 if Celsius < 14.8;<br/>or 1.19 × Celsius + 32.4 if Celsius ≥ 14.8.</center>

Due to average temperature records increasing almost every year as a result of {{w|climate change}},<ref>https://www.space.com/last-12-months-broke-temperature-records</ref> Randall's new °X scale must be re-calibrated each year. While such °X values for everyday temperatures will vary over time, more extreme values like absolute zero or the {{w|Tungsten#Physical properties|melting point of tungsten}} will shift vastly more.

("Surface" temperatures are measured 1.5 meters above ground inside a shaded shelter, to accurately represent air temperature, because measurements closer to the ground are usually quite different due to sunlight, {{w|albedo}}, and the thermal capacity of soil.)
|}

[[File:Temperature Scales.png|center|600px]]

===Examples===

Some temperatures in the above scales:

{| class=wikitable style="text-align: center;"
! Unit scale
! Typical {{w|room temperature}}
! {{w|Properties of water#Melting point|Freezing point of water}}
! {{w|Boiling point#Boiling point of water with elevation|Boiling point of water}}
! Midrange {{w|human body temperature|human body core temperature}}
! Recommended {{w|Refrigerator#Temperature zones and ratings|refrigerator temperature}}<ref>https://www.realsimple.com/food-recipes/shopping-storing/food/refrigerator-temperature</ref>
! Recommended {{w|Refrigerator#Freezer|freezer temperature}}<ref>https://www.fsis.usda.gov/food-safety/safe-food-handling-and-preparation/food-safety-basics/freezing-and-food-safety</ref>
! Typical warm bath temperature<ref>https://www.kohlerwalkinbath.com/blog/everything-you-need-to-know-about-the-ideal-bath-temperature/</ref>
! Typical {{w|Coffee#Brewing|hot coffee}} temperature
|-
| Celsius || 22 °C || 0 °C || 100 °C || 37 °C || 2.5 °C || –18 °C || 39 °C || 77 °C
|-
| Kelvin || 295 K || 273 K || 373 K || 310 K || 276 K || 255 K || 312 K || 350 K
|-
| Fahrenheit || 72 °F || 32 °F || 212 °F || 98.6 °F || 36.5 °F || 0 °F || 102 °F || 171 °F
|-
| Réaumur || 17.6 °Ré || 0 °Ré || 80 °Ré || 29.6 °Ré || 2 °Ré || –14.4 °Ré || 31.2 °Ré || 61.6 °Ré
|-
| Rømer || 19.1 °Rø || 7.5 °Rø || 60 °Rø || 26.9 °Rø || 8.8 °Rø || –2 °Rø || 28 °Rø || 47.9 °Rø
|-
| Rankine || 531 °Ra || 492 °Ra || 672 °Ra || 558 °Ra || 496 °Ra || 459 °Ra || 562 °Ra || 630 °Ra
|-
| Newton || 7.1 °N || 0 °N || 34 °N || 12 °N || 0.8 °N || –5.8 °N || 12.7 °N || 26 °N
|-
| Wedgwood || –7.71 °W || –8 °W || –6.7 °W || –7.52 °W || –7.97 °W || –8.23 °W || –7.49 °W || –7 °W
|-
| Galen || 0 || –4 || 4 || 0.8 || –3.5 || –7.3 || 0.9 || 2.8
|-
| ''Real'' Celsius || 78 || 100 || 0 || 63 || 98 || 118 || 61 || 23
|-
| Dalton || 24.8 || 0 || 100 || 40.7 || 2.9 || –21.9 || 42.8 || 79.6
|-
| °X || 59 °X || 43 °X || 151 °X || 76.4 °X || 44.1 °X || 34.3 °X || 78.8 °X || 124 °X
|-
| Felsius || 47 || 16 || 156 || 67.8 || 19.5 || –9.2 || 70.6 || 123.8
|}

Here are the conversion formulas for the [[1923: Felsius|Felsius scale]]:
<center>Celsius = (Felsius − 16) / 1.4.</center>
<center>Felsius = Celsius * 7/5 + 16.</center>

==Transcript==

:Temperature Scales

:[A table with five columns, labelled: Unit, Water freezing point, Water boiling point, Notes, and Cursedness. There are eleven rows below the labels.]

:[Row 1:] Celsius, 0, 100, Used in most of the world, 2/10
:[Row 2:] Kelvin, 273.15, 373.15, 0K is absolute zero, 2/10
:[Row 3:] Fahrenheit, 32, 212, Outdoors in most places is between 0–100, 3/10
:[Row 4:] Réaumur, 0, 80, Like Celsius, but with 80 instead of 100, 3/8
:[Row 5:] Rømer, 7.5, 60, Fahrenheit precursor with similarly random design, 4/10,
:[Row 6:] Rankine, 491.7, 671.7, Fahrenheit, but with 0°F set to absolute zero, 6/10
:[Row 7:] Newton, 0, 33-ish, Poorly defined, with reference points like "the hottest water you can hold your hand in", 7-ish/10
:[Row 8:] Wedgewood, –8, –6.7, Intended for comparing the melting points of metals, all of which it was very wrong about, 9/10
:[Row 9:] Galen, –4?, 4??, Runs from –4 (cold) to 4 (hot). 0 is "normal"(?), 4/–4
:[Row 10:] ''Real'' Celsius, 100, 0, In Anders Celsius's original specification, bigger numbers are ''colder''; others later flipped it, 10/0
:[Row 11:] Dalton, 0, 100, A nonlinear scale; 0°C and 100°C are 0 and 100 Dalton, but 50°C is 53.9 Dalton, 53.9/50

== References ==
{{reflist}}

{{comic discussion}}

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