Draft:Kirchhoff-Clausius's Law

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 named this law in honor of Gustav Kirchhoff and Rudolf Clausius for the first time in his 1901 article> justifying his black body distribution law.

The Law

Max Planck's statement in 1914

“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.”

The modern statement

"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."

Origin

Gustav Kirchhoff's formula in 1860

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

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 1864

" 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."

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)