The energy density u of a system is given by the relation u = ( x k_B T ) , where x is distance, k_B is the Boltzmann constant, and T is absolute temperature. The SI base unit of the constant is:

Step-by-step solution

The argument of the sine function must be dimensionless. Therefore, [ x k_B T ] = [ M ^0 L ^0 T ^0] The term k_B T represents thermal energy, so its dimensional formula is [ M L ^2 T ⁻²] . Substituting the dimensions of distance x as [ L ] : [ ] = [k_B T] [x] = [ M L ^2 T ⁻²] [ L ] = [ M L T ⁻²] The quantity u is energy density (energy per unit volume), so its dimensional formula is: [u] = [ M L ^2 T ⁻²] [ L ^3] = [ M L ⁻¹ T ⁻²] From the given equation, the dimensions of u must equal the dimensions of : [ ] = [ ] [