The entropy of any system is given by

${S}=\alpha^{2} \beta \ln \left[\frac{\mu {kR}}{J \beta^{2}}+3\right]$

Where $\alpha$ and $\beta$ are the constants. $\mu, J, K$ and $R$ are no. of moles, mechanical equivalent of heat, Boltzmann constant and gas constant repectively. [Take ${S}=\frac{{dQ}}{{T}}$ ]

Choose the incorrect option from the following:

• A

  ${S}, \beta, {k}$ and $\mu {R}$ have the same dimensions.

• B

  $\alpha$ and ${J}$ have the same dimensions.

• C

  ${S}$ and $\alpha$ have different dimensions.

• D

  $\alpha$ and ${k}$ have the same dimensions.