= Transparent-gas addition at fixed absorber mass
{title2=$T_s=T_eD^{R_a/c_{pa}}$}
In a well-mixed convective column with fixed absorber mass and constant mass opacity, adding a perfectly transparent gas leaves total <optical depth> $D$ unchanged. The absolute <effective emission pressure> scales with total surface pressure, but their ratio remains $D$. In the thick-column emitting-level model, $T_s=T_eD^{R_a/c_{pa}}$; added gas warms the surface only if its specific-gas-constant to heat-capacity ratio exceeds that of the original gas. Pressure broadening would violate the fixed-opacity assumption and must be treated separately.
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