= Closed-vessel thermal transpiration
{title2=$\Delta p=2p_0q(q-1)/(q+1)$}
Two equal sealed vessels of fixed <volume (thermodynamics)>, initially at $T_0,p_0$, exchange an <ideal gas> through a thin effusive opening. Hold one at $T_1$ and the other at $T_0$, with both interiors locally thermalized. Zero net <particle> transfer gives $p_h/\sqrt{T_1}=p_c/\sqrt{T_0}$. Writing $q=\sqrt{T_1/T_0}$, conservation of total <particle number> gives $p_h=2p_0q^2/(1+q)$ and $p_c=2p_0q/(1+q)$. Thus $\Delta p=2p_0q(q-1)/(1+q)$. The alternative $p_c=p_0$, $\Delta p=p_0(q-1)$ requires a cold reservoir whose <pressure> is externally held fixed; it is not the closed equal-volume problem.
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