Question

Consider the efficiency of Carnot's engine is given by $η=\frac {αβ}{sinθ}log_e\frac {βx}{kT}$, where $α$ and $β$ are 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.

• A. Dimensions of $β$ is same as that of force.
• B. Dimension of $α^{-1}x$ is same as that of energy.
• C. Dimension of $η^{-1} sinθ$ is same as that of $αβ$.
• D. Dimensions of $α$ is same as that of $β$

Answer 1

Answer: (D)

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

Answer 2

Here , $βx$ will be having the units of energy.

So $β$ will have same dimensions of force.

$αβ=η=sin θ$ =Dimentionless $η^{-1}sinθ =αβ$ =D.L.

So $α^{-1}$ will have the dimensions of force.

So $α^{-1}x$ will have the dimensions of energy.