Stefan-Boltzmann law of radiation

Definition

The Stefan-Boltzmann law of radiation states that the total energy radiated per unit surface area of a black body is directly proportional to the fourth power of the black body's absolute temperature. Mathematically, it is expressed as $E = \sigma T^4$, where $E$ is the emissive power, $\sigma$ is the Stefan-Boltzmann constant, and $T$ is the absolute temperature.

5 Must Know Facts For Your Next Test

1. The Stefan-Boltzmann constant ($\sigma$) has a value of approximately $5.67 \times 10^{-8}$ W/m²K⁴.
2. The law applies specifically to ideal black bodies which are perfect emitters and absorbers of radiation.
3. It indicates that even small increases in temperature result in significant increases in radiative energy output due to the fourth power dependence on temperature.
4. Real objects emit less radiation than a perfect blackbody and their emission can be described using an emissivity factor (ε), modifying the equation to $E = εσT^4$.
5. This law plays a crucial role in understanding stellar physics, particularly in determining the luminosity and temperature relationship for stars.

Review Questions

• What does the Stefan-Boltzmann law state about radiative energy and temperature?
• How does emissivity affect the total energy radiated by real objects compared to ideal black bodies?
• What is the value of the Stefan-Boltzmann constant and what are its units?

Related terms

Black Body: An idealized physical object that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.

Emissivity: A measure of how efficiently an object radiates energy compared to an ideal black body; ranges between 0 and 1.

Wien's Displacement Law: A principle stating that the wavelength at which a black body's radiation spectrum peaks inversely correlates with its absolute temperature.