Question

As per the Stefan-Boltzmann law the total energy emitted by a black body is directly proportional to

• A. The third power of its absolute temperature
• B. The fourth power of its absolute temperature
• C. The fifth power of its absolute temperature
• D. The sixth power of its absolute temperature

Hint:

The Stefan-Boltzmann law (\( E = \sigma T^4 \)) shows that a black body’s emitted energy increases rapidly with temperature (\( T^4 \)).

Answer 1

The Correct Option is B

Step 1: Recall the Stefan-Boltzmann law.
The Stefan-Boltzmann law describes the total energy radiated by a black body, which is an idealized object that absorbs all incident radiation and emits the maximum possible radiation at a given temperature. The law states: \[ E = \sigma T^4, \] where:
\( E \): Total energy emitted per unit area per unit time (W/m²),
\( \sigma \): Stefan-Boltzmann constant (\( 5.670 \times 10^{-8} \, \text{W/m}^2\text{K}^4 \)),
\( T \): Absolute temperature of the black body (in Kelvin).
The total energy emitted is directly proportional to the fourth power of the absolute temperature. Step 2: Evaluate the options.
(1) The third power of its absolute temperature: Incorrect, as the exponent in the Stefan-Boltzmann law is 4, not 3. Incorrect.
(2) The fourth power of its absolute temperature: Correct, as the Stefan-Boltzmann law states \( E \propto T^4 \). Correct.
(3) The fifth power of its absolute temperature: Incorrect, as the exponent is 4, not 5. Incorrect.
(4) The sixth power of its absolute temperature: Incorrect, as the exponent is 4, not 6. Incorrect.
Step 3: Select the correct answer.
As per the Stefan-Boltzmann law, the total energy emitted by a black body is directly proportional to the fourth power of its absolute temperature, matching option (2).