density and diffusion of gases measured by displacement interferometry
TRANSCRIPT
Density and Diffusion of Gases Measured by Displacement InterferometryAuthor(s): Carl BarusSource: Proceedings of the National Academy of Sciences of the United States of America,Vol. 10, No. 4 (Apr. 15, 1924), pp. 153-155Published by: National Academy of SciencesStable URL: http://www.jstor.org/stable/83987 .
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VOL. 10, 1924 PHYSICS: C. BARUS 153
DENSITY AND DIFFUSION OF GASES MEASURED BY DIS- PLACEMENT INTERFEROMETRY
BY CARL BARUS
DEPARTMENT OF PHYSICS, BROWN UNIVERSITY
Communicated February 26, 1924
1. Apparatus.-The present method is singularly simple and expe- ditious, and should nevertheless give results well within 1%. I have carried it through preliminarily to exhibit its entire feasibility and to sug- gest appropriate modifications of apparatus. The plan is virtually a U- tube 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
t50-
4'54
7o/0 _--i '_ _._-
0 2 4 6 8 10O 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 sllank 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 in- terferometer. 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 90? counter- clockwise 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 appre- ciable diffusion has set in.
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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 adjust- ment 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 mod- ify 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 mer- cury head of density p,,, xthe reading of the slide micrometer normal to mirror, s the reading of the ocular micrometer and 0 the angle of reflec- tion of the rays of the quadratic interferometer. Then the equations
Ah = Ax cos 6, 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 = 46.8? (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 dis- placements s proportional to pressures p and the abscissas the correspond- ing 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--6- 1180, p = .000686; or under normal conditions p = .00075. This result is a pretty close hit in order of value; but for definite results the tempera- ture 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' = l- (AxcosO/H) (pm/p'), if the last factor is evalu- ated. Tests made for.the coefficient of expansion of the gas in the warmed tube also proved serviceable.
Equations for Diffusion.-If bp/bt a2blp/bx2 where p is the density of the gas at time t and a distance x from the end of the tube, the coeffi- cient 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 = po throughout the whole gas filled space. The general solution was long ago given by Riemann and for the present simple case, if x/2aN/t = y, leads to
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VOL. 10, 1924 . PHYSICS: G. GLOCKLER 155
p= ((2po/V) J e-Pd 2 = (2po/V/7r) --3 3 + - Y5
Since for the vertical tube dp = pgdx, an integration gives p = (2x pog/ /7r)(y/2 - y/12 y/60 - ...). Putting xpog = Po and recalling that p/po = slso and that the tube length of x = 1, the equation solved for a reads
a = sV VK1 - 1/24a2t - 1/ 480a t2-
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 = 4~ Q sn - - 12/96a2t + / 7680 a4t . . N /, 4:N/t
Data for I)Jfusion.---Inserting the data of figure 2
t - 0, so = 168; t = 300 sec., s - 83; I = 68.4 cm.
the first term is .6508, so that a'2 would be .4236. The first correction -12 /'6a2t = -.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 BEHAVIOR OF LOW VELOCITY ELECTRONS IN METHANE GAS
BY GEORGE GLOCKLER1
GATES CHEMICAL LABORATORY, CALIFORNIA INSTITUTE OF 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-
VOL. 10, 1924 . PHYSICS: G. GLOCKLER 155
p= ((2po/V) J e-Pd 2 = (2po/V/7r) --3 3 + - Y5
Since for the vertical tube dp = pgdx, an integration gives p = (2x pog/ /7r)(y/2 - y/12 y/60 - ...). Putting xpog = Po and recalling that p/po = slso and that the tube length of x = 1, the equation solved for a reads
a = sV VK1 - 1/24a2t - 1/ 480a t2-
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 = 4~ Q sn - - 12/96a2t + / 7680 a4t . . N /, 4:N/t
Data for I)Jfusion.---Inserting the data of figure 2
t - 0, so = 168; t = 300 sec., s - 83; I = 68.4 cm.
the first term is .6508, so that a'2 would be .4236. The first correction -12 /'6a2t = -.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 BEHAVIOR OF LOW VELOCITY ELECTRONS IN METHANE GAS
BY GEORGE GLOCKLER1
GATES CHEMICAL LABORATORY, CALIFORNIA INSTITUTE OF 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-
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