Weighted Sum of Gray Gas WSGG Spectral Model

In Eqs. (5-156), fy is some gray gas absorption coefficient and L is some appropriate path length. In practice, Eqs. (5-156) usually yield acceptable accuracy for P 3. For P = 1, Eqs. (5-156) degenerate to the case of a single gray gas. 

For P = 2 and path length LM, Eqs. (5-156) yield the following expression for the gas emissivity 

Equation (5-158) constitutes a two-parameter model which may be fitted with only two empirical emissivity data points. To obtain the constants ag and xg in Eq. (5-158) at fixed composition and temperature, denote the two emissivity data points as eg = tg(2pL) Eg i = Eg(pL) and recognize that 1 = og( 1 - xg) and g 2 = og( 1 - xj) = o.g( I - xg)(l + xg) = g i(l + Xg). These relationslead directly to the final emissivity fitting equations 

The clear plus gray WSGG spectral model also readily leads to values for gas absorptivity and transmissivity, with respect to some appropriate surface radiation source at temperature 7, for example, 

In Eqs. (5-160) the gray gas transmissivity xg is taken to be identical to that obtained for the gas emissivity Eg. The constant agl in Eq. (5-160a) is then obtained with Knowledge of one additional empirical value for agl which may also be obtained from the correlations in Table 5-5. Notice further in the definitions of the three parameters Eg, a 1, and xg l that all the temperature dependence is forced into the two WSGG constants ag and a 1. 

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