Effusive cooling
= Effusive cooling
{title2=$T\propto N^{1/3}$}
If a classical monatomic gas re-equilibrates by collisions while losing atoms by <effusion>, the escaping atoms carry mean <kinetic energy> $2k_BT$. Without wall heating, <conservation of energy> gives $d(3Nk_BT/2)=2k_BT\,dN$ and therefore $T\propto N^{1/3}$. This assumes a fixed container <volume (thermodynamics)> and a small aperture in the molecular-flow regime.