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Wien's displacement law
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==Examples== [[Image:Blacksmith at work02.jpg|thumb|upright=1.45|right|[[Blacksmith]]s work [[iron]] when it is hot enough to emit plainly visible [[thermal radiation]].]] [[File:Orion 3008 huge.jpg|thumb|upright=1.3|The color of a star is determined by its temperature, according to Wien's law. In the constellation of [[Orion (constellation)|Orion]], one can compare [[Betelgeuse]] (''T'' ≈ 3800 K, upper left), [[Rigel]] (''T'' = 12100 K, bottom right), [[Bellatrix]] (''T'' = 22000 K, upper right), and [[Mintaka]] (''T'' = 31800 K, rightmost of the 3 "belt stars" in the middle).]] Wien's displacement law is relevant to some everyday experiences: *A piece of metal heated by a [[blow torch]] first becomes "red hot" as the very longest [[visible wavelength]]s appear red, then becomes more orange-red as the temperature is increased, and at very high temperatures would be described as "white hot" as shorter and shorter wavelengths come to predominate the black body emission spectrum. Before it had even reached the red hot temperature, the thermal emission was mainly at longer [[infrared]] wavelengths, which are not visible; nevertheless, that radiation could be felt as it warms one's nearby skin. *One easily observes changes in the color of an [[incandescent light bulb]] (which produces light through thermal radiation) as the temperature of its filament is varied by a [[light dimmer]]. As the light is dimmed and the filament temperature decreases, the distribution of color shifts toward longer wavelengths and the light appears redder, as well as dimmer. *A wood fire at 1500 K puts out peak radiation at about 2000 nanometers. 98% of its radiation is at wavelengths longer than 1000 nm, and only a tiny proportion at [[Visible spectrum|visible wavelengths]] (390–700 nanometers). Consequently, a campfire can keep one warm but is a poor source of visible light. *The effective temperature of the [[Sun]] is 5778 Kelvin. Using Wien's law, one finds a peak emission per nanometer (of wavelength) at a wavelength of about 500 nm, in the green portion of the spectrum near the peak sensitivity of the human eye.<ref>Walker, J. Fundamentals of Physics, 8th ed., John Wiley and Sons, 2008, p. 891. {{ISBN|9780471758013}}.</ref><ref>Feynman, R; Leighton, R; Sands, M. The Feynman Lectures on Physics, vol. 1, pp. 35-2 – 35-3. {{ISBN|0201510030}}.</ref> On the other hand, in terms of power per unit optical frequency, the Sun's peak emission is at 343 THz or a wavelength of 883 nm in the near infrared. In terms of power per percentage bandwidth, the peak is at about 635 nm, a red wavelength. About half of the Sun's radiation is at wavelengths shorter than 710 nm, about the limit of the human vision. Of that, about 12% is at wavelengths shorter than 400 nm, ultraviolet wavelengths, which is invisible to an unaided human eye. A large amount of the Sun's radiation falls in the fairly small [[visible spectrum]] and passes through the atmosphere.<ref>{{Cite |title=Shedding Light on PACE|url=https://pace.oceansciences.org/atmos_light.cgi}}</ref> *The preponderance of emission in the visible range, however, is not the case in most [[stars]]. The hot supergiant [[Rigel]] emits 60% of its light in the ultraviolet, while the cool supergiant [[Betelgeuse]] emits 85% of its light at infrared wavelengths. With both stars prominent in the constellation of [[Orion (constellation)|Orion]], one can easily appreciate the color difference between the blue-white Rigel (''T'' = 12100 K) and the red Betelgeuse (''T'' ≈ 3800 K).<ref>{{Cite journal |last1=Neuhäuser |first1=R |last2=Torres |first2=G |last3=Mugrauer |first3=M |last4=Neuhäuser |first4=D L |last5=Chapman |first5=J |last6=Luge |first6=D |last7=Cosci |first7=M |date=2022-07-29 |title=Colour evolution of Betelgeuse and Antares over two millennia, derived from historical records, as a new constraint on mass and age |url=https://academic.oup.com/mnras/article/516/1/693/6651563 |journal=Monthly Notices of the Royal Astronomical Society |volume=516 |issue=1 |pages=693–719 |doi=10.1093/mnras/stac1969 |doi-access=free |issn=0035-8711|arxiv=2207.04702 }}</ref> While few stars are as hot as Rigel, stars cooler than the Sun or even as cool as Betelgeuse are very commonplace. *[[Mammals]] with a skin temperature of about 300 K emit peak radiation at around 10 μm in the far infrared. This is therefore the range of infrared wavelengths that [[pit viper]] snakes and [[Thermographic camera|passive IR cameras]] must sense. *When comparing the apparent color of lighting sources (including [[fluorescent lights]], [[LED lighting]], [[computer monitor]]s, and [[photoflash]]), it is customary to cite the [[color temperature]]. Although the spectra of such lights are not accurately described by the black-body radiation curve, a color temperature (the [[Correlated color temperature#Correlated color temperature|correlated color temperature]]) is quoted for which black-body radiation would most closely match the subjective color of that source. For instance, the blue-white fluorescent light sometimes used in an office may have a color temperature of 6500 K, whereas the reddish tint of a dimmed incandescent light may have a color temperature (and an actual filament temperature) of 2000 K. Note that the informal description of the former (bluish) color as "cool" and the latter (reddish) as "warm" is exactly opposite the actual temperature change involved in black-body radiation.
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