Imagine you are heating a piece of metal. At first it’s dark, then red, then yellow, and even blue. Wien's displacement law explains how the color of the glow depends on temperature: the hotter the body, the shorter (bluer) the waves it emits. It is as if you move a color slider on a screen: more heat — go to blue, less — to red. The formula is simple: λ_max × T = constant, where λ_max is the wavelength at which most light is emitted, and T is the temperature in Kelvin.
History
At the end of the 19th century, the radiation spectrum of heated bodies was actively studied experimentally. Wilhelm Wien, relying on ideas of adiabatic compression of radiation in a cavity, showed that the product of temperature and the wavelength of the maximum should be constant. He came to this conclusion in 1893, and in 1896 he proposed an empirical formula for the energy distribution in the spectrum. These works stimulated Max Planck to discover quantization, and in 1911 Wien was awarded the Nobel Prize. The law played a key role in the formation of quantum physics and later found application in astrophysics: Edwin Hubble used it to study stars and galaxies.
How it works
Wien's displacement law is applicable to black-body radiation and holds well for many astronomical objects (stars, star clusters). It allows estimating a star's temperature from the color of its radiation with good accuracy if interstellar absorption is small. It is also used in optical pyrometry for non-contact measurement of high temperatures in metallurgy and glassmaking. Boundary conditions: the law is accurate only for black bodies or gray bodies with non-selective radiation; in real objects, especially gases, line radiation distorts the spectrum, and the maximum may shift.
Fun fact
Thanks to this law, astronomers determine the temperature of stars by their color! Bluish stars are hotter than red ones — like a gas burner flame: blue flame is hotter than yellow. The most famous star, the Sun, with a surface temperature of about 5800 K, shines in the yellow-green range, which gives us the maximum light precisely in the visible part of the spectrum — not by chance, but according to Wien's law.
Effective temperature of the surface — temperaturekelvin
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constant
Proportionality constant relating blackbody radiated power to temperature — stefan boltzmann constant= 5.670374419e-8watt per metre squared per kelvin to the fourth
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