Volume emission coefficient

When Te has been measured, the volume emission coefficient for a collisionally-excited line is given by... 

Kirchhoff s law States that for an opaque surface the absorpion coefflcient is equal to the emission coefficient. For an extended medium such as the atmosphere, assumed to be in local thermodynamic equilibrium, Kirchhoff s law relates the thermal volume emission coefficient to the Planck function. 

Consider continuous radiation with specific intensity I incident normally on a uniform slab with a source function 5 = Bv(Tex) unit volume per unit solid angle to the volume absorption coefficient Kp and is equal to the Planck function Bv of an excitation temperature Tcx obtained by force-fitting the ratio of upper to lower state atomic level populations to the Boltzmann formula, Eq. (3.4). For the interstellar medium at optical and UV wavelengths, effectively S = 0. 

We shall now apply the concepts developed in Chapter 9 to a discussion of the emission and absorption of radiation by an excited gas. We start by deriving the equation of radiative transfer in terms of the volume emission and absorption coefficients for line radiation and consider simple solutions for the case of uniformly excited sources. The terms source function and optical thickness are defined and the effect of self absorption and self reversal in optically thick sources is outlined. 

We now assume that the volume emission and absorption coefficients are independent of x, i.e. the atomic densities and N and the lineshape factor g(w) are constant. The equation of transfer, equation (10.5), may then be solved by multiplication by the integrating factor exp(iC x), giving... 

Fig. 8. Dependence of (A) corrected diffusion coefficient (D), (B) steady-state fluorescence intensity, and (C) corrected number of particles in the observation volume (N) of Alexa488-coupled IFABP with urea concentration. The diffusion coefficient and number of particles data shown here are corrected for the effect of viscosity and refractive indices of the urea solutions as described in text. For steady-state fluorescence data the protein was excited at 488 nm using a PTI Alphascan fluorometer (Photon Technology International, South Brunswick, New Jersey). Emission spectra at different urea concentrations were recorded between 500 and 600 nm. A baseline control containing only buffer was subtracted from each spectrum. The area of the corrected spectrum was then plotted against denaturant concentrations to obtain the unfolding transition of the protein. Urea data monitored by steady-state fluorescence were fitted to a simple two-state model. Other experimental conditions are the same as in Figure 6.

The classical emission profile, Eq. 5.72, may be converted to an absorption profile with the help of Kirchhoff s law, Eq. 2.70, which relates the absorption coefficient a to the emitted power per unit frequency interval per unit volume, with the help of Planck s law, Eq. 2.71, according to... 

Perfetti et al. (131) described a method for the determination of ethoxyquin in milk. Milk solids were precipitated by adding acetonitrile, and the water-acetonitrile supernatant was washed with hexane to remove fat. The addition of NaCl caused the water-acetonitrile solution to separate into an aqueous phase and an acetonitrile phase, thus separating ethoxyquin from most water-soluble impurities. A large volume of water was then added to the acetonitrile layer, and ethoxyquin was partitioned into hexane and removed at reduced pressure. The residue was dissolved in the mobile phase and analyzed on a 250-mm X 4.6-mm-ID. Ultrasphere ODS column using fluorescence detection with excitation of 230 nm, and emission of 418 nm, respectively. A mixture of water and acetonitrile with a diethylamine-acetic acid buffer was the mobile phase. Recoveries from milk samples fortified at 1, 5, and 10 ng/g averaged 78%, with a coefficient of variation of 5.0%. Low concentrations (less than 1 ng/g) of apparent ethoxyquin were detected in commercial milk samples analyzed by this method. 

Note that Eq. (5-136b) is identical to the expression for the gas emissivity for a column of path length ft. In Eqs. (5-136) the gas absorption coefficient is a function of gas temperature, composition, and wavelength, that is, Kb = Kb(T,X). The net monochromatic radiant flux density at dAi due to irradiation from the gas volume is then given by... 

In Equation 46)Yx,r is a compoimded transmission coefficient of the reactor wall (considering absorption and reflections). The value of Pa,z. was verified with radiometer measurements. Equations (45) and (46) give the radiation contribution of an arbitrary direction 0,) to the point 7 (x, 0, (f>) inside the reactor. The next step is to integrate all possible directions of irradiation from the lamp volume of emission to the point I (Figure 15b). 

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