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 was obtained. Also the nondimensional parameter bounding the emissivity, its derivative, and the wavelength in the radiation spectral maximum were obtained. The value range of this parameter where use of the obtained equation reduces the required temperature uncertainty was determined. A dimensionless parameter characterizing the deviation of the thermal radiation of the real materials from the Wien displacement law was determined. The interconnection of the obtained parameters was 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.