Radiative Properties of Stoichiometric Hafnium, Titanium, and Zirconium Carbides: Thermodynamics of Thermal Radiation

Abstract

The true temperatures of the thermal radiation of stoichiometric hafnium, titanium, and zirconium carbides are defined from the generalized Wien displacement law. It is shown that Wien’s displacement law for the investigated stoichiometric carbides decreases linearly with increasing temperature. The uncertainties in the determination of the true temperature are no greater than 1 %. For determining the true temperature of stoichiometric carbides, the experimental values of the position of the maximum of the spectral density power are needed. By extrapolating the generalized Wien displacement laws in the ultra-high-temperature region, the positions of the maximum of the normal energy density of hafnium, titanium, and zirconium carbides at melting temperatures are obtained. Thermodynamics of thermal radiation of stoichiometric carbides is constructed by using the temperature dependences of the generalized Stefan–Boltzmann law. The calculated values of the normal total emissivity for the investigated carbides at different temperatures are in good agreement with experimental data. For determining the true temperatures of the thermal radiation of stoichiometric carbides, experimental values of either the normal total emissivity or the normal total energy density are needed. The temperature dependences of the Helmholtz free energy, entropy, heat capacity at constant volume, pressure, enthalpy, and internal energy of the thermal radiation of stoichiometric carbides at high temperature are obtained. It is shown that thermodynamic function values increase with increasing temperature as a power law.