Consider two Boltzmannian gases (A) and (B), at pressures (P_{A}) and (P_{B}) and temperatures (T_{A}) and (T_{B}),

Question:

Consider two Boltzmannian gases $A$ and $B$, at pressures $P_{A}$ and $P_{B}$ and temperatures $T_{A}$ and $T_{B}$, respectively, contained in two regions of space that communicate through a very narrow opening in the partitioning wall; see Figure 6.8. Show that the dynamic equilibrium resulting from the mutual effusion of the two kinds of molecules satisfies the condition
\[
P_{A} / P_{B}=\left(m_{A} T_{A} / m_{B} T_{B}ight)^{1 / 2}
\]
rather than $P_{A}=P_{B}$ (which would be the case if the equilibrium had resulted from a hydrodynamic flow).

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