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This is similar to, but not quite a duplicate, of Why isn't temperature measured in joules per mole (J/mol)? , which underspecifies Joule/mol rather than "mean disordered translational kinetic energy per direction per mole", and Why isn't temperature measured in Joules? which suggests energy/particle rather than per mole and doesn't work with macroscopic units

One of the main advantages of the SI unit system is that units are consistent, such that conversion factors are nearly always 1. For example, $F=ma$ using $N$,$kg$,$ms^{-2}$, compared to $F=0.031ma$ in $lbf$, $lb$, $fts^{-2}$, with the non-unity constant $0.031\frac{lbf}{lb.ft.s^{-2}}$. Normally when an equation has a fixed constant, that constant has a physical meaning (such as $g$ in weight=$mg$).

However, the universal gas constant seems like it's a non-unity conversion factor between $J/mol$ and $K$. So we get $PV=n\overline{R}T$, instead of the $PV=nT$ if temperature were defined as "mean disordered translational kinetic energy per direction per mole", with a unit of Joule per mole. ($\overline{R}$ is the universal gas constant in the convention I'm using, where overlines denote molar quantities)

And similarly we currently have the molar heat capacities $\overline{c_v}=\frac{d}{2}\overline{R}$, where $d$ is the number of fully-excited degrees of freedom, rather than $\overline{c_v}=\frac{d}{2}$.

So the question(s):

-Why is $K$ used rather than the more consistent unit of $J/mol$, specifically Joule of disordered translational kinetic energy per direction per mole?

-Is there any actual advantage to having the size of $1K$ derived from the original size of $1^oC$ (other than slight extra convenience with heating water, in which case why is $J$ the SI unit for energy rather than $cal$)?

-Does the universal gas constant have any physical meaning beyond being a conversion factor?

-Is this something that could ever be changed (such as people using $J/mol$ with the above caveats alongside $K$, until $K$ becomes obsolete, with the approval or support of BIPM), or is it too deeply embedded like the other non-ideal convention quirks (kg being SI unit rather than g, sign convention for charge being the wrong way round)?

sqek
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    99.999% of the population has no idea what a Joule or mol is. Changing a century old unit to convenience a handful of people seems overboard. Besides, I prefer eV as the temperature unit, so we should change to that instead. – Jon Custer May 20 '22 at 14:57
  • People who don't know what a Joule or mol is use degrees centigrade or Fahrenheit depending on continent. Kelvin is exclusively used in science, so surely it makes sense to make it convenient for scientists? – sqek May 20 '22 at 15:05
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    When the meter was redefined in terms of the speed of light, the SI could have thrown it out, and adopted the foot, slightly redefined so that the conversion was 1 Gft/s. But they didn't ツ – John Doty May 20 '22 at 15:07
  • Well, as I said, I prefer eV so you need to change "K" to make it equal to 1 eV/mol so it would be convenient for me. Or, scientists just learn to deal with units and convert between them as needed, which we already do. Your convenience is my pain in the neck. – Jon Custer May 20 '22 at 15:07
  • @JohnDoty - with a little poetic license, we could have defined a pentameter. Then a unit of force called the iam, so torque would be in units of iambic pentameters... – Jon Custer May 20 '22 at 15:08
  • @JonCuster to be pedantic, eV isn't a unit of temperature, eV/particle is. If using macroscopic equivalents of electron charge (coulomb) and particle (mol), you get coulomb-volt/mol, or J/mol. Yes unit selection is arbitrary, but there are a set of behaviours that make SI more convenient for technical work than imperial, one of which is broken by the choice of K, trying to find out why (also should we move the discussion and puns to chat?) – sqek May 20 '22 at 15:25

1 Answers1

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Historical reasons.

The Kelvin unit stems from the Kelvin scale, which in turn is a shifted Celsius scale.

The Metre convention happened in 1875 and while the gas constant was scentifically introduced an year or two earlier, its importance was not recognized until much later.

This is why meter and kilogram are somewhat related (sizes and masses were known to appear in everyday calculations for centuries) and everything else is "we just settle on something and we agree on how to reproduce it, right?".

(I am still lost about why candela is a base unit as of 2022.)

fraxinus
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