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Kinetic Theory : Effusion |
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In the phenomenon of effusion, studied by Graham, a gas is forced by pressure through a small aperture in a metal plate exposed to the air. The relative rates of effusion of different gases are in the inverse ratio of the square roots of the molecular weights, or densities. By means of this result, it is possible to compare the molecular weights of different gases. The apparatus used, devised by Bunsen, is called an effusiometer. Expt. 1. - A glass cylinder has two marks, m1, m2, scratched upon it, and is placed in a cylinder of water. The amount of work spent in forcing each gas through the aperture, which is represented by the rise of level of the liquid, is the same, hence the kinetic energy imparted to each gas is the same. If u1, u2 are the velocities of bulk motion of the gases, i.e., the speeds at which the liquid level rises, we shall have:
At the top of the tube is a stopcock, communicating with the free air through a tube closed by a thin platinum plate, in which a hole has been pierced with a fine needle. The tube is filled with gas to a level below the lower mark, m1 and the tap is opened. The gas streams out through the fine hole, and the time, t, required for the liquid surface to pass from m1 to m2 is taken by a stop-watch. The experiment is repeated with a gas of known molecular weight, e.g., oxygen. The ratio of the squares of the times is the ratio of the molecular weights. If mercury is used, a float is fitted inside the tube, having a line marked on its upper end. The time taken for this mark to pass between two marks on the upper surface of the cylinder is noted. ½ m1u12 = ½ m2u22 where m1 and m2 are the masses of the gases expelled. These occupy the same volume, hence m1/m2 = D1/D2 = M1/M2, where D is the density and M the molecular weight. Again, u1/u2 = t1/t2, where t is the effusion time. Hence: t12/t22 = D1/D2 = M1/M2 If the effusion is not isothermal, as assumed above, this equation will not apply. For adiabatic effusion, the ratio of specific heats cp/cv = γ is involved. |
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