H,5 • CALCULATION OF GAS EMISSIVITIES 



on the basis of effective band widths. At sufficiently high total pressures 

 the calculated emissivities are too low, because the individual spectral 

 lines become broadened in such a way that their tails "spill" effectively 

 across the estimated widths of the bands. For overlapping spectral lines, 

 using the concept of effective band widths, the emissivity e at any tem- 

 perature is given by an expression of the form 



. = ^(l_e-.^)(£if^) (5-1) 



where Pk is the average absorption coefficient for the spectral region of 

 width AcoK. 



It is apparent from Fig. H,5a that at 300°K the principal contribution 

 to € must result from spectral lines in the regions between 600 and 800 cm~^ 

 and between 950 and 1050 cm~^, because the factor {l/W)^^^^Rldw will 

 be very small for other vibration-rotation bands. Furthermore, for very 

 small values of X (i.e. X < 0.1 ft-atm), PkX is effectively zero for all 

 bands except the one identified as OPO — > 00°0; thus, for small values 

 of X, e is practicallj'' determined by a single vibration-rotation band to 

 which, however, the isotopic species C^^0\^ makes an appreciable con- 

 tribution. As X increases, other bands become important and may pro- 

 duce a comphcated dependence of e on X. On the other hand, as noted 

 earlier in this discussion, e will be relatively insensitive to total pressure 

 above a limiting pressure where the spectral lines of a band are prac- 

 tically overlapping. For CO 2 this limiting pressure at room temperature 

 is somewhat above 1 atm [22], for H2O about 3 atm, for CO about 10 atm 

 [18], etc. 



Fig. H,5b shows that, for CO2 at 600°K, the major contributions are 

 made by 600 to 1050 cm-^ and 1800 to 2400 cm"^ regions with, how- 

 ever, non-negligible contributions arising from the spectral region around 

 3600 cm-^ Since the important contributions to e are made by differ- 

 ent vibration-rotation bands at different temperatures, the dependence 

 of e on T for fixed values of X and total pressure may be complicated, 

 particularly for polyatomic gases and for gas mixtures. Hence any 

 extrapolations to temperatures higher than those for which measure- 

 ments are available lead to questionable results. 



Fig. H,5c shows that at 1500°K the region between 1500 and 500 cm-^ 

 makes the important contributions to e, unless as-yet-unobserved com- 

 bination and overtone bands of sizable intensity occur at larger values 

 of w. 



In view of the apparent dangers inherent in indiscriminate extrapo- 

 lation of empirical data on gas emissivities, it is of importance to ask to 

 what extent theoretical considerations can serve as a useful guide for gas 

 mixtures of the type encountered in combustion devices. In answer to 



< 499 ) 



