Black-body radiation and the maximum entropy production regime

A thermodynamical analysis is carried out for isothermal Lambertian radiating bodies emitting isotropic non-polarized radiation. We show that of all bodies which radiate the same quantity of energy a black body is that which produces the largest amount of entropy, and also of all isothermal radiating bodies at the same temperature a black body is that which produces the largest amount of entropy, and, as is well known, it is that which radiates the largest quantity of energy. From the above results and the second law of thermodynamics, the well known fact that the emissivity per frequency interval as well as the global emissivity are bounded above by unity is recovered in a novel manner. Finally, a new approximation different from that of a grey body is proposed for non-black bodies. We call this approximation a 'dark body' and compare it with both black and grey bodies.