PlanckRadiationLaw

PlanckRadiationLaw[temperature,λ]

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

PlanckRadiationLaw[temperature,f]

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

PlanckRadiationLaw[temperature,property]

returns the value of the property for the specified temperature.

PlanckRadiationLaw[temperature,{λ1,λ2}]

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

PlanckRadiationLaw[temperature,{f1,f2}]

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 verses wavelength
  • Spectral radiance is returned in SI units.

Examples

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Basic Examples  (2)

Find the spectral radiance:

Determine spectral radiance by frequency:

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 emissivity by approximating the integral of Planck's law by integrating the dominant part of the spectrum:

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:

Introduced in 2014
 (10.0)
 |
Updated in 2016
 (11.0)