JEE Mains · Physics · STD 11 - 11. thermodynamics
Consider the efficiency of Carnot's engine is given by \(\eta=\frac{\alpha \beta}{\sin \theta} \log _{e} \frac{\beta x}{k T}\), 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.
- A Dimensions of \(\beta\) is same as that of force.
- B Dimensions 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 Dimensions of \(\alpha\) is same as that of \(\beta\)
Answer & Solution
Correct Answer
(D) Dimensions of \(\alpha\) is same as that of \(\beta\)
Step-by-step Solution
Detailed explanation
\([\alpha \beta]=[\eta]=[\sin \theta]=\) Dimensionless \(\left[\eta^{-1} \sin \theta\right]=[\alpha \beta]=\text { D.L. }\)
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