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==
{{incomplete|Created by an TOTALLY CONFORMING TEMPERATURE SYSTEM. Do NOT delete this tag too soon.}}

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 1742 {{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}}, which uses the same scale as degrees 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 °Fahrenheit, is now officially defined relative to kelvins). Kelvins have 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 kelvin.

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 are real, but may be considered obsolete to varying degrees. Please see also [[1923: Felsius]], a combination of degrees Fahrenheit and Celsius.

{| 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 kelvins. 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 || Kelvin (plural with a lowercase 'k' as a temperature unit; or as the symbol 'K', without the degrees symbol '°', unlike most other such units) is a unit of temperature devised by {{w|Lord Kelvin}} in 1848. It uses the same scale as Celsius but is 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 kelvin is very useful for calculations in {{w|thermodynamics}} and material physics, it 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 were favored in science over powers of ten, which is why the freezing and boiling points of water are set 180° apart. Devised around 1724, {{w|Daniel Fahrenheit}} chose not to base 0° on the freezing point of water, instead ofiginally setting it at 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 because everyday weather conditions usually fall handily all across the range 0–100°F, and 100°F is {{w|Human body temperature#Historical understanding|coincidentally close to normal human body temperature}}. The Fahrenheit scale remains officially used only in Randall's home country (the U.S., and 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 Celsius; 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 (°Ra), devised in 1859 by {{w|William Rankine}}, is to Fahrenheit what kelvin is to Celsius, an absolute scale rather than a relative one. 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>
Another comic, [[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 the °N symbol. Sadly, the degrees of temperature specified do not correlate exactly with amounts of {{w|heat}}. The cursedness rating (7-ish/10) is a joke about the vagueness of the scale's definition.
<center>Celsius = Newton × 100/33</center>
<center>Newton = Celsius × 33/100</center>
Very few scientists other than Newton ever used this scale,{{Actual citation needed}} but it did appear on commercial thermometers around 1758.<ref>https://www.scienceandsociety.co.uk/results.asp?image=10413117&wwwflag=&imagepos=43</ref>
|-
| {{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 inaccurate.
<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 called Wedgwood, without the second 'e'. 
|-
| 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 A.D.,<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.
<center>Galen = ((Celsius - 22) / 100) × 8</center>
<center>Celsius = (Galen × 100 / 8) + 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 (or cursedness itself) would be Randall's invention. 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 (possibly to the equivalent of 1.42x10<sup>32</sup>K, considered [https://doi.org/10.4236/jamp.2024.1210198 the maximum attainable physical temperature]) will be negative in this implementation. 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 only changed, 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 Celsius at 0 and 100:
<center>Dalton = 320.55 × {{w|Natural logarithm|''ln''(}} (Celsius + 273.15) / 273.15 )</center>
<center>Celsius = 273.15 × ''e''<sup>(Dalton / 320.55)</sup> - 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 differs from Celsius by as much as 3.9 degrees between 0 and 100, but diverges much more for more extreme temperatures. The rating (53.9/50) is a joke about the unit, as 53.9 Dalton would be 50 degrees Celsius — i.e., the cursedness could be understood as 50/50, or entirely cursed, but perhaps instead as 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>

"Surface" temperatures are measured at 1.5 meters above ground inside a shaded shelter, to accurately represent the temperature of the air, because temperatures closer to the ground are often quite different due to the heating effects of sunlight (or a lack therof, e.g., at night or under clouds), and the thermal capacity of soil.

{{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}}
Due to high and average temperature records now increasing almost every year as a result of {{w|climate change}}, Randall's new °X scale must be re-calibrated each year. While the value given to everyday (non-record) 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.

==Trivia==

Here are the {{w|room temperature}}, water freezing and boiling, {{w|human}} {{w|Thermoregulation|body temperature}}, recommended refridgerator and freezer, warm bath, and hot coffee temperature values for those scales:

;[Warning, not proofread.]

{| class=wikitable style="text-align: center;"
! Unit scale
! Room temperature
! Water freezing temperature
! Water boiling temperature
! Body temperature
! Recommended refrigerator temperature
! Recommended freezer temperature
! Warm bath temperature
! 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 || -0.4 °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 || 7.3 °N || 0 °N || 33 °N || 12.2 °N || 0.8 °N || -5.9 °N || 12.9 °N || 25.4 °N
|-
| Wedgwood || -7.71 °W || -8.00 °W || -6.70 °W || -7.52 °W || -7.97 °W || -8.23 °W || -7.49 °W || -7.00 °W
|-
| Galen || 0.00 || -1.76 || 6.24 || 1.20 || -1.56 || -3.20 || 1.36 || 4.40
|-
| ''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
|}

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:Temperature Scales

:[A table with five columns, labelled: Unit, water freezing point, water boiling point, notes, 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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