Consider the efficiency of Carnots engine is given by \( \eta=\frac{\alpha \beta}{\sin \theta} \... VIDEO
Consider the efficiency of Carnots engine is given by \( \eta=\frac{\alpha \beta}{\sin \theta} \log _{e} \frac{\beta x}{k T} \), where \( \alpha \) and \( \beta \) are constants. If \( T \) is temperature, \( k \) is Boltzmann constant, \( \theta \) is angular displacement and \( x \) has the dimensions of length. Then, choose the incorrect option.
(a) Dimension of \( \beta \) is same as that of force.
(b) Dimension of \( \alpha^{-1} x \) is same as that of energy.
(c) Dimension of \( \eta^{-1} \sin \theta \) is same of \( \alpha \beta \).
(d) Dimension of \( \alpha \) is same of \( \beta \).
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