Question

The dimension of radiant emittance of a blackbody as per Stefan-Boltzmann law is:

• A. \( M^0 L^1 T^{-1} \)
• B. \( M^1 L^{-1} T^{-2} \)
• C. \( M^1 L^2 T^{-2} \)
• D. \( M^1 L^0 T^{-3} \)

Hint:

The Stefan-Boltzmann law relates radiant emittance to the fourth power of temperature, which gives the dimension of radiant emittance as \( M^1 L^0 T^{-3} \).

Answer 1

The Correct Option is D

The Stefan-Boltzmann law states that the radiant emittance of a blackbody is proportional to the fourth power of its temperature. The radiant emittance \( E \) is given by: \[ E = \sigma T^4 \] where \( \sigma \) is the Stefan-Boltzmann constant, and \( T \) is the temperature. The dimensions of \( E \) are given by: \[ E = \frac{\text{Energy}}{\text{Area} \cdot \text{Time}} = \frac{M L^2 T^{-2}}{L^2 T} = M T^{-3} \] Thus, the dimension of radiant emittance is \( M^1 L^0 T^{-3} \). Final Answer: (D) \( M^1 L^0 T^{-3} \)