Radiative Equilibrium

  • Shih-I Pai


The simplest case of thermal radiation is the condition of radiative equilibrium at which the temperature of the medium must be a constant throughout the medium. Under the thermodynamic equilibrium, there is a definite relation between the absorption coefficient and the emission coefficient. We are going to discuss the laws of radiation under equilibrium condition in §§ 2 to 4. When there is a radiation field in the flow field, the thermodynamic relations change according to the relative strength of the radiation pressure and the gas pressure. We shall discuss these relations in §§ 4 and 5. For the case of complete thermodynamic equilibrium, the temperature of the whole region must be constant. In the flow field of a gas, the temperature is usually different at different points. Hence we usually will not have the thermodynamic equilibrium condition. However, since in ordinary flow problem, we usually may define a temperature at each point in the flow field, it is a good approximation to assume that the radiative equilibrium is reached locally according to the local temperature. In other words, we may assume that the emission of radiation is according to the local temperature as if the thermodynamic equilibrium condition is reached. Of course, we can not assume that the radiation absorbed is also according to the local temperature, because the radiation to be absorbed comes from other points in the flow field which has different temperature from the local temperature. We shall discuss the local thermodynamic equilibrium condition in § 7 which is very useful in the analysis of radiation gasdynamics.


Thermodynamic Equilibrium Radiation Pressure Black Body Radiation Local Thermodynamic Equilibrium Thermodynamic Equilibrium Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aller, L. H.: Astrophysics: The Atmosphere of the sun and stars. Ronald Press Co., New York, second edition, 1963.Google Scholar
  2. 2.
    Born, M.: Atomic Physics. Hafner Publishing Company, Inc., New York, 1946.Google Scholar
  3. 3.
    Chandrasekhar, S.: Stellar Structure. Dover Publications, Inc., 1957.Google Scholar
  4. 4.
    Godske, C. L., T. Bergeron, J. Bjerknes, R. C. Bundgaard: Dynamics meteorology and weather forecasting. American Meteorological Society and Carnegie Institution of Washington, 1957.Google Scholar
  5. 5.
    Johnson, J. C.: Physical Meteorology. John Wiley & Sons, New York, 1954.Google Scholar
  6. 6.
    Jakob, M.: Heat Transfer. Vol. I, John Wiley & Sons, Inc., New York, 1955.Google Scholar
  7. 7.
    Planck, M.: The theory of heat radiation. Dover publications, Inc., New York, 1959.MATHGoogle Scholar

Copyright information

© Springer-Verlag / Wien 1966

Authors and Affiliations

  • Shih-I Pai
    • 1
  1. 1.Institute for Fluid Dynamics and Applied MathematicsUniversity of MarylandCollege ParkUSA

Personalised recommendations