Question

Which of the following is correct as per the Stefan-Boltzmann law? (where, $M$ = total radiant emitted from the surface of a material, $\sigma$ = Stefan-Boltzmann constant and $T$ = absolute temperature)

• A. $M = \sigma T^4$
• B. $M = \sigma T^3$
• C. $M = \sigma T^2$
• D. $M = \sigma T$

Hint:

Stefan-Boltzmann law: $M = \sigma T^4$; radiant energy scales with $T^4$.

Answer 1

The Correct Option is A

The Stefan-Boltzmann law describes the power radiated from a black body in terms of its temperature. Mathematically, this law is expressed as:

$M = \sigma T^4$

Where:

• $M$ is the total radiant heat energy emitted from a surface per unit area.
• $\sigma$ is the Stefan-Boltzmann constant with a value of approximately $5.67 \times 10^{-8} \text{Wm}^{-2}\text{K}^{-4}$.
• $T$ is the absolute temperature of the material in Kelvin.

Among the given options, the equation that correctly represents the Stefan-Boltzmann law is: $M = \sigma T^4$