Planck's Law expresses the spectral radiance of a black body as a function of which variables?

Planck's Law expresses the spectral radiance of a black body as a function of which variables?

• A. Wavelength and temperature.
• B. Pressure and volume.
• C. Velocity and frequency.
• D. Mass and energy.

Answer: (A)

Planck's law tells us how much radiant power a black body emits at each wavelength, and it shows that this spectral radiance depends on two variables: the wavelength and the body's absolute temperature. The formula B(λ, T) reveals how the radiance scales with λ (the λ^−5 factor) and how the exponential term involves λ and T together. At a fixed temperature, the spectrum has a characteristic shape across wavelengths; at a fixed wavelength, increasing the temperature raises the radiance significantly. The peak of the emission shifts to shorter wavelengths as temperature rises (Wien’s displacement), and the total emitted power scales as T^4 (Stefan–Boltzmann law) when you sum over all wavelengths. This makes clear why spectral radiance is described with wavelength and temperature rather than pressure, volume, velocity, mass, or energy. If you ever express the law in terms of frequency instead of wavelength, it’s still two variables (frequency and temperature), but the standard form shown uses wavelength.

Planck's law tells us how much radiant power a black body emits at each wavelength, and it shows that this spectral radiance depends on two variables: the wavelength and the body's absolute temperature. The formula B(λ, T) reveals how the radiance scales with λ (the λ^−5 factor) and how the exponential term involves λ and T together. At a fixed temperature, the spectrum has a characteristic shape across wavelengths; at a fixed wavelength, increasing the temperature raises the radiance significantly. The peak of the emission shifts to shorter wavelengths as temperature rises (Wien’s displacement), and the total emitted power scales as T^4 (Stefan–Boltzmann law) when you sum over all wavelengths. This makes clear why spectral radiance is described with wavelength and temperature rather than pressure, volume, velocity, mass, or energy. If you ever express the law in terms of frequency instead of wavelength, it’s still two variables (frequency and temperature), but the standard form shown uses wavelength.