H • PHYSICAL BASIS OF THERMAL RADIATION 



which vary from one band to another, the intensity of the vibration- 

 rotation bands. The customary spectroscopic designation is used to 

 identify the bands involved. Also shown in Fig. H,5a, H,5b, and H,5c 

 is the ratio i?V(i2S)max at temperatures of 300, 600, and 1500 °K, 

 respectively. 



Each of the vibration-rotation bands consists of a series of spectral 

 lines which produce nonzero absorption coefl&cients at wave numbers in 

 the vicinity of the indicated band centers. The spectral lines have finite 

 widths [7,8,9,10] which increase with pressure. At sufficiently low pres- 

 sures the spectral lines may be considered to be completely separated, 

 whereas at sufficiently high pressures they merge to form a more or less 

 continuous region in which the spectral absorption coefficient varies 



Fig. H,5d. Experimentally observed [23] spectral absorption coefficient Pa as a 

 function of w for the fundamental vibration-rotation band of CO at a pressure of 

 700 lb/in.2 abs (CO-H2 mixtures). The "effective bandwidth" and "average absorp- 

 tion coefficient" are indicated roughly by dotted lines. 



roughly as shown in Fig. H,5d. For separated spectral lines simple ana- 

 lytical procedures [16,16] can be developed for evaluating both e^, and e; 

 the results obtained are applicable only to such molecules as HCl and HF 

 at pressures up to several atmospheres for optical densities of the order 

 of a few cm-atm or less. For the important chemical species occurring in 

 combustion chambers, a useful analytical procedure [11,12,13,14,17] in- 

 volves approximating each vibration-rotation band by a rectangular box 

 of calculable width ("effective band width") with a suitably determined 

 •'average absorption coefficient" (see Fig. H,5d). For regions of over- 

 lapping between bands, the average absorption coefficients are added. 

 It is to be expected that an analysis utilizing average absorption coef- 

 ficients and effective band widths will become better at elevated pressures. 

 In general, for fixed values of the optical density, the emissivities increase 

 with total pressure, approach, and then slowly exceed results calculated 



< 498 > 



