Effusion is molecular passage through a small opening whose dimensions, including its thickness, are much smaller than the intermolecular mean free path. For an equilibrium ideal gas, the one-way particle rate through a thin hole of area is . This weights molecules by their wall-normal velocity, rather than just counting all molecules in the reservoir. [ref]
https://farside.ph.utexas.edu/teaching/355/Surveyhtml/node224.html. Fitzpatrick, Molecular Effusion, equations 5.284–5.285
An equilibrium Maxwell-Boltzmann gas has number flux onto a plane. Molecules crossing the plane are weighted by their positive normal velocity, so their mean translational kinetic energy is , rather than the bulk value . The translational energy flux is therefore . Internal degrees of freedom contribute their mean energy per crossing molecule when independent of translational velocity.
For an isotropic two-dimensional velocity distribution, a straight opening of width in a region of number per area loses particles at the displayed rate. The angular integral is . At fixed equilibrium kinetic energy the speed distribution scales as , so the rate has the same scaling. A fixed second moment alone does not determine the first moment without a distribution assumption.
During collisionless effusion, selective loss changes the distribution of surviving particle velocities without collision-driven relaxation to a new Maxwell-Boltzmann distribution. The loss law depends on flight paths and on the wall-reflection rule. Speed-dependent depletion and, for specular walls, directional structure can remain.
If a classical monatomic gas re-equilibrates by collisions while losing atoms by effusion, the escaping atoms carry mean kinetic energy . Without wall heating, conservation of energy gives and therefore . This assumes a fixed container volume and a small aperture in the molecular-flow regime.
For a species in two well-mixed vessels of equal volume joined by a thin opening of area , the effusion law gives . Each species' total inventory is conserved. With fixed temperatures and total density sum , the left density relaxes exponentially with time constant to .
At equal temperatures, , and initially separated species mix at different rates. At unequal temperatures, the final density ratio is for every species, while the partial-pressure ratio is . The mass-independent final ratios do not imply mass-independent transient rates. Maintaining different temperatures requires external heat exchange even after net particle transfer vanishes.
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Effusion is the process by which gas particles escape from a container through a small hole or opening into a vacuum or a lower-pressure area. This process occurs without any significant collision of particles between them or with particles of the surrounding medium. Effusion is described by Graham's law, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. This means lighter gases will effuse faster than heavier gases.