Generalized Wien’s Displacement Law in Determining the True Temperature of $\text{ ZrB }_{2}$–SiC-Based Ultrahigh-Temperature Ceramic: Thermodynamics of Thermal Radiation

Abstract

The temperature dependence of the generalized Wien displacement law is investigated. For determining the true temperature of a $\text{ ZrB }_{2}$–SiC-based ultrahigh-temperature ceramic, the experimental values of the position of the maximum of the spectral density power are needed. Thermodynamics of the thermal radiation of $\text{ ZrB }_{2}$–SiC is constructed by using the temperature dependence of the generalized Stefan–Boltzmann law. The calculated values of the normal total emissivity for $\text{ ZrB }_{2}$–SiC at different temperatures are in good agreement with experimental data. The total radiation power emitted from a surface of $\text{ ZrB }_{2}$–SiC specimens at different temperatures is calculated. The temperature dependences of the Helmholtz free energy, entropy, heat capacity at constant volume, pressure, enthalpy, and internal energy of the thermal radiation of $\text{ ZrB }_{2}$–SiC are obtained. For determining the true temperature, experimental values of either the normal total emissivity or the normal total energy density are needed. The uncertainty in the determination of the true temperature is no greater than 1 %. A new universality class of bodies with a new relationship between the temperature $T$ and the position of the spectral energy density maximum is established.