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Q.

Consider the efficiency of Carnot's engine is given by η = αβsinθlogeβxkT, where α and βare 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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a

Dimension of η-1sinθ  is same as that of αβ

b

Dimensions of β is same as that of force.

c

Dimension of α-1x  is same as that of energy.

d

Dimensions of α is same as that of β

answer is D.

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Detailed Solution

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Here , βx will be having the units of energy.

So β will have same dimensions of force.

αβ = η = sinθ = Dimensionless η-1sinθ = αβ = D.L.

So α-1 will have the dimensions of force, So α-1x will have the dimensions of energy.

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Consider the efficiency of Carnot's engine is given by η = αβsinθlogeβxkT, where α and βare 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.