A general and tractable method is developed for calculating the pressure, density, and temperature distributions within a gaseous-core nuclear reactor by solving the appropriate radiation heat transfer equation. Numerical results are presented for the case of a gray gas with a spatially independent gas density distribution, and these results are compared with a more accurate integral solution. A qualitative study of the behavior of the gaseous core with respect to a variation in fuel opacity is also made. It is found that the diffusion approximation with second-order jump boundary conditions describes the pressure, density, and temperature variations of the gaseous-core reactor quite accurately over a wide range in parameters. In a fixed geometry, as the absorption coefficient increases from very small initial values, the gas temperature first decreases, passes through a minimum, and then increases for all further increases in absorption coefficient. Thus if the lowest possible temperature is desired, a gas should be chosen that has an absorption coefficient near the minimum value. 31 pp. Ref.