Skip to main content

Advertisement

SpringerLink
Log in

Exergy of Blackbody Radiation and Monochromatic Photon

  • Published:
International Journal of Thermophysics Aims and scope Submit manuscript

Abstract

The study of radiation exergy has important significance for solar energy and high-temperature engineering. In this paper, several exergy expressions of blackbody radiation were discussed and the differences between Petela’s expression of exergy and two other expressions were analyzed. Considering that radiant energy and thermal energy are different, the radiation machine model was established; furthermore, the validity of Petela’s formula was indicated by this model. Based on the concept of radiation equivalent temperature, the integral form expression of monochromatic photon exergy was put forward by establishing the infinite-staged Carnot heat engine model. At the same time, an approximate relation between equivalent temperature and radiation wavelength was given. The error of this relation is negligible when calculating the exergy of blackbody radiation within the temperature range of the engineering field. Finally, the monochromatic photon entropy was discussed by considering the infinite-staged Carnot heat engine model, and an expression of photon entropy with integral form was given. The monochromatic photon entropy and exergy proposed in our paper satisfy the thermodynamic relation and can reflect the differences between radiant energy and thermal energy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Abbreviations

a :

Radiation constant \((7.561 \times 10^{-19}\, \hbox {kJ}\cdot \hbox {m}^{-3}\cdot \hbox {K}^{-4})\)

\(b_{BR}\) :

Blackbody radiation exergy flux \((\hbox {W}\cdot \hbox {m}^{-2})\)

c :

Radiation propagation speed in vacuum \((2.988 \times 10^{8}\,\hbox {m}\cdot \hbox {s}^{-1})\)

\(c_{1}\) :

First radiation constant \((3.74 \times 10^{-16}\,\hbox {W}\cdot \hbox {m}^{2})\)

\(c_{2}\) :

Second radiation \(\hbox {constant}(1.4388 \times 10^{-2}\,\hbox {m}\cdot \hbox {K})\)

E :

Exergy (J)

f :

Coefficient in equivalent temperature expression

h :

Planck’s constant \((6.626 \times 10^{-34} \,\hbox {J}\cdot \hbox {s}^{-1})\)

H :

Enthalpy of substance (J)

\(H_{0}\) :

Enthalpy of substance under ambient conditions (J)

\(i_{b,\lambda }\) :

Monochromatic radiation intensity of blackbody \((\hbox {W}\cdot \hbox {m}^{-3})\)

k :

Coefficient in equivalent temperature expression

m :

Coefficient in equivalent temperature expression

n :

Coefficient in equivalent temperature expression

\(p_{0}\) :

Ambient pressure (Pa)

Q :

Heat (J)

\(Q_{f}\) :

Heat flow \((\hbox {W}\cdot \hbox {m}^{-2})\)

\(R_{in}, R_{out}\) :

Blackbody radiation energy flow input to radiation engine model or output from radiation engine model \((\hbox {W}\cdot \hbox {m}^{-2})\)

S :

Entropy (\(\hbox {J}\cdot \hbox {K}^{-1}\))

\(S_0\) :

Entropy under ambient conditions (\(\hbox {J}\cdot \hbox {K}^{-1}\))

\(S_{f}\) :

Entropy flow \((\hbox {W}\cdot \hbox {m}^{-2}\cdot \hbox {K}^{-1})\)

\(S_{in}, S_{out}\) :

Blackbody radiation entropy flow input to radiation engine model or output from radiation engine model \((\hbox {W}\cdot \hbox {m}^{-2}\cdot \hbox {K}^{-1})\)

\(s_{v},s_{v{\textit{0}}}\) :

Entropy of monochromatic photon with a frequency of v or a critical frequency of \(v_{0}\;(\hbox {J}\cdot \hbox {s}\cdot \hbox {K}^{-1})\)

T :

Temperature of substance (K)

\(T_{0}\) :

Ambient temperature (K)

\(T_{r}\) :

Temperature used to characterize the exergy of the photon (K)

\(T_{(\lambda )}, T_{(v)}\) :

Equivalent temperature of the photon with a wavelength of \(\lambda \) or a frequency of v (K)

U :

Blackbody radiation energy (J)

u :

Exergy of monochromatic photon (J)

V :

Volume \((\hbox {m}^{3})\)

v :

Frequency \((\hbox {s}^{-1})\)

W :

Work (J)

\(W_{f}\) :

Work flow \((\hbox {W}\cdot \hbox {m}^{-2})\)

\(W_{u}\) :

Useful work (J)

\(W_{e}\) :

Work spent for ‘compression of the environment’ (J)

\(\varDelta \) :

Increment

\(\varepsilon _{1}\) :

Error for radiation temperature above ambient

\(\varepsilon _{2}\) :

Error for radiation temperature below ambient

\(\eta \) :

Exergy-to-energy coefficient

\(\eta _{J}\) :

Exergy-to-energy coefficient of blackbody radiation proposed by Jeter

\(\eta _{p}\) :

Exergy-to-energy coefficient of blackbody radiation proposed by Petela

\(\eta _{S}\) :

Exergy-to-energy coefficient of blackbody radiation proposed by Spanner

\(\eta _{u}\) :

Exergy-to-energy coefficient of monochromatic radiation photon

\(\lambda \) :

Wavelength \((\upmu \hbox {m})\)

\(\lambda _{0}\) :

Critical wavelength \((\upmu \hbox {m})\)

\(\upsigma \) :

Stefan–Boltzmann constant \((5.67 \times 10^{8}\, \hbox {W}\cdot \hbox {m}^{-2}\cdot \hbox {K}^{-1})\)

BR:

Blackbody radiation

HE:

Heat engine

References

  1. S. Wright, Int. J. Thermodyn. 10, 27 (2007)

    Google Scholar 

  2. M.J. Moran, E. Sciubba, J. Eng. Gas. Turbines Power 116, 285 (1994)

    Article  Google Scholar 

  3. R. Petela, J. Heat Transf. 86, 187 (1964)

    Article  Google Scholar 

  4. V. Badescu, Int. J. Sol. Energy 20, 149 (2000)

    Article  Google Scholar 

  5. R. Petela, Sol. Energy 74, 469 (2003)

    Article  ADS  Google Scholar 

  6. S.M. Jeter, Sol. Energy 26, 231 (1981)

    Article  ADS  Google Scholar 

  7. D.C. Spanner, Introduction to Thermodynamics (Academic Press, London, 1964)

    Google Scholar 

  8. R.H. Edgerton, Energy 5, 693 (1980)

    Article  ADS  Google Scholar 

  9. L.N.M. Duysens, Brookhaven Symp. Biol. 11, 18 (1958)

    Google Scholar 

  10. R.S. Knox, in Primary Processes of Photosynthesis, ed. by J. Barber (Elsevier, Amsterdam, 1977)

    Google Scholar 

  11. J.D. Lewins, Int. J. Mech. Eng. Educ. 31, 283 (2003)

    Article  Google Scholar 

  12. A. De Vos, H. Pauwels, J. Phys. C Solid State 16, 6897 (1983)

    Article  ADS  Google Scholar 

  13. P.T. Landsberg, G. Tonge, J. Phys. A Math. Gen. 12, 551 (1979)

    Article  ADS  Google Scholar 

  14. P.T. Landsberg, P. Baruch, J. Phys. A Math. Gen. 22, 1911 (1989)

    Article  ADS  Google Scholar 

  15. V. Badescu, J. Phys. D Appl. Phys. 23, 289 (1990)

    Article  ADS  Google Scholar 

  16. S. Sieniutycz, P. Kuran, Int. J. Heat Mass Transf. 49, 3264 (2006)

    Article  Google Scholar 

  17. V.I. Laptev, J. Appl. Phys. 98, 124905 (2005)

    Article  ADS  Google Scholar 

  18. S.E. Wright, M.A. Rosen, J. Sol. Energy Eng. 126, 673 (2004)

    Article  Google Scholar 

  19. A. Bejan, J. Sol. Energy Trans. ASME 109, 46 (1987)

    Article  Google Scholar 

  20. S.E. Wright, M.A. Rosen, D.S. Scott, J.B. Haddow, Int. J. Exergy 2, 24 (2002)

    Article  Google Scholar 

  21. A.H. Carter, Classical and Statistical Thermodynamics (Pearson Education, London, 2001)

    Google Scholar 

  22. R. Petela, Engineering Thermodynamics of Thermal Radiation for Solar Power Utilization (McGraw Hill, New York, 2010)

    MATH  Google Scholar 

  23. V. Badescu, Cent. Eur. J. Phys. 6, 344 (2008)

    ADS  Google Scholar 

  24. T. Markvart, G.H. Bauer, Appl. Phys. Lett. 101, 193901 (2012)

    Article  ADS  Google Scholar 

  25. S. Lems, H.J. Van Der Kooi, J. De Swaan Arons, Int. J. Exergy 7, 333 (2010)

    Article  Google Scholar 

  26. D. Juretić, P. Županović, Comput. Boil. Chem. 27, 541 (2003)

    Article  Google Scholar 

  27. J. Lavergne, P. Joliot, in Energy Transduction in Membranes, ed. by W.A. Cramer (Biophysical Society, Rockville, 2000)

    Google Scholar 

  28. G. Meszéna, H.V. Westerhoff, O. Somsen, J. Phys. A. Math Gen. 33, 1301 (2000)

    Article  ADS  Google Scholar 

  29. Z. Chen, S. Mo, Prog. Nat. Sci. 17, 1250 (2007)

    Google Scholar 

  30. R. Petela, Int. J. Exergy 7, 89 (2010)

    Article  Google Scholar 

  31. M.F. Modest, Radiative Heat Transfer, 3rd edn. (Elsevier, New York, 2013)

    Google Scholar 

  32. M. Planck, The Theory of Heat Radiation (Blakistons, Philadelphia, 1914)

    MATH  Google Scholar 

  33. E. Ito, T. Komatsu, H. Suzuki, Biophys. Chem. 74, 59 (1998)

    Article  Google Scholar 

  34. A.D. Kirwan Jr., Int. J. Eng. Sci. 42, 725 (2004)

    Article  Google Scholar 

Download references

Acknowledgements

The support of this work by the National Key Technology Support Program of China (No. 2015BAA04B03) is gratefully acknowledged.

Author information

Authors and Affiliations

  1. State Key Laboratory of Clean Energy Utilization, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    Zhijun Zhou, Shiquan Shan, Liping Chen & Yanwei Zhang

Authors
  1. Zhijun Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shiquan Shan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liping Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yanwei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yanwei Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhou, Z., Shan, S., Chen, L. et al. Exergy of Blackbody Radiation and Monochromatic Photon. Int J Thermophys 38, 57 (2017). https://doi.org/10.1007/s10765-017-2196-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10765-017-2196-8

Keywords

Search

Navigation