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:

Q: 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:

d $S=\alpha^{2} \beta \ell {n}\left(\frac{\mu K R}{j \beta^{2}}+3\right)$ $S=\frac{Q}{T}=\text { Joule } / k$ $P V=n R T \quad\left[\frac{\mu K R}{J \beta^{2}}\right]=1$ ${R=\frac{\text { Joule }}{K}}$ ${\Rightarrow \beta=\left(\frac{\text { Joule }}{K}\right)}$ ${\Rightarrow \alpha=\text { dimensionless }}$

Question

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.

JEE MAIN 2021, Diffcult

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