An expression for a dimensionless quantity P is given by P = α β log e k T β x ; where α and β are constants, x is distance; k is Boltzmann constant and T is the temperature. Then the dimensions of α will be

Step-by-step solution

Given p = α β ln k T β x We know that expression inside log is dimensionless. Therefore,   k T β x is dimensionless ⇒ β = k T x = ML 2 T - 2 K - 1 × K × L - 1 = MLT - 2 Since p is dimensionless ∴   p = α β = M 0 L 0 T 0 ⇒ α = β ⇒ α = MLT - 2