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Blackbody Radiation

Wien's peak wavelength and the Stefan-Boltzmann flux, with the luminosity of a star at the radius you type.

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Blackbody Radiation screenshot

Wien's displacement law and Stefan-Boltzmann, computed rather than looked up. Give it a temperature and it returns the peak wavelength of the Planck curve and the flux leaving each square metre; give it a radius as well and the flux becomes a stellar luminosity. Type a luminosity instead and it inverts the fourth power to recover the surface temperature that would produce it.

WIEN'S LAW STEFAN-BOLTZMANN
Peak wavelength
Total luminosity
Surface flux
Working
Read-out

  

    Wien's displacement law puts the peak of the Planck curve at
    lambda_max = 2898 um K / T, so a hotter body peaks at a shorter wavelength and
    the whole curve squeezes toward the blue. Stefan-Boltzmann integrates that
    curve over all wavelengths to give the flux leaving a unit area,
    M = sigma T^4 with sigma = 5.670374419e-8 W/m^2/K^4. The fourth power is the
    entire reason stellar luminosity is so sensitive to temperature: a star 1.1
    times as hot is about 1.46 times as luminous. A real star is not a perfect
    blackbody and most of its light lands outside the visible band, so a Wien peak
    read off the visible colour of an object is only an approximation of the
    physical peak.
  




  

  


  




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