Optical and radiant characteristics of tungsten at high temperatures

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.Keywords Enthalpy · Entropy · Generalized Wien's displacement and Stefan-Boltzmann's laws · Heat capacity · Helmholtz free energy · A. I. Fisenko (B) · V. Lemberg

“…In [17,18], it was shown that in the case of a blackbody, Eq. 1 differs negligibly from the Wien displacement law [21].…”

Section: Generalized Wien's Displacement Lawmentioning

confidence: 98%

Section: Determination Of the True Temperature Of Stoichiometric Hafnmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Fisenko¹,

Lemberg²

2012

Determination of the True Temperature of Molybdenum and Luminous Flames from Generalized Wien’s Displacement and Stefan–Boltzmann’s Laws: Thermodynamics of Thermal Radiation

Fisenko¹,

Ivashov

2009

The true temperature of thermal radiation of molybdenum and luminous flames is defined from the temperature dependences of generalized Wien's displacement and Stefan-Boltzmann's laws. For determining the true temperature of molybdenum, experimental values of either the position of the maximum of the spectral emitted density or the total emitted density are needed. It is shown that the thermal radiation of molybdenum belongs to the same universality class as that of tantalum, tungsten, and zirconium and titanium carbides. The thermodynamic functions of thermal radiation of molybdenum and luminous flames are constructed.

Polylogarithmic Representation of Radiative and Thermodynamic Properties of Thermal Radiation in a Given Spectral Range: I. Blackbody Radiation

Fisenko¹,

Lemberg²

2015

Using polylogarithm functions the exact analytical expressions for the radiative and thermodynamic properties of blackbody radiation, such as the Wien displacement law, Stefan-Boltzmann law, total energy density, number density of photons, Helmholtz free energy density, internal energy density, enthalpy density, entropy density, heat capacity at constant volume, and pressure in the finite range of frequencies are constructed. The obtained expressions allow us to tabulate these functions in various finite frequency bands at different temperatures for practical applications. As an example, the radiative and thermodynamic functions using experimental data for the monopole spectrum of the Cosmic Microwave Background (CMB) radiation measured by the COBE FIRAS instrument in the 60 -600 GHz frequency interval at the temperature T = 2.725 K are calculated. The expressions obtained for the radiative and thermodynamic functions can be easily presented in wavelength and wavenumber domains.