An expression of energy density is given by u = α β sin α x k t , where α , β are constants, x is displacement, k is Boltzmann constant and t is the temperature. The dimensions of β will be

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Given that energy density U = α β sin α x k t As α x k t should be dimensionless, the dimensions of α x and k t should be same. ⇒ α x = k t ⇒ α = k t x Now, U = α β ⇒ β = α U = k t x E V = E t t x E V ⇒ β = L 3 L = M 0 L 2 T 0

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