= Solution
Cold air is denser than room air at approximately the same <pressure>. The <ideal gas law> gives a fractional <mass density> contrast of order $\Delta\rho/\rho\sim\Delta T/T$. The initial outflow is therefore a <gravity current> driven by <reduced gravity>
$$
g'=g\frac{\Delta\rho}{\rho}\sim g\frac{\Delta T}{T}.
$$
For an illustrative refrigerator height $H\sim1\ \mathrm m$, room <temperature> $T\sim295\ \mathrm K$ and <temperature> difference $\Delta T\sim20\ \mathrm K$, this gives $g'\sim0.66\ \mathrm{m\,s^{-2}}$. Balancing the released <potential energy> with <kinetic energy> gives $U\sim\sqrt{g'H}\sim0.8\ \mathrm{m\,s^{-1}}$. The <buoyancy exchange time of a cold-air enclosure> is consequently
$$
\boxed{t\sim\frac H{\sqrt{g'H}}=\sqrt{\frac H{g'}}
\sim1\text{–}2\ \mathrm s,\quad\text{of order seconds}.}
$$
Using constant <acceleration> over height $H$ gives $\sqrt{2H/g'}\sim1.7\ \mathrm s$, consistent at this level. Warm air enters as cold air leaves, so unrestricted vacuum free fall is not the right <acceleration> model. No dimensions or temperatures are specified in the source, so an order-of-magnitude estimate with explicit representative values is the appropriate result; shelves and mixing can delay complete replacement.
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