On temperature determination of opaque materials through the spectral maximum of thermal radiation

For the thermal radiation spectral maximum of an opaque freely radiating body, an equation relating the wavelength, the emissivity, and the thermodynamic (the true) temperature of the body is derived. Also a nondimensional parameter bounding the emissivity, its derivative, and the wavelength is identified in the radiation spectral maximum. A value range of this parameter where use of the obtained equation reduces the required temperature uncertainty is determined. Furthermore, a dimensionless parameter characterizing the deviation of the thermal radiation of the real materials from the Wien displacement law is found. The interconnection of the obtained parameters is revealed. By means of a computer experiment, it is shown that, for selectively radiating materials such as tungsten at 2600–3000 K, determination of the true temperature according to the Wien displacement law results in deviations from the true temperature by more than 200 K.