Draft:Kirchhoff-Clausius's Law

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In thermal radiation using geometrical optics, the Kirchhoff-Clausius law was named after Gustav Kirchhoff and Rudolf Clausius, who published their initial findings in 1862 and 1863.

The Kirchhoff-Clausius law state that:

Rudolf Clausius:

" The radiations of perfectly black bodies of the same temperature are different in different media; they are inversely proportional to the squares of the velocities of propagation in those media, and therefore directly proportional to the squares of their coefficients of refraction."

Max Planck:

“The specific intensities of radiation of a certain frequency in the two media are in the inverse ratio of the squares of the velocities of propagation or in the direct ratio of the squares of the indices of refraction.”

John D. Barrow & João Magueijo

"The rate at which a body emits heat radiation is inversely proportional to the square of the speed at which the radiation propagates in the medium in which the body is immersed."

History

Before Kirchhoff's law was recognized,

In physics, the Kirchhoff-Clausius Law is defined by:

Temperature

$B(T)={\frac {1}{c^{2}}}\cdot f(T)$ (SI units: W⋅m^-2)

Wavelength and temperature

$B(\lambda ,T)={\frac {1}{c^{2}}}\cdot f(\lambda T)$ (SI units: W⋅m^-2⋅sr^-1⋅nm^-1)

Frequency and temperature

$B(\nu ,T)={\frac {1}{c^{2}}}\cdot f({\frac {T}{\nu }})$ (SI units: W⋅m^-2⋅sr^-1⋅Hz^-1)

Max Planck interpreted and used this law for the first time in his 1901 article> justifying his black body distribution law.

Origin

Gustav Kirchhoff's formula in 1862

$I'=n^{2}\cdot I$

So, with n=c/c'

The Clausius form is obtained by:

$I'c'^{2}=Ic^{2}$

and the Planck form:

$I={\frac {1}{c^{2}}}\cdot (I'c'^{2})$

($I$ as heat radiation intensity in vacuum and $I'$in media, c as speed of light, and n as refractive index)

Rudolf Clausius's statement in 1863

He gives these formulas:

$e_{a}v{_{a}^{2}}=e_{c}v{_{c}^{2}}$

$e_{a}:e_{c}=v{_{c}^{2}}:v{_{a}^{2}}$

$e_{a}:e_{c}=n{_{a}^{2}}:n{_{c}^{2}}$

(Here $e$ for heat radiation intensity and $v$ for the speed of light, for the medium planes a and c)