Ideal gas constant applied to water, lead, and other non-gases

I've asked a number of chemists why the ideal gas constant is in the equation for Gibbs free energy, and all say the same thing: "The name is a relic of the argon gas chamber used to determine energy and temperature at different pressures and temperatures, but it applies to every thermodynamic system." This sounds great and I understand names of constants can be relics, but why can a conversion factor that only appears to pertain to ideal gases be used for other substances? *R* assumes elastic collisions, where energy is not lost during molecular collisions, but only ideal gases have this property. Wouldn't you use a different conversion factor for something much denser and fluid like water or even more dense like lead to convert from temperature to energy? I've heard that *R* is used for free electrons as well, which are pretty different from atoms much less gases. Would "*R*-specific" be best to use everywhere, as I've heard they do in engineering, so maybe every substance has its own temperature-energy conversion factor? 




It is a very good question: Why does R appear everywhere in equations even though it is *apparently* related to or derived from the ideal gas law? Yes historically R was derived from the limiting gas law in the 1830s.


The beauty of R is that it is related to two physical constants called the Boltzmann constant and Avogadro's constant. Read here 


<https://en.wikipedia.org/wiki/Gas_constant#Relationship_with_the_Boltzmann_constant>


The Boltzmann constant appears everywhere in thermodynamics, semiconductors and statistical mechanics: <https://en.wikipedia.org/wiki/Boltzmann_constant>




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> 
> "The name is a relic of the argon gas chamber used to determine energy
>  and temperature at different pressures and temperatures, but it
>  applies to every thermodynamic system."
> 
> 
> 


I feel this is nothing but fiction. Not sure why people make up stories. William B Jensen traces the history of R in the Journal of Chemical Education.


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The profoundly universal significance of $\rm\bf R$ ultimately stems from Boltzmann's [equipartition theorem](https://en.wikipedia.org/wiki/Equipartition_theorem), which states that (roughly speaking) you are guaranteed to have $\rm kT/2$ of energy per one *degree of freedom* of whatever nature, or, consequently, $\rm{\bf R}T/2$ per mole of those. It is only in **this** sense that $\rm\bf R$ may be perceived as a some kind of intermediary between temperature and energy. Real compounds all have different number of degrees of freedom, and hence different temperature-to-energy coefficients (*[heat capacities](https://en.wikipedia.org/wiki/Heat_capacity)*, as we call them).


So you see that $\rm\bf R$ is not derived from ideal gases at all, to the point that calling it the "*ideal gas constant*" might be considered a misnomer. Their relation is of different nature. Like all ideal things, ideal gases are simple; they only have 3 well-defined degrees of freedom per particle, hence the simple formula for their heat capacity. No wonder it is hinged on a universal constant.


Long story short, your bewilderment is misplaced. It is as if we happened to name $\rm CO$ *"the Ford gas"*, because of its presence in the exhaust of Ford cars, and then marveled at its widespread appearance in nature, all the way up to deep space. How could old man Ford put it there? **He didn't**.


So it goes.


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