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Consider the efficiency of carnot’s engine is given by η = (αβ/sinθ) log e (βx/kT) 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 incorrect option. (1) Dimensions of β is same as that of force. (2) Dimensions of α−1x is same as that of energy. (3) Dimensions of η−1 sinθ is same as that of αβ. (4) Dimensions of α is same as that of β.
- Dimensions of β is same as that of force.
- Dimensions of α−1x is same as that of energy.
- Dimensions of η−1 sinθ is same as that of αβ.
- Dimensions of α is same as that of β.
Correct answer: Dimensions of η−1 sinθ is same as that of αβ.
Solution
The efficiency η is a dimensionless quantity, and since sinθ is also dimensionless, η⁻¹ sinθ remains dimensionless. Therefore, it must have the same dimensions as αβ, which is consistent with the equation, making this option correct.
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