= Adiabatic parcel gradient in a hydrostatic environment
{title2=$dT_g/dz=-(g/C_p)T_g/T_{\rm env}$}
A dry parcel in rapid pressure balance with an ambient <ideal gas> has $dT_g/dP=T_g\mathcal R/(PC_p)$. Ambient <hydrostatic equilibrium> gives $dP/dz=-Pg/(\mathcal RT_{\rm env})$, hence $dT_g/dz=-(g/C_p)T_g/T_{\rm env}$. At a temperature-matched launch point this equals the <dry adiabatic lapse rate>, supplying the local linear stability test. A substantially hotter parcel does not exactly follow the ambient density's hydrostatic adiabat.
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