Stefan-Boltzmann & Blackbody Radiation Cheat Sheet

Key Facts

• The Stefan-Boltzmann law for total emitted power is $P = \sigma A T^{4}$ for an ideal blackbody.
• For a real surface, emitted power is $P = e\sigma A T^{4}$, where $0 \le e \le 1$ is emissivity.
• The net radiated power between an object and its surroundings is $P_{\text{net}} = e\sigma A\left(T^{4} - T_{\text{surr}}^{4}\right)$.
• The Stefan-Boltzmann constant is $\sigma = 5.67 \times 10^{-8}\ \text{W}\,\text{m}^{-2}\,\text{K}^{-4}$.
• Wien's displacement law is $\lambda_{\max}T = b$, where $b = 2.90 \times 10^{-3}\ \text{m}\cdot\text{K}$.
• All temperatures in radiation formulas must be measured in kelvins, so $T_{\text{K}} = T_{^\circ\text{C}} + 273.15$.
• The intensity of blackbody radiation increases rapidly with temperature because total emitted power is proportional to $T^{4}$.
• A blackbody spectrum is continuous, and increasing temperature shifts the peak wavelength toward shorter wavelengths.

Vocabulary

Blackbody

An ideal object that absorbs all incident electromagnetic radiation and emits the maximum possible radiation for its temperature.

Emissivity

A number $e$ between $0$ and $1$ that compares how well a real surface emits radiation to an ideal blackbody.

Stefan-Boltzmann Law

The law stating that the total radiant power emitted by a blackbody is $P = \sigma A T^{4}$.

Wien's Law

The law stating that the peak wavelength of emitted radiation satisfies $\lambda_{\max}T = b$.

Radiant Power

The rate at which energy is emitted as electromagnetic radiation, measured in watts.

Thermal Equilibrium

A condition in which an object absorbs and emits energy at equal rates, so its temperature remains constant.