Density and Diffusion of Gases Measured by Displacement Interferometry

PHYSICS: C. BARIUS

VoL. 10, 1924

153

DENSITY AND DIFFUSION OF GASES MEASURED BY DISPLACEMENT INTERFEROMETRY By CARiD BARUS

DPrDARTMUNT OF PHYSICS, BROWN UNIVIRSITY Communicated February 26, 1924

1. Apparatus.-The present method is singularly simple and expeditious, and should nevertheless give results well within 1%. I have carried it through preliminarily to exhibit its entire feasibility and to suggest appropriate modifications of apparatus. The plan is virtually a Utube comparison of the pressure of a rather long column of gas with that of an identical column of air. In figure 1 (diagram) tt is the quill tube

7'0

0 2

4

68 8

0

12 14- 16 18

(68 cm. long) in which the gas (here coal gas, lighter than air) is to be stored. This communicates by the three-way stopcock C with one shank G (10 cm. in diam., 1 cm. deep) of the interferometer U-gauge. M shows the flat charge of mercury, p the sealed cover glass, L one component beam of the interferometer. The other shank (not seen) is merely open to the atmosphere. With C -set as in figure, the gas arriving at g is passed in excess through tt. After a few minutes the plug of C is suddenly rotated 900 counterclockwise and the pressure produced at M read off in fringe displacements in the telescope of the interferometer. The zero of the ocular scale will usually have to be set by the slide micrometer. The operation should be repeated many times to obviate any marked throw of fringes, as the reading of the ocular micrometer must be made (say within 5 sec.), before appreciable diffusion has set in.

154

PHYSICS: C. BARUS

PROC. N. A. S.

If a stopwatch is started when the gas is definitely shut off, the progress of the diffusion phenomena (here occurring at both ends of tt) is registered by the displacement of fringes from minute to minute. C should be slightly above M, the tubulure s slanting upward toward the left. The adjustment given is convenient in requiring but little gas and it may also possibly serve for vapor density; but for greater precision it is desirable to so modify the apparatus that the region GsCt may all be filled with gas initially and diffusion take place from the bottom of tt only. 2. Equations for Density.-Let p be the observed pressure, h the mercury head of density Pm, x the reading of the slide micrometer normal to mirror, s the reading of the ocular micrometer and 0 the angle of reflection of the rays of the quadratic interferometer. Then the equations Ak = Ax cosO, Ap = Ax cos Op,g = HApg follow in succession, if H is the length of the gas tube tt and Ap = p' -p, the difference of density of air and gas. Hence Ap = Ax cos 0 pm/H. In the apparatus 0 = 46.80 (provisionally measured) and Ax = 10-621.5 As. This makes Ap = 10-62.94 As. 3. Data for Density.-An example of the results obtained both for diffusion and density is given in figure 2, the ordinates being fringe displacements s propottional to pressures p and the abscissas the corresponding times in steps of 1 minute. One notes the cusps indicated by the arrows with three branches ((1), (2), (3)), which may be due to the diffusion out of different constituents of the gas; or more probably, to the sudden release from the surface viscosity of mercury. As only the beginning and end (15 min.) of the curves will be used, I did not tap the gauge to avoid commotion of fringes; but this is also non-essential. The repeated filling of the tube gave me an initial As = 168 which should be trustworthy to about one unit. Hence Ap = 10-6 X 494 whence, if for air p' = 10-61180, p = .000686; or under normal conditions p = .00075. This result is a pretty close hit in order of value; but for definite results the temperature of the gas in the tube itself should be taken, etc. One may note that if the tube is warmed, the method should include the measurement of vapor densities p/p' = 1- (AxcosO/H) (pm/p'), if the last factor is evaluated. Tests made for the coefficient of expansion of the gas in the warmed tube also proved serviceable. Equations for Diffusion.-If bp/lt = a2?2p/bx2 where p is the density of the gas at time t and a distance x from the end of the tube, the coefficient sought is a2 (cm.2/sec.). The problem is virtually that of diffusion in one direction in infinite space, bounded on one side by a plane at which p = 0 for all time. Initially p = p0 throughout the whole gas filled space. The general solution was long ago given by Riemann and for the present simple case, if x/2aV"t = y, leads to

PHYSICS: G. GLOCkLER

VOL. 10, 1924 p =

2dd

((2po/v)r

2p

=

Since for the vertical tube dp

155

y3 +

-

y5

)

pgdx, an integration gives p = (2x = po and recalling that p/pO = s/so and that the tube length of x 1, the equation solved for a reads =

pog/V'i)(y/2 - y3/12 + y5/60- ...). Putting xpog

s 2v/t(-l/24a2t + 14/480a4t2-

a =

seeing that an approximate a sufficies in the corrections. Hence so would be the initial (t = 0 sec.) and s the final (t = 300 sec.) fringe displacement as given by figure 2; but as in this experiment diffusion takes place at both ends of the tube (two tubes each of length 1/2) the equation becomes finally a

=

5

4

(

-

12/96a2t + 14/7680 a4t2

-

Data for Difjusion.-Inserting the data of figure 2 t=0, so = 168; t = 300 sec., s = 83; 1 =68.4 cm. the first term is .6508, so that a'2 would be .4236. The first correction -12/96a2t = -.1278; the second correction 14/8680a4t2 = .0196 whence a = .580 and a2 = .337. This datum is again a hit of the right order of value, but in need of the modifications already instanced. In particular diffusion from both ends not strictly identical is objectionable.

THE BEHA VIOR OF LOW VELOCITY ELECTRONS IN METHANE GAS By GEORGZ GLOCKLER' GAThS CHEMICAL LABORATORY, CALIFORNIA INSTITUTE or TECHNOLOGY Communicated February 26, 1924

The radiation and ionization potentials of most of the monatomic vapors have been determined2 experimentally. The natural extension of such research would be the determination of these constants for molecules. The simple molecule hydrogen has been investigated extensively3 and the results can be reasonably well interpreted in terms of modern atomistics. When atoms and molecules for which no spectroscopic data exists are investigated by the current-potential method, it must be born in mind that not only a radiation-potential but also the phenomenon of trans-