Wien's Displacement Law - Explanation and Familiar Approximate Applications

Explanation and Familiar Approximate Applications

The law is named for Wilhelm Wien, who derived it in 1893 based on a thermodynamic argument. Wien considered adiabatic, or slow, expansion of a cavity containing waves of light in thermal equilibrium. 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. 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.

Max Planck reinterpreted a constant closely related to Wien's constant b as a new constant of nature, now called Planck's constant, which relates the frequency of light to the energy of a light quantum.

Wien's displacement law implies that the hotter an object is, the shorter the wavelength at which it will emit most of its radiation, and also that the wavelength for maximal or peak radiation power is found by dividing Wien's constant by the temperature in kelvins.