Why does the blackbody spectrum depend only on temperature?

Why does the blackbody spectrum depend only on temperature?

• A. Emissivity is constant for all temperatures.
• B. The spectrum is determined by Planck's law which depends on temperature.
• C. Wien's law governs the spectrum.
• D. The Stefan-Boltzmann law governs the spectrum.

Answer: (B)

Planck's law is the description that matters here. It gives the spectral radiance of a blackbody as a function of wavelength (or frequency) and temperature, with the temperature appearing both in the exponential and the normalization. Because of this, changing the temperature changes the population of photon energies across all wavelengths, reshaping the entire spectrum. As temperature increases, the peak shifts to shorter wavelengths and the overall intensity grows, which is why a hotter body glows brighter and bluer. Wien's displacement law and Stefan-Boltzmann's law describe specific features—the peak position and the total power, respectively—but neither alone captures the full temperature-dependent spectrum. For an ideal blackbody, emissivity is unity and does not set the spectrum by itself; the Planck distribution is the fundamental reason the spectrum depends on temperature.

Planck's law is the description that matters here. It gives the spectral radiance of a blackbody as a function of wavelength (or frequency) and temperature, with the temperature appearing both in the exponential and the normalization. Because of this, changing the temperature changes the population of photon energies across all wavelengths, reshaping the entire spectrum. As temperature increases, the peak shifts to shorter wavelengths and the overall intensity grows, which is why a hotter body glows brighter and bluer. Wien's displacement law and Stefan-Boltzmann's law describe specific features—the peak position and the total power, respectively—but neither alone captures the full temperature-dependent spectrum. For an ideal blackbody, emissivity is unity and does not set the spectrum by itself; the Planck distribution is the fundamental reason the spectrum depends on temperature.