I. What is a Blackbody?
A blackbody is an idealized physical model under thermal equilibrium (energy conservation), which completely absorbs all wavelengths of incident electromagnetic radiation without reflection or transmission.

Per the law of conservation of energy:

• Transparent objects: Incident radiant energy = Absorption + Reflection + Transmission
• Opaque objects: Incident radiant energy = Absorption + Reflection

When an opaque object has 0 reflectance, its absorptivity and thermal emissivity reach maximum.

An absolute blackbody is an idealized physical model that fully converts absorbed energy into thermal radiation. Its spectral power distribution (SPD) depends solely on absolute temperature (unit: Kelvin, K), independent of material composition or geometric shape.

In the CIE 1931 xy chromaticity diagram (see Figure 1), the chromaticity coordinates of a blackbody at different temperatures form a continuous curve known as the Planckian locus. As the temperature increases, the dominant hue of the radiation shifts from warm red (low frequency, long wavelength) to cool blue (high frequency, short wavelength). This locus is an important basis for defining correlated color temperature (CCT) and is widely used in light sources, imaging systems, and color calibration.

Figure 1[1]: CIE 1931 xy chromaticity diagram and Planckian locus

II. Blackbody Simulation Model
In engineering and experimental applications, a constant-temperature cavity with a small aperture is commonly used as an approximate blackbody model (Figure 2). When incident electromagnetic waves enter the aperture, they undergo multiple reflections inside the cavity and are fully absorbed, making it difficult to re-emit. This achieves a reflectance approaching 0, allowing the cavity to be regarded as an approximate ideal blackbody.

Figure 2[2]: Schematic of a constant-temperature cavity blackbody simulator
Source: https://en.wikipedia.org/wiki/Black_body#/media/File:Black_body_realization.svg

III. Blackbody Radiation Laws
The thermal radiation characteristics of a blackbody strictly follow three fundamental laws:
(1) Planck's Law of Blackbody Radiation
This law describes the relationship between the spectral radiant exitance of a blackbody, wavelength, and absolute temperature. Its core formula is:
$$M_\lambda(\lambda, T) = \frac{c_1}{\lambda^5} \frac{1}{e^{\frac{c_2}{\lambda T}} - 1}$$

where:
$M_\lambda$: Spectral radiant exitance ($W \cdot m^{-3}$);
$\lambda$: Wavelength (m);
$T$:Absolute temperature (K);
$c_1 = 2\pi h c^2$: First radiation constant ($W \cdot m^2$);
$c_2 = \frac{hc}{k_B}$: Second radiation constant ($m \cdot K$);
$k_B $: Boltzmann constant ($J \cdot K^{-1}$).

Figure 3[3]:Schematic Diagram of Planck's Law of Blackbody Radiation
Source:https://en.wikipedia.org/wiki/Black_body#/media/File:Black_body.svg

As shown in Figure 3, rising blackbody temperature shifts the peak wavelength to shorter wavelengths (Wien's Displacement Law), while total radiant energy increases with the fourth power of temperature (Stefan-Boltzmann Law).

(2) Wien's Displacement Law
This law reveals the inverse relationship between the peak radiation wavelength $\lambda_m$ of a blackbody and its absolute temperature $T$. Its core formula is:
$$\lambda_m T = b$$ where:
$\lambda_m$: Peak wavelength ($m$)
$T$: Absolute temperature ($K$)
$b$: Wien's displacement constant ($m \cdot K$),$b \approx 2.897771955 \times 10^{-3} \, m \cdot K$
This law explains that as a blackbody's temperature rises, the peak wavelength of its emission spectrum shifts to shorter wavelengths.

(3) Stefan-Boltzmann Law
This law describes the relationship between the total radiant exitance $M$ of a blackbody (integrated over all wavelengths) and the 4th power of its absolute temperature $T$.Its core formula is:
$$M(T) = \int_0^\infty M_\lambda(\lambda, T) d\lambda = \frac{c_1 \pi^4}{15 c_2^4} T^4 = \sigma T^4$$ where:
$M $: Total radiant exitance ($W \cdot m^{-2}$)
$T$: Absolute temperature(K)
$c_1 = 2\pi h c^2$: First radiation constant($W \cdot m^2$)
$c_2 = \frac{hc}{k_B} $: Second radiation constant ($m \cdot K$)
$\sigma$: Stefan-Boltzmann constant ($W \cdot m^{-2} \cdot K^{-4}$)

Figure 4[4]: Schematic Diagram of Stefan-Boltzmann Law
Source:https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law#/media/File:Stefan_Boltzmann_001.svg

The $T^4$ dependence demonstrates the extreme temperature sensitivity of blackbody radiation: even a small rise in temperature leads to a dramatic increase in total radiant energy, quantitatively validating that an ideal absorber is also an ideal radiator.

Image sources:
[1] https://upload.wikimedia.org/wikipedia/commons/thumb/b/ba/PlanckianLocus.png/960px-PlanckianLocus.png
[2]https://en.wikipedia.org/wiki/Black_body#/media/File:Black_body_realization.svg
[3] https://commons.wikimedia.org/wiki/File:BlackbodySpectrum_loglog_en.svg
[4]https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law#/media/File:Stefan_Boltzmann_001.svg