text: For surfaces which are not black bodies, one has to consider the (generally frequency dependent) emissivity factor . This factor has to be multiplied with the radiation spectrum formula before integration. If it is taken as a constant, the resulting formula for the power output can be written in a way that contains  as a factor:
  This type of theoretical model, with frequency-independent emissivity lower than that of a perfect black body, is often known as a grey body. For frequency-dependent emissivity, the solution for the integrated power depends on the functional form of the dependence, though in general there is no simple expression for it. Practically speaking, if the emissivity of the body is roughly constant around the peak emission wavelength, the gray body model tends to work fairly well since the weight of the curve around the peak emission tends to dominate the integral.