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Q.

Consider the efficiency of carnot’s engine is given by $η = \frac{α β}{\sin θ} \log_{e} (\frac{β x}{k T})$ , where $α and β$ are constants. If $T$ is temperature, $k$ is Boltzmann constant, $θ$ is angular displacement and $x$ has the dimensions of length. Then, choose the correct option:

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a

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

b

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

c

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

d

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

answer is A, B, C.

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Detailed Solution

$[α β] = [η] = [\sin θ] =$ Dimensionless
So, $[α] \times \frac{1}{[β]} \Rightarrow [α] \neq [β]$
$[η^{- 1} \sin θ] = [α β] = D . L$

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Consider the efficiency of carnot’s engine is given by η=αβsinθloge(βxkT), where α and β are constants. If T is temperature, k is Boltzmann constant, θ is angular displacement and x has the dimensions of length. Then, choose the correct option: