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 versus wavelength - Spectral radiance is returned in SI units.
Examples
open allclose allBasic Examples (2)
Determine spectral radiance by frequency:
Examine the shape of spectral radiance at Quantity[100,"DegreesCelsius"]:
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 Stefan–Boltzmann 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 Rayleigh–Jeans 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:
Text
Wolfram Research (2014), PlanckRadiationLaw, Wolfram Language function, https://reference.wolfram.com/language/ref/PlanckRadiationLaw.html (updated 2016).
CMS
Wolfram Language. 2014. "PlanckRadiationLaw." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. https://reference.wolfram.com/language/ref/PlanckRadiationLaw.html.
APA
Wolfram Language. (2014). PlanckRadiationLaw. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PlanckRadiationLaw.html