Question

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 Boltzman constant, $\theta$ is angular displacement and $x$ has the dimensions of length. Then, choose the incorrect option.

• A. Dimensions of $\beta$ is same as that of force.
• B. Dimensions of $\alpha^{-1} x$ is same as that of energy.
• C. Dimensions of $\eta^{-1} \sin \theta$ is same as that of $\alpha \beta$
• D. Dimensions of $\alpha$ is same as that of $\beta$

Answer 1

Answer: (D)

$ {[\alpha \beta]=[\eta]=[\sin \theta]=\text { Dimensionless }} $
$ [\eta^{-1} \sin \theta]=[\alpha \beta]=\text { D.L. }$