Heating and cooling balance in the interstellar medium ($\mathcal{C}=n^2\Lambda (T)-n\Gamma$)

A useful optically thin model subtracts volumetric heating from radiative cooling. At equilibrium its net cooling vanishes. Pressure-confined temperature perturbations are governed by the derivative of net cooling per unit mass at fixed pressure, so a negative derivative is unstable. The heating law, species abundances and radiation field must be specified before predicting an equilibrium curve. thermal conduction and finite sound-crossing times limit the isobaric approximation.