The entropy of any system is given by, S = α ^ 2 [ J β ^ 2 + 3]...

S = {\alpha}^{2}\betaℓn\left(\dfrac{\mukR}{J{\beta}^{2}} + 3\right)$<br />$S = \dfrac{Q}{T} = Joule{k}^{- 1}$<br />\left[{\alpha}^{2}\beta\right] = Joule{k}^{- 1}$
$PV = nRT\left[\dfrac{\mukR}{J{\beta}^{2}}\right] = 1$

$R = \dfrac{\text{Joule}}{k}$
$⇒ R = \dfrac{\text{Joule}}{k}, k = \dfrac{\text{Joule}}{R}$
$⇒ \beta = \left(\dfrac{\text{Joule}}{k}\right)$
${\alpha}^{2}\beta = \left(\dfrac{\text{Joule}}{k}\right)$
$⇒ \alpha =$ dimensionless