Consider the efficiency| Unit and Measurement |JEE-MAIN 2022

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JEE MAIN 2022

28-07-2022 S2

Question

Consider the efficiency of Carnot's engine is given by $\eta=\frac{\alpha \beta}{\sin \theta} \log _{\mathrm{e}} \frac{\beta \mathrm{x}}{\mathrm{kT}}$, 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.

Select the correct option:

A

dimension of $\beta$ is same as that of force

B

Dimension 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

Dimension of $\alpha$ is same as that of $\beta$

✓ Correct! Well done.

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Solution

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