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 EXPONENTIAL TEMPERATURE SYSTEM. Do NOT delete this tag too soon.}}

Since the invention of the thermometer, a number of different temperature scales have been proposed. In modern times, most of the world uses {{w|Celsius}} for everyday temperature measurements, as it is part of the {{w|metric system}} that has been widely adopted for official uses. A small number of countries (namely Liberia, the USA and its three associated free states in the Pacific) retain the US customary (or 'imperial') system, which uses the ''slightly'' older {{w|Fahrenheit}} scale (°F was initially proposed in 1724, and refined in later years; °C, more or less as we currently know it, was established in 1743). The other widely used temperature scale is {{w|kelvin}}, which uses the same scale 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 Fahrenheit, is now officially defined directly against the kelvin). Even in countries that use Fahrenheit regularly, scientific measurements are typically done in Celsius and/or kelvin.

The strip proceeds to compare these scales, and a number of others, on a scaled of "cursed"-ness. The joke is highlighting how strange and generally difficult to use many older proposed systems were. All of the listed scales are real, but may be considered obsolete to varying degrees. See also [[1923: Felsius]], a combination of 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 || Celsius (°C) is defined (indirectly, these days, by way of comparison to kelvin) so that the freezing and boiling points of pure water at standard atmospheric pressure are 0 and 100 degrees respectively. This is considered the joint least-cursed temperature system (along with kelvin), amongst those with a meaningful rank given. An inherent degree of cursedness is therefor implied for all systems.
|-
| {{w|Kelvin}} || 273.15 || 373.15 || 0K is absolute zero || 2/10 || Kelvin (officially written in full with a small-k, when not given a grammatical capital; or a large-K as its symbol, without any "degrees" glyph) is a scientific unit of measure invented by {{w|Lord Kelvin}} that intends to use the same scale as degrees Celsius, but is offset by 273.15, in order to set the zero point at absolute zero (by way of using the {{w|Boltzmann constant}}, as of 2019). This is very practical for the math of thermodynamics, but unintuitive for non-expert users. Kelvin and Celsius are, by far, the most common units used in scientific measurements and calculations, which feature heavily in Randall's experience. Their more global utility and consistency seem to make them the least "cursed".
|-
| {{w|Fahrenheit}} || 32 || 212 || Outdoors in most places is between 0–100 || 3/10 || Fahrenheit (°F) is officially used in several countries across the globe, and unofficially in several others. It was derived in an era where factors of 360 were more popular in science than powers of ten, so water freezing and water boiling were calibrated to be 180° apart. In addition, Daniel Fahrenheit believed that pure water freezing was not worthy of the 0° benchmark and resolved to set 0° to the coldest possible temperature he could create: the freezing point of ammonium chloride brine. While modern scholars find these benchmarks arbitrary and outdated, it gained usage, primarily in Anglophone countries, likely due to the scale being considered intuitively useful for some common functions. The range roughly matches the typical span of temperatures, for various commonly encountered weather conditions across various latitudes/seasons, and the 100 point is quite near normal human body temperature (though 90 was initially presumed to be this). Due to later revisions, 4&nbsp;°F is now the temperature of the original brine/ice point. While it was largely displaced by the Celsius scale, the US, [[Randall]]'s home country, continues to typically use it. It is ranked as slightly more cursed than Celsius.
|-
| {{w|Réaumur scale|Réaumur}} || 0 || 80 || Like Celsius, but with 80 instead of 100 || 3/8 || Often abbreviated to °Ré, a historical French system used in some places until the early 20th century. In modern times mostly used in cheesemaking. 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, labelling 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 || Usually abbreviates as °Rø, created by the Danish astronomer Ole Christensen Rømer in around 1702, while the Fahrenheit scale was proposed in 1724. Much like Fahrenheit, it uses 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 Ole Rømer, but the scale was later updated to fix it to 7.5.  The scale is also the last common ancestor of Celsius and Fahrenheit, as Reuamur was inspired by it, and Celsius by Reamur, and Fahrenheit specifically wanted a Rømer scale with more steps to avoid using decimals.
|-
| {{w|Rankine scale|Rankine}} || 491.7 || 671.7 || Fahrenheit, but with 0°F [''sic;'' should be 0°R] set to absolute zero  || 6/10 || As the chart mentions, Rankine (°Ra) 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. By rating, it is inexplicably more "cursed" than the otherwise identical Fahrenheit, ''despite'' being rooted at a more practical zero-point. [[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 || Created by Isaac Newton, measuring "degrees of heat", usually given the °N symbol. The cursedness rating (7-ish/10) is a joke 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 potter Josiah Wedgwood in the 18th century. The measurement (°W) was based on the shrinking of clay when heated above red heat, but was found to be very inaccurate. The comic has a typo, as the scale is called Wedgwood (''without the e''). 
|-
| Galen || –4? || 4?? || Runs from –4 (cold) to 4 (hot). 0 is "normal"(?) || 4/–4 || {{w|Galen}}, in his medical writings, is said to have proposed a standard "neutral" temperature made up of equal quantities of boiling water and ice; on either side of this temperature were four degrees of heat and four degrees of cold, respectively. The rating (4/–4) is a joke about the scale (with no common abbreviation) being defined between positive and negative 4, and at face value could be interpreted as –100% cursedness (the least of all those given), though it's not clear what negative cursedness would mean, or "cursedness" itself.
|-
| {{w|Celsius#History|''Real'' Celsius}} || 100 || 0 || In Anders Celsius's original 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 (an indefinite range of them) will be negative. The rating (10/0) is a joke on the scale "flipping" the fixed points of modern Celsius. Division by zero is problematic, so this rating may either be undefined/undefinable or "infinitely" cursed.
The original logic was that zero could be easily calibrated to the height of a 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 direction 'survives' in the historic {{w|Delisle scale}}, which predates (and arguably helped greatly inspire, though with a different factor) the classic version of °C. The version originally used by Anders was only 'corrected' posthumously, but nobody seemed bothered enough to do the same with Delisle's scale.
|-
| [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. The scale is defined so that absolute zero is at negative infinity, with the exponent chosen to match Celsius at 0 and 100. 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 10/10, 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." || ''not provided'' || 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.[https://wmo.asu.edu/content/world-lowest-temperature] The average surface temperature as of 2023, the most recent available, is 14.4°C (57.2°F.)[https://climate.copernicus.eu/climate-indicators/temperature] 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.[https://wmo.asu.edu/content/world-highest-temperature]

Usually temperature records are measured at a fixed distance above ground, to consistently represent the temperature of the air, as temperatures of the actual surface (and just above it) can be much higher. It is uncertain if Randall actually meant "surface" or just the usual ground-station temperature records (as opposed to upper-atmospheric measurements) like the ones mentioned here.

{{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

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 low and high temperature records now being broken nearly every year as a result of {{w|climate change}}, and the average constantly changing by {{w|random walk}}ing, this scale is necessarily recalibrated each year. While extreme values like Absolute Zero or the {{w|Tungsten#Physical properties|melting point of tungsten}} will shift more significantly over time, everyday temperatures will need adjustment much less and the latest low/high/average values will (by definition) only ever be 0, 100 and 50. No indication of cursedness is given, being outside the comic's table, but it won't be zero.
|}

==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

{{comic discussion}}

[[Category:Charts]]
[[Category:Science]]