The Emissivity of Transparent Materials

The emission of thermal radiation by transparent materials is reviewed from first principles and is compared with the more familiar emission of radiation by opaque surfaces. The comparison leads to an expression for volume emissive power, which is an important concept for discussions of radiative effects in glass. The present treatment differs from that of McMahon in that it takes account of the diffuse character of radiation. As a result, it also constitutes a simple proof of the often overlooked fact that the radiant flux within a transparent radiator exceeds that emitted into air by a factor approximately equal to the square of the refractive index. Using these concepts, the spectral emissivities of isothermal transparent sheets are expressed in terms of their thickness and the optical properties of their materials. The results are illustrated by a discussion of the total hemispherical emissivities of sheets of window glass at various temperatures. The commonly accepted value of about 0.91 is the same for all glasses having a refractive index of 1.5. However, it applies only for sheets above a certain minimum thickness. For window glass this ranges from 3/16 in. at 200°C. to as much as 8 in. at 1000°C. At 1000°C. a sheet 3/16 in. thick has an emissivity of only 0.59. The application of results to calculations of the radiative cooling of transparent sheets is briefly indicated.