Graham effusion

Thomas Graham studied the effusion of gases, that is their escape from a container through a small hole. The following table gives the time required for 227 cubic inches of a variety of gases to escape through a hole in a small brass plate at 68°F. The table also gives the density of the gases relative to that of air (i.e., in units such that air = 1).

gas time (s) relative density
oxygen 909 1.10563
air 865.5 1
hydrogen 242 0.06926
carburetted hydrogen 623 0.5549
carbonic oxide 849.5 0.96779
nitrogen 850.5 0.97137
carbonic acid 1052 1.52901
(Download a spreadsheet file containing Graham's data by clicking here.)

gas	time (s)	relative density
oxygen	909	1.10563
air	865.5	1
hydrogen	242	0.06926
carburetted hydrogen	623	0.5549
carbonic oxide	849.5	0.96779
nitrogen	850.5	0.97137
carbonic acid	1052	1.52901

Is there a relationship between time and density? If so, what is it? Try plotting the effusion time t vs. the density ρ, then ln t vs. ρ, and then ln t vs. ln ρ. Is the result of any of the plots a straight line? If so, note the slope m and y-intercept b, and write the resulting equation y = mx + b in terms of t and ρ. Finally, solve that equation for t as a function of ρ; that is the relationship between effusion time and gas density.

Reference

Thomas Graham, "On the Motion of Gases," Philosophical Transactions of the Royal Society of London 136, 573-631 (1846).

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