Consider the efficiency of Carnot's engine is given by η = α β sin θ log e β x k T , 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.

Step-by-step solution

Given that, η = α β sin θ log β x k T . Since expression inside the logarithm is dimensionless β x = k T Since the dimensions of k T are equivalent to that of energy, β = k T x = E x = ML 2 T - 2 L = MLT - 2 Therefore, β has dimensions of force. Since efficiency is a dimensionless ratio, α β = M 0 L 0 T 0 ⇒ β = 1 α Therefore, dimensions of α is not same as that of β . Hence option D is incorrect statement and the answer. x α = β x