On Kirchhoff's law and its generalized application to absorption and emission by cavities

Abstract

Several authurs have made the assumption that Kirchhoff's Law holds for the apparent local spectral emittance and apparent local spectral absorptance of any point on the interior surface of a cavity. The correctness of this assumption is demonstrated under certain general conditions, and its practical application to the calculation of the total flux absorbed by a cavity or spacecraft is discussed. A further application to the case of a nonisothermal cavity or spacecraft is derived. By this derivation an easy method for determining the total flux emitted from such a nonisothermal cavity is found when the distribution of the apparent local spectral emittance of the isothermal cavity is known. The economy and versatility of this method is shown by the calculation of the total flux emitted from a nonisothermal cylindrical cavity for several arbitrary cases of temperature distribution on the interior surface of the cavity. Finally, the integral equation for a diffuse cavity whose wall emittance varies with position on the wall is transformed to an equation having a symmetric kernel.