returns the spectral radiance for the specified temperature and wavelength λ.

returns the spectral radiance for the specified temperature and frequency f.

returns the value of the property for the specified temperature.

returns the integrated result of the spectral radiance over the wavelength range λ1 to λ2.

returns the integrated result of the spectral radiance over the frequency range f1 to f2.

# Details • Inputs temperature, λ, and f should be Quantity objects.
• Properties include:
•  "Color" color of the peak wavelength "MaxFrequency" peak frequency "MaxWavelength" peak wavelength "MeanFrequency" average frequency "MeanWavelength" average wavelength "SpectralPlot" plot of spectral radiance versus wavelength
• Spectral radiance is returned in SI units.

# Examples

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## Basic Examples(2)

Examine the shape of spectral radiance at Quantity[100,"DegreesCelsius"]:

Find the average wavelength:

Discover the color of the peak wavelength:

## Scope(3)

Explore all the properties of PlanckRadiationLaw:

Find the peak wavelength for 6000 K and its color:

Determine the peak frequency at 6000 K:

Find the integrated spectral radiance over wavelength or frequency:

## Applications(5)

Calculate the maximum radiance as a function of wavelength:

Calculate the maximum radiance as a function of frequency:

Note that the peak values do not correspond to the same wavelength of light:

Examine how the spectral radiance varies as a function of frequency:

Use the directional temperature, corrected for relativistic effects, to see how the peak for spectral radiance is shifted to longer wavelengths for an object moving at relativistic speeds:

Demonstrate Wien's displacement law, that the peak wavelength is inversely proportional to the temperature:

Find the radiant exitance by approximating the integral of Planck's law by integrating the dominant part of the spectrum and using Lambert's cosine law to derive the angular factor for a point on the black body's surface:

Divide by the fourth power of the temperature to find the StefanBoltzmann constant:

## Properties & Relations(1)

The formula used by PlanckRadiationLaw is the same as presented by FormulaData:

## Neat Examples(2)

Compare Planck's radiation law to Wien's distribution law:

Compare Wien's distribution law to the RayleighJeans law and Planck's radiation law:

In a micrometer-sized box, quantum effects cause the minimum frequency possible to be the following:

Plot the energy density within this box, accounting for the finite size effect relative to a blackbody in an infinite cavity: