A Constant Serial Killer

From the post "Copper Coins And Silver Coins" dated 11 May 2016,

$\cfrac{A_v}{N_A}=\cfrac{6.02214e26}{2.73159734e26 }=2.204622\approx2.5\approx \left(\cfrac{3}{2}\right)^2$

$\cfrac{A_D}{A_v}=\cfrac{9.029022e26}{6.02214e26}=1.49930\approx \cfrac{3}{2}$

the ratios appears as numerals coefficients to specific heat capacities for monatomic gas, $\cfrac{3}{2}R$ per mole atoms/particles, and for diatomic gas, $\cfrac{5}{2}R$ per mole molecules/particles.

How did they sneaked in?  And this is way ridiculous, the gas constant $R$ is,

$R=2*\cfrac{4}{3}\pi=8.377580$

twice the leading numeral constant to $A_D$,

$A_{\small{D}}=\cfrac{4}{3}\pi(2c)^3$

the definition of the Durian constant.  And the actual specified values for $R$ is,

$R=8.3144598$

$R$ is just twice the volume of a unit sphere!

Yes, I did it.  Alright!  Wait till you see what temperature in kelvin $K$ is all about...

Note:  Since $R$ has absorbed a $2$ from the $(2c)^3$, we are left to a factor $4$.  That can pop up anywhere as the gas constant $R$ is indeed universal.

The definition of $R$ also suggests that $N_A$, the Avogadro constant is without the factor $\cfrac{4}{3}\pi$.

There might be an error in $R$; that it should be $R\rightarrow \cfrac{1}{2}R$, ie without the factor 2.