A physical quantity X is defined by the relation X = K T^3 , where K is the thermal conductivity, is the Stefan-Boltzmann constant, and T is the absolute temperature. The SI base unit of the quantity X is:

Step-by-step solution

First, we determine the SI base units of thermal conductivity K . From the formula for heat conduction, H = dQ dt = K A T x . The unit of H is J s ⁻¹ = kg m ^2 s ⁻³ . Therefore, the unit of K is kg m ^2 s ⁻³ m ^2 ( K / m ) = kg m s ⁻³ K ⁻¹ . Next, we determine the SI base units of the Stefan-Boltzmann constant . From the Stefan-Boltzmann law, the radiated power P = A T^4 . The unit of P is J s ⁻¹ = kg m ^2 s ⁻³ . Therefore, the unit of is kg m ^2 s ⁻³ m ^2 K ^4 = kg s ⁻³ K ⁻⁴ . The unit of absolute temperature T is