H • PHYSICAL BASIS OF THERMAL RADIATION 



Theoretical calculations of gas emissivities therefore require determi- 

 nation of Po, in terms of atomic or molecular parameters, followed by 

 evaluation of the integral appearing in Eq. 4-9. In this connection it is 

 of particular importance to note that absorption coefficients P^ for gas 

 mixtures are additive but that neither spectral nor total emissivities can 

 be added. As the result of this requirement, neither e„ nor e can exceed 

 unity for equilibrium radiation. 



H,5. Theoretical Calculation of Gas Emissivities. Theoretical 

 calculations of gas emissivities require evaluation of P^ from atomic or 

 molecular parameters. The connection with basic theory is made con- 

 veniently through the Einstein theory [6] of absorption and emission of 

 radiation, followed by introducing a precise description of the shape of 

 spectral lines [7,8,9,10]. The details involved in establishing this connec- 

 tion between P„ and fundamental physical principles are described else- 

 where [11,12]. In the present discussion it appears desirable to summarize 

 the physical notions and the conclusions reached as the result of more 

 detailed studies. For quantitative calculations of gas emissivities the inter- 

 ested reader is referred to a series of journal articles [13,14,15,16,17] as 

 well as to several survey papers [11,12,18]. 



Since gas emits radiation as the result of electronic, vibrational, and 

 rotational transitions from excited energy levels to lower energy levels, 

 the emitted radiant energy corresponding to these transitions is dis- 

 tributed over a well-defined wavelength region. In general, the radiation 

 emitted as the result of electronic transitions is concentrated in the visible 

 and ultraviolet regions of the spectrum, whereas vibration-rotation bands 

 are responsible for the emission of light in the near infrared. Pure ro- 

 tational transitions give rise to absorption bands at long wavelengths 

 (i.e. 30jLt or more) in the infrared. As the temperature of the emitters is 

 raised, the discrete emission lines or bands occurring at progressively 

 shorter wavelengths make the more important contributions to the 

 emitted radiant energy, because the black body distribution curve has its 

 maximum value at progressively lower wavelengths (see below). At the 

 temperatures of interest in connection with studies of equilibrium radiant 

 heat transfer in combustion chambers, only the transitions corresponding 

 to the infrared vibration-rotation bands make significant contributions 

 to the observed radiant flux. 



The physical principles involved in emissivity calculations can be 

 understood by referring to Fig. H,5a, H,5b, and H,5c, where we have 

 indicated the positions of the centers of vibration-rotation bands of CO 2 

 determined from room temperature absorption experiments, and calcula- 

 ble with great precision from expressions for energy levels derived by 

 spectroscopists [19,20,21]. The abscissa in Fig. H,5a, H,5b, and H,5c is 

 the wave number whereas the ordinate represents, in arbitrary units 



< 494 ) 



