Physica VII, no 10 December 1940

SOUND ABSORPTION IN LIGHT GASES by A. VAN ITTERBEEK and P. MARIENS

Natuurkundig Laboratorium, Leuven (Belgie)

Zusammenfassung

Schallabsorptionsmessungen wurden ausgefiihrt in leichten Gasen (H2, D2 und He) bei verschiedenen Drucken und Temperaturen (0”-100°C). In H2 und D2 haben wir eine Zunahme des Absorptionskoeffizienten mit abnehmendem Druck gefunden. Fiir He fanden wir eine Abnahme der Absorption mit abnehmendem Druck.

Was H2 und D2 betrifft kann man die zu grosse Absorption teilweise durch eine Verzogerung des Energieaustausches von Translations- und Rotationsenergie erkllren. So haben wir aus unseren Absorptionsmessun- gen die Einstellzeit fiir die Rotationsenergie berechnet und haben folgen- de Werte gefunden: fur H2; PAT. 10s = 1,9 und ftir D2; PAT. 10s = 1,l. Man kann dabei bemerken dass das Verhaltnis dieser beiden Einstellzeiten gerade tlbereinstimmt mit dem Verhaltnis der iibereinstimmenden (selbes J) Rotationsenergiewerte. Weiter findet manauch dass fiir die beiden Gase die gefundenen Einstellzeiten dem Druck umgekehrt proportional sind.

Fur die zu grosse Absorption in He haben wir keine Erkllrung gefun- den.

$ 1. Introdztctioi. As is well known the fact that the absorption of sound in light gases (HZ, D2 and He) is stronger than one would expect from the classical absorption coefficient was up to now a difficult question to understand. In 1938 one of us published to- gether with L. T h y s l) a series of measurements carried out at room-temperature on the absorption of sound in H2, D2, He and Ne. As was established from these measurements the absorption of sound in HZ is about 20 times the classical theoretical value, for D2 the experimental value is a factor 10 too great, for He and Ne respectively a factor 4 and 3.

Up to the present it was’not certain wether this too great absorp- tion in H2 and.D2 was due to a lag of the transfer of the rotation energy. It is clear that for He and Ne there must be another cause.

- 938 -

SOUND ABSORPTION IN LIGHT GASES 939

H a 1 p e r n “) has pointed out, in a preliminary note which appear- ed in Physical Review of last year, a possible explanation for the phenomenon occurring in light gases.

We have now studied experimentally the absorption of sound in H2, D2 and He as a function of pressure and temperature (O” and 90°C). From these measurements we arrived at the following con- clusion: the too great observed absorption must be ascribed to two causes : 1”) the rotational lag which appears to exist in the case of HZ and D2; 2”) some other phenomenon which we do not know and which seems to be connected with a general property of all light gases.

From our absorption measurements in H2 and D2, we found that the absorption of sound increases with decreasing pressure. From these measurements we computed the relaxation times for the rota- tional energy; we found respectively: for H2, FAT . 10s = 1,9 and for DZ2 PAT. 10s = 1,l. We can remark, therefore, that the ratio between these two relaxation times is equal to the ratio between the corre- sponding (same J) rotational energy-states. We also found that the relaxation times obtained at different pressures are inversely pro- portional to these pressures.

The absorption of sound in He-gas decreases with decreasing pressure. This phenomenon could not be explained and, as was also remarked by H a 1 p e r n, we have here and in the case of all light gases probably to deal with an unknown general property.

$2. Measurements in H2 and D2. As in our previous measure- ments, we used the frequency 598,99 Kc. The gases in question are purified very carefully. The hydrogen we used was taken from liquid hydrogen. To that end a small tube was introduced into a liquid hydrogen bath. In this manner the hydrogen is taken from the inte- rior part of the liquid. The same operation was carried out for the * D2-gas. A very nice proof of the purity of the investigated gases is that the experimental values obtained for the velocity of sound are in very good agreement with the computed ones (see tables I and II). The results obtained for the absorption of sound in H2 and D2 are communicated in tables I and II. The values obtained for the ab- sorption of sound in HZ and D2 at room temperature as a function of pressure are represented in fig. 1.

940 A. VAN ITTERBEEK AhrD P. MARIENS

TABLE I

Absorption-coefficients and velocities of sound in Hz

& 1 .p, j :zc / $::, 1 piz.i;:- 1 a0 .:04 l(OY-ao~.lc

2 0,976 1270 1269 511 27 484

lb 1,003 1299 1300 561 27 534

18 0,99 1 1309 1305 591 20 563

18 0,99 I 1307 1305 580 28 552 18 0,812 1307 1305 652 .34 618 18 0,611 1306 1305 705 45 660

18 0,418 1306 1305 076 66 810

48 1,000 1373 1368 593 29 564

67 1,005 1410 1407 608 30 578

81 1,021 .I438 1436 575 31 544 81 0,797 I433 1436 607 40 567

80 0,600 1432 I434 755 53 702 81 0,355 1440 1436 1250 09 1161

TABLE II

Absorption-coefficients and velocities of sound in D2

jc 1 ,P, 1 zgc 1 zLc j <iF- / pz.fj- / kt,,-cd.10

-- 1 0,696 892,b 092,4 471 53 418 1 0,50 1 092,7 092,4 592 74 518

15 0,751 916,b 9 15,o 465 51 414

18 0,770 922.3 919,7 427 50 377 18 0,583 921,9 919.7 540 66 474 17 0,516 918,b 918,l 616 75 541 17 0,476 9 19,9 918,l 633 81 552 17 0,392 919,7 918,l 739 90 641

17 0,295 919,l 918,l 923 131 792

55 0,804 976,9 976,4 446 52 394

78 0,836 1011 1010 500 53 447 77 0,674 1009 1009 559 65 494 78 0,520 1013 1010 746 85 661

79 0,407 1016 1012 886 108 770 79 0,322 1010 1012 1012 137 . 075

SOUND ABSORPTION IN LIGHT GASES 941

In tables I and II, FL’,,/, and LV,,, denote respectively the experi- mental and the throrctical velocity of sound. W,,, is computed by means of the theoretical formula dC,/C,, . RT (C, and C,, being the specific heats, T the absolute temperature and Ii the gas constant). CZ,,~,, denotes the experimental absorption of sound pro wave-length, and x0 the classical absorption coefficient computed by means of the formula of L c b c d c w (see our previous publications).

$ 3. Dimrssion of the ~ewlts obtaiued for H2 and D2. From the results of tables I and II, we can observe in the first place, that there is a very good agreement between the experimental values obtained for the velocity of sound and the computed ones. This can be con- sidercd as a proof of the purity of the invcstigatcd gases.

Secondly WC can observe that as a function of pressure the ab- sorption of sound m the two considered gases increases with dccrea- sing pressure. This fact points out that the phenomenon in question is connected with collision mechanism.

From the values obtained for (a,, - Q) . lo4 of tables I and II, we computed the relaxation time for the rotational energy. To this end WC used the formulas established for the vibrational energy transfer (see Physica VI, 51 I, 1939). In a paper shortly to appear, it will bc established by one of us that the formulas in question can also be applied to rotational-energy transfer. In the formulas mentioned the vibrational specific heat must then be replaced by the rotational specific heat. The values obtained for the relaxation times for the rotational energy are given in the tables III and IV.

The values in columns 5 of the tables III and IV, arc the computed reduced absorption coefficients corresponding to one atm. One sees that WC‘ obtain a nearly constant value. The existing deviations arc discussed in 3 4.

As a very interesting fact we can put forward that the ratio between the relaxation times found for H2 and D2 is equal to about 2. On the other hand the ratio between the corresponding (same I), separated rotational energies of H2 and D2 is also equal to about 2 (inversely proportional to the moments of inertia).

In a previous paper E u c k e n and B e c k c r “) remarked that they had not found a dispersion effect in H2-gas even up to an ultra- sonic frequency of 1600 kc. We computed by means of our obtained relaxation time (2.108 set) the theoretical values for the velocity of

942 A. VAN ITTERBEEK AND P. MARIENS

TABLE III

Relaxation times for the transfer of the rotational energy in Hz

t ‘C

2

16

18

48

67

81

-i-

T

-

P atm

___-

(a,-ao) . 104 p. 108

set p (atm.) . 108

set

0,976 484 13 198

1,003 534 230 a3

0,991 563 2,1 291 0,991 552 291 291 0,812 618 2,3 189 0,611 660 2,5 1,5 0,418 810 391 1,3 1,000 564 %I 2,1

1,005 578 291 a1

1,021 544 290 2,o ‘0,797 567 291 197 0,600 702 286 I,6 0,355 1161 4,3 195 -

TABLE IV

Relaxation times for the transfer of the rotational energy in D2

t “C

1

15

17

55

78

-

-

-

P atm

0,696 0,501

0,75 1

0,778 0,583 0,516 0,476 0,392 0,295

0,804

0,836 0,674 0,520 0,407 0,322

-

I -

-

.-

:aez - a0) . l@ p. 108

SW

418 518

195

199

415 1,5

377 1,4 474 13 541 w 552 2,1 641 2,4 792 2,9

394 1,5

447 1,7 494 13’3 661 2,5 778 2,9 875 3,3

-7 -

3 (atm.) . 10s set

____-

19 I,0

191

I,1 190 I,0 19

099 0,9

12

194 12 193 12 I,1

SOUND ABSORPTION IN LIGHT GASES 9.43

TABLE V

t “C

I’ atm

21 1,029 21 0,805 19 0,804

21 0,680 22 0,503

22 0,37 1

22 0,250

57 0,864

74 0,888 72 0,725 71 0,543 70 0,313

Absorption coefficients and velocities of sound in He gas -

-

-

~000 -

800 -

600 -

400 -

)!oo - P

3 8 O-

we, m/set

1010,3 1010,2 1005,9 lOd9,7 1010,b 1011,o 1010,7 1072,2 1097,3 1095,4 1092,8

1090,3

- I - 1

wth m/set

1009,3 1009,3 1005,9 1009,3 101 I,0 101 l,o 1011,o 1069,2 1096,4 1092,3 1091,7 1090, I

- I L

-

a,, . 10’

354 362 342 339 322 331 380 391 307 299 331 -

-

-

-

a0 . 10’

62 79 78 93

126 171

254 79 79 97

129 -

- ( - I

a,,-d.l@

292 283 264 246 196 160 126

312 228 202 202 -

I

Oep 0.2 0.9 06 08 iOAt

Fig. 1. Absorption of sound in H 2, D2 and He at room temperature as a function of pressure.

944 SOUND ABSORFTION IN LIGHT GASES

sound corresponding to 1000 kc and 1600 kc. We found respectively: 1309,4 m/set and 1310,5 m/set., for low frequencies the theoretical value is equal to 1308,7 m/set. It is comprehensible, therefore, that no dispersion effect can be detected.

3 4. MeaszGrements in He-gas. The helium gas is purified as follows. The gas is taken from commercial He-gas (impurity 1 %), which we let slowly stream through a tube filled with active charcoal and cooled with liquid air. From the values for the velocity of sound in table V, we can again observe that there is a good agreement between the theoretically computed values and those obtained by us.

The results obtained for the absorption of sound at room-tempera- ture are represented in fig. 1, together with those obtained for HZ and D2.

From the results of table V, we see that there is a decrease of the absorption of sound with decreasing pressure. We have not found an explanation for the phenomenon occurring in He. In our opinion, however, the observed phenomenon must be connected with some unknown property, of the light gases and the deviations found for Hz and D* are due to the same phenomenon.

Received September 7th, 1940. Louvain, 21 August 1940.

REFERENCES

I) A. van I t t e r b e e k and L. T h y s, Physica 5, 889, 1938. 2) E. Hal pern, Phys. Rev. 52, 882, 1939. 3) A. E u c k e n and R. B e c k e r, Z. phys. Chem. E 27,235, 1934.