= Buoyancy exchange time of a cold-air enclosure
{title2=$t\sim\sqrt{H/g'},\quad g'\simeq g\Delta T/T$}
Cold air leaving an opened enclosure must displace warmer air, so its driving acceleration is set by <reduced gravity>, rather than by unrestricted fall through vacuum. The <ideal gas law> at approximately common <pressure> gives a fractional <mass density> contrast of order $\Delta T/T$. Balancing gravitational potential energy against <kinetic energy> gives exchange speed $U\sim\sqrt{g'H}$ over height $H$, and time $H/U$. Geometry, entrainment and shelves change its coefficient and can lengthen the time for complete replacement. The estimate describes the initial <buoyancy>-driven exchange.
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