International Journal of Thermophysics

, Volume 34, Issue 3, pp 486–495 | Cite as

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

  • Anatoliy I. Fisenko
  • Vladimir Lemberg


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.


Enthalpy Entropy Free energy Generalized Wien’s displacement and Stefan–Boltzmann’s laws Internal energy Normal total emissivity  True temperature \(\text{ ZrB }_{2}\)–SiC-based ultrahigh-temperature ceramic 



The authors cordially thank Professor L.A. Bulavin, Professor N. P. Malomuzh, and Professor V.A. Masur for fruitful discussion. Special thanks to Professor S. Meng for providing us with experimental data on the normal spectral emissivity.


  1. 1.
    S.R. Levine, E.J. Opila, M.C. Halbig, J.D. Kiser, M. Singh, J.A. Salem, J. Eur. Ceram. Soc. 22, 2757 (2002)Google Scholar
  2. 2.
    E. Wuchina, E. Opila, M. Opeka, W. Fahrenholtz, I. Talmy, UHTCs: Ultra-High Temperature Ceramic Materials for Extreme Environment Applications. Interface 16, 30 (2007)Google Scholar
  3. 3.
    P.T.B. Shaffer, in Engineered Materials Handbook, vol. 4, Ceramics and Glass (ASM International, Metals Park, OH, 1991), pp. 804–811Google Scholar
  4. 4.
    F.Y. Yang, X.H. Zhang, J.C. Han, S.Y. Du, Mater. Des. 29, 1817 (2008)CrossRefGoogle Scholar
  5. 5.
    S.H. Meng, G.Q. Liu, Y. Guo, X.H. Xu, F. Song, Mater. Des. 30, 2108 (2009)CrossRefGoogle Scholar
  6. 6.
    L. Kaufman, E.V. Clougherty, in Proceedings of the 5th Plansee Seminar (Reuter, Australia, 1963), pp. 722–738Google Scholar
  7. 7.
    S.H. Meng, G.Q. Liu, S.L. Sun, Mater. Des. 31, 556 (2010)CrossRefGoogle Scholar
  8. 8.
    J.L. Cao, Q. Xu, S.Z. Zhu, J.F. Zhao, F.C. Wang, Key Eng. Mater. 368–372, 1743 (2008)CrossRefGoogle Scholar
  9. 9.
    J.C. Han, P. Hu, X.H. Zhang, S.H. Meng, Key Eng. Mater. 368–372, 1722 (2008)CrossRefGoogle Scholar
  10. 10.
    S.Z. Zhu, Q. Xu, C. Feng, J.F. Zhao, J.L. Cao, F.C. Wang, Key Eng. Mater. 368–372, 1727 (2008)CrossRefGoogle Scholar
  11. 11.
    F.Y. Yang, X.H. Zhang, S.Y. Du, Key Eng. Mater. 368–372, 1753 (2008)CrossRefGoogle Scholar
  12. 12.
    W.W. Wu, G.J. Zhang, Y.M. Kan, P.L. Wang, Key Eng. Mater. 368–372, 1758 (2008)CrossRefGoogle Scholar
  13. 13.
    S. Meng, H. Chen, J. Hu, Z. Wang, Mater. Des. 32, 377 (2011)CrossRefGoogle Scholar
  14. 14.
    L. Scatteia, R. Borrelli, G. Cosentino, E. Beche, J.L. Sans, M. Balat-Pichelin, J. Spacecraft Rockets 43, 1004 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    J.F. Justin, A. Jankowiak, Onera J. Aerospace Lab. 3, 1 (2011)
  16. 16.
    A.I. Fisenko, S.N. Ivashov, Int. J. Thermophys. 30, 1524 (2009)ADSCrossRefGoogle Scholar
  17. 17.
    A.I. Fisenko, V. Lemberg, Int. J. Thermophys. 33, 513 (2012)ADSCrossRefGoogle Scholar
  18. 18.
    A.I. Fisenko, S.N. Ivashov, J. Phys. D: Appl. Phys. 32, 2882 (1999)ADSCrossRefGoogle Scholar
  19. 19.
    L.D. Landau, E.M. Lifshitz, Statistical Physics, Course of Theoretical Physics, vol. 5 (Pergamon Press, Oxford, New York, 1980), p. 484Google Scholar
  20. 20.
    A. Kaw, E. Kalu, Numerical Methods with Applications, 1st edn. (, 2008), p. 728
  21. 21.
    A.D. Aleksandrov, A.N. Kolmogorov, M.A. Lavrent’ev, Mathematics: Its Content, Methods and Meaning (Dover Publications, Mineola, NY, 1999), p. 1120Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.ONCFEC Inc.St. CatharinesCanada

Personalised recommendations