Editing Wien's displacement law (section)

==Discovery==
The law is named for [[Wilhelm Wien]], who derived it in 1893 based on a thermodynamic argument.<ref>
{{cite book
 |last1=Mehra |first1=J. |author-link1=Jagdish Mehra
 |last2=Rechenberg |first2=H. |author-link2=Helmut Rechenberg
 |year=1982
 |title=The Historical Development of Quantum Theory
 |at=Chapter 1
 |publisher=Springer-Verlag
 |location=New York City
 |isbn=978-0-387-90642-3
}}</ref> Wien considered [[adiabatic]] expansion of a cavity containing waves of light in thermal equilibrium. Using [[Doppler Effect|Doppler's principle]], he showed that, under slow expansion or contraction, the energy of light reflecting off the walls changes in exactly the same way as the frequency. A general principle of thermodynamics is that a thermal equilibrium state, when expanded very slowly, stays in thermal equilibrium.

Wien himself deduced this law theoretically in 1893, following Boltzmann's thermodynamic reasoning. It had previously been observed, at least semi-quantitatively, by an American astronomer, [[Samuel Pierpont Langley|Langley]]. This upward shift in <math>\nu_\mathrm{peak}</math> with <math>T</math> is familiar to everyone—when an iron is heated in a fire, the first visible radiation (at around 900 K) is deep red, the lowest frequency visible light. Further increase in <math>T</math> causes the color to change to orange then yellow, and finally blue at very high temperatures (10,000 K or more) for which the peak in radiation intensity has moved beyond the visible into the ultraviolet.<ref>{{Cite web|url=https://chem.libretexts.org/Courses/Pacific_Union_College/Quantum_Chemistry/01%3A_The_Dawn_of_the_Quantum_Theory/1.01%3A_Blackbody_Radiation_Cannot_Be_Explained_Classically|title = 1.1: Blackbody Radiation Cannot be Explained Classically|date = 18 March 2020}}</ref>

The adiabatic principle allowed Wien to conclude that for each mode, the [[adiabatic invariant]] energy/frequency is only a function of the other adiabatic invariant, the frequency/temperature. From this, he derived the "strong version" of Wien's displacement law: the statement that the blackbody spectral radiance is proportional to <math> \nu^3 F(\nu/T) </math> for some function {{mvar|F}} of a single variable. A modern variant of Wien's derivation can be found in the textbook by Wannier<ref>{{cite book |last1=Wannier |first1=G. H. |author1-link=Gregory Wannier |year=1987 |orig-year=1966 |title=Statistical Physics |publisher=[[Dover Publications]] |isbn=978-0-486-65401-0 |oclc=15520414 |at=Chapter 10.2}}</ref> and in a paper by E. Buckingham<ref>{{cite journal |last1=Buckingham |first1=E. |title=On the Deduction of Wien's Displacement Law |journal=Bulletin of the Bureau of Standards |date=1912 |volume=8 |issue=3 |pages=545–557 |doi=10.6028/bulletin.196 |url=https://nvlpubs.nist.gov/nistpubs/bulletin/08/nbsbulletinv8n3p545_A2b.pdf |access-date=18 October 2020 |archive-date=6 December 2020 |archive-url=https://web.archive.org/web/20201206222927/https://nvlpubs.nist.gov/nistpubs/bulletin/08/nbsbulletinv8n3p545_A2b.pdf |url-status=dead}}</ref>

The consequence is that the shape of the black-body radiation function (which was not yet understood) would shift proportionally in frequency (or inversely proportionally in wavelength) with temperature. When [[Max Planck]] later formulated the correct [[Planck's law|black-body radiation function]] it did not explicitly include Wien's constant <math>b</math>. Rather, the [[Planck constant]] <math>h</math> was created and introduced into his new formula. From the Planck constant <math>h</math> and the [[Boltzmann constant]] <math>k</math>, Wien's constant <math>b</math> can be obtained.