Consider the efficiency of carnot's 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 :

Question

Dimensions of $\beta$ is same as that of force.

Dimensions of $\alpha^{-1} x$ is same as that of energy.

Dimensions of $\eta^{-1} \sin \theta$ is same as that of $\alpha \beta$.

Dimensions of $\alpha$ is same as that of $\beta$.

Solution

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