The entropy of any system is given by \ $ S=\alpha^{2} \beta \ln \left[\frac{\mu k R}{J \beta^{2}}+

Question

The entropy of any system is given by \ $ S=\alpha^{2} \beta \ln \left[\frac{\mu k R}{J \beta^{2}}+3ight] $\ where $\alpha$ and $\beta$ are the constants. $\mu, J, K$ and $R$ are number of moles, mechanical equivalent of heat, Boltzmann constant and gas constant respectively. [Take $S=\frac{d Q}{T}$ ]. Choose the incorrect option from the following.\

Professor PC Thomas Classes · Answer

(b) : Dimensions of $S=\left(\frac{Q}{\Delta T}ight)=\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}ight]$ \ Dimensions of $K=\frac{	ext { Energy }}{T}=\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}ight]$ \ Dimensions of $R=\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}ight]$; Dimensions of $J=\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^0ight]$ \ Dimensions of $[\beta]=\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}ight]$; \ Dimensions of $\alpha=\left[\mathrm{M}^0 \mathrm{~L}^0 \mathrm{~T}^0ight]$ \  So, option (b) is correct.