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Consider the efficiency of Carnot's engine is given by $η = \frac{α β}{\sin θ} \log_{e} \frac{β x}{k T}$ , where $α a n d β$ are constants.
If T is temperature, k is Boltzman constant, $θ$ is angular displacement and x has the dimensions of length. Then, choose the incorrect option.

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Dimension of $η^{- 1} \sin θ$ is same as that of $α β$

Dimensions of $β$ is same as that of force.

Dimension of $α^{- 1}$ x is same as that of energy.

Dimensions of $α$ is same as that of $β$

answer is D.

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Detailed Solution

Here , $β x$ will be having the units of energy.

So $β$ will have same dimensions of force.

$[α β] = [η] = [\sin θ] = D i m e n s i o n l e s s [η^{- 1} \sin θ] = [α β] = D . L .$

So $α^{- 1}$ will have the dimensions of force, So $α^{- 1}$ x will have the dimensions of energy.

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