Effusion and Wall Collisions

Effusion is a process by which molecules of a gas pass through a small hole into a vacuum. The hole must be small enough so that the gas does not flow through the hole as a fluid, but passes as individual molecules. According to Graham s law of effusion, at a given temperature and a given pressure the rate of effusion of a gas is inversely proportional to the square root of its density. 

Our analysis of effusion will be similar to that of the pressure in Section 9.5 except that we will now compute the number of molecules striking an areainstead of the force exerted on this area. If this area is a hole in the wall, we obtain the rate of effusion. If the area is a section of the wall, we obtain the rate of wall collisions. The number of molecules with velocities in the velocity interval dvxdvydv that will strike the area in time t is given by Eq. (9.5-9)  

The integral in this equation can be performed by the method of substitution. We let w = v, so that the integral becomes 

The number of particles that strike the area in time x is proportional to the area js/, proportional to the length of time x, proportional to the number of particles per unit 

This equation for the rate of wall collisions also gives the rate of effusion per unit area in the case of a small hole in the wall. The effusion rate predicted by Eq. (9.6-6) is inversely proportional to the square root of the mass of the particles, and thus to the square root of the density, in agreement with Graham s law of effusion. 

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