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:

Pick an option to check your answer.

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Answer & Solution

Correct Answer

(D) \(\alpha\) and \({k}\) have the same dimensions.

Detailed explanation

\(S=\alpha^{2} \beta \ell {n}\left(\frac{\mu K R}{j \beta^{2}}+3\right)\)

\(S=\frac{Q}{T}=\text { Joule } / k\)

\(P V=n R T \quad\left[\frac{\mu K R}{J \beta^{2}}\right]=1\)

\({R=\frac{\text { Joule }}{K}}\)

\({\Rightarrow \beta=\left(\frac{\text { Joule }}{K}\right)}\)

\({\Rightarrow \alpha=\text { dimensionless }}\)

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