By S. S. Penner
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Aside from yielding results in semianalytic form, their procedure appears to be a reasonable one since the supplementary approximations introduced do not obviously lead to larger errors for band and total emissivities than those already anticipated because of the use of the harmonic oscillator intensity formulae. 7-μ, region are associated with combination bands that are strictly forbidden in the harmonic-oscillator approximation; nevertheless, band intensities are calculated theoretically, in good approximation, by using harmonicoscillator wave functions and an appropriate power-series expansion for the electric dipole moment.
PQv ;'■-&[-(--£■)]['-(--£)l· me2 B = C = Be , u' = hc | ω — ω0 I kT, and y = hcBJkT. T h u s the identification Eq. 22a) with Eq. (11-141) of Penner 77 has been established. of 32 1. 25) since [see Eq. (7-91) of Penner 77 ] Z m <*m,m+2 ^ a Z-ra m , w + l /2 5 u a N __ € χ ρ 0,l ^ / _ \ hc ™0 Xl"^ kl /\ [1 — exp(— 2hcw0lkT)] _ a0t2 '° [1 - e x p ( - Α*ω0/*Γ)] " « o . 26) b. Approximate calculation of hemispherical engineering emissivities for transparent gases. For transparent gases distributed uniformly throughout the optical depth pi, the emitted spectral radiancy is πΙω = Rœ = R°œPœpl, where R% is the spectral blackbody radiancy.
Band than we have employed. ;104>113 REPRODUCED FROM PENNER A N D V A R A N A S I . 1. The approximate procedure described in Section 1-6B has been employed in computing the band absorption contributions from various bands at different temperatures and optical depths. From the band absorption results, the total emissivity of water vapor is estimated on the basis of the defining relation Σ* MA where R% is the blackbody radiancy evaluated at the center of the ith vibration-rotation band and σ denotes the Stefan-Boltzmann constant.