Wien's Displacement Law for real bodiesIt is known that for perfect blackbodies, λ T = cwhere λ = peak wavelength T = Absolute temperature c = Wien's constantBut this is for perfect blackbodies only, which have no theoretical existence. Does a similar formula exist for real bodies, which expresses λ T in terms of its emissitivity ϵ? I googled it, but found no relevant results.

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Wien&#039;s Displacement Law for real bodiesIt is known that for perfect blackbodies,  λ  T  =  cwhere   λ  =  peak wavelength  T  =  Absolute temperature  c  =  Wien&#039;s constantBut this is for perfect blackbodies only, which have no theoretical existence. Does a similar formula exist for real bodies, which expresses   λ  T in terms of its emissitivity   ϵ? I googled it, but found no relevant results.

Braeden Shannon · Accepted Answer

&quot;But this is for perfect blackbodies only, which have no theoretical existence.&quot;Just for clarification, the Wien displacement law is not valid for emission spectrum &quot;of blackbodies only&quot;. It is valid for any radiation in thermodynamic equilibrium with matter (equilibrium radiation), which is a more general concept that does not require presence of any black body. This equilibrium radiation has energy density spectrum given by the Planck function      ρ          P      l      a      n      c      k        (  λ  ,  T  )  =            8      π      h      c              λ      5            1                  e                                            h              c                                      λ              k              T                                          −      1      and can be produced and maintained by non-black bodies, for example by enclosure of any material brought to thermodynamic equilibrium at temperature   T. Wien&#039;s displacement law says that the product of   T and       λ          m      a      x       for which the energy density spectrum is maximum is the same for all temperatures.&quot;Does a similar formula exist for real bodies, which expresses λT in terms of its emissitivity ϵ?&quot;Let me rephrase your question : for emission intensity spectrum   I  (  λ  ,  T  ) of non-black body with known emissivity   ϵ  (  λ  ,  T  ), is there a simple relation between the wavelength of maximum and temperature, similar to above Wien&#039;s displacement law ?The answer is that in general, most probably no, because the emission radiation of real body has intensity spectrum proportional to  I  (  λ  ,  T  )  ∝      ρ          P      l      a      n      c      k        (  λ  ,  T  )  ϵ  (  λ  ,  T  )  ,which means that the number, positions and height of peaks are modified by the emissivity   ϵ  (  λ  ,  T  ). This depends on the body, its material and thickness and can be fairly general function of   λ and   T. There may be some general restriction on this function due to physical laws, but Planck&#039;s formula does not imply any, apart from the condition that   0  &amp;lt;  ϵ  ≤  1 for all frequencies. One would have to study more detailed model of matter explaining value of   ϵ  (  λ  ,  T  ) to find such relations.

Wien's Displacement Law for real bodies It is known that for perfect blackbodies, λ<!

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