= Solution
For the linear <Planck function> profile, direct integration gives
$$
I_0=\pi B_0+\pi\alpha(1-e^{-\tau_s})\longrightarrow\boxed{\pi(B_0+\alpha)}
$$
in the optically thick limit. A sudden doubling of absorber abundance doubles <optical depth> at every physical height while initially leaving the <temperature> profile fixed. With $\widetilde\tau=2\tau$, the same profile is $B=B_0+(\alpha/2)\widetilde\tau$, not $B_0+\alpha\widetilde\tau$. Thus
$$
\boxed{\widetilde I_0=\pi(B_0+\alpha/2),\qquad \Delta I_0=-\frac{\pi\alpha}{2}.}
$$
If temperature increases downward, $\alpha>0$ and outgoing <spectral irradiance> decreases immediately because the effective emitting region moves upward into cooler gas. Subsequent thermal adjustment is outside this instantaneous comparison.
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