Theoretical analysis of laboratory blackbodies. 1: a generalized integral equation.

The integral equations describing radiative equilibrium in a blackbody cavity are presented. Solving these equations in terms of the power sources in the furnace surrounding the cavity is not practical. However, if provisions are made for measuring the temperature over some surface between the power sources and the cavity interior, the analysis is feasible. This restriction and some realistic assumptions lead to a single, linear, inhomogeneous integral equation that approximately describes the interaction of the cavity geometry, the thermal radiative properties of the cavity wall, and the temperature gradientswithin the cavity in reducing the quality of the blackbody. The formulation is general enough to accommodate realistic reflectance and temperature distributions for high quality blackbodies, and the accuracy of calculations based upon it will probably not be limited by approximations involved in its derivation, but by the present state of the art in the knowledge of the thermal radiative properties of materials.