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.
