Molecular Velocity Determination through Gas Effusion: Intermediate Laboratory Experiment

Abstract

An experiment is described to determine the average velocity of gas molecules in a container while effusion takes place through a small hole into vacuum. When the mean free path of the molecules becomes large compared to the hole diameter, the measurement of pressure as a function of time permits the average velocity to be extracted. The equipment and procedure are simple, and an agreement to within 10% of the kinetic theory of gas value has been obtained using an inexpensive McLeod gauge. The experiment has been performed using air, helium, and argon; measurements on air and helium were performed both at room and dry ice temperatures. A formula has been derived to take into account the effect of outgassing of the container walls at low pressures. Average velocities may be extracted either by a hand calculation between pairs of data points, or by using a short computer program for least-squares analysis. A derivation is given in an Appendix for the effect on the effusion of the hole being drilled in a wall of thickness small, but not negligible, compared to the hole diameter. During the initial pump-down period, while the container pressure is still comparable to atmospheric, the pressure-versus-time data can be analyzed in terms of hydrodynamic theory and used to deduce a virtual hole area for the streaming molecules. Measurements of pressure-increase with time in a sealed-off system gave poor agreement with the rate of outgassing needed to fit the effusion data.