= Isobaric thermal instability
{title2=$\sigma=-c_p^{-1}(\partial\mathcal L/\partial T)_p$}
At <thermal equilibrium>, let $\mathcal L(\rho,T)$ be net cooling per unit <mass>, including a specified heating law. A gas perturbation that stays at constant <pressure> obeys $c_p\,d\delta T/dt=-(\partial\mathcal L/\partial T)_p\delta T$. It grows when this derivative is negative. The isobaric approximation requires <pressure> communication faster than thermal evolution; a volumetric cooling function instead introduces a background <mass density> in the denominator. <Thermal conduction> alters the short-wavelength criterion.
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