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Measurements on the velocity and absorption of sound in various gases between + 100°C and − 100°C.—Influence of pressure on the absorption
S~hysica IV, n o 8
A u g u s t u s 1937
MEASUREMENTS ON THE VELOCITY AND ABSORPTION OF SOUND IN VARIOUS GASES B E T W E E N + 100~ A N D - - lC0~ - - I N F L U E N C E O F P R E S S U R E ON T H E A B S O R P T I O N by A. VAN ITTERBEEK and P. MARIENS Natuurkundig Laboratorium, Leuven (Belgi6)
Summary \Ve h a v e c a r r i e d o u t n e w m e a s u r e m e n t s o n t h e v e l o c i t y a n d a b s o r p t i o n of s o u n d i n gases like 02, H2 a n d CO as a f u n c t i o n of t e m p e r a t u r e a n d pressure. F r o m t h e r e s u l t s o b t a i n e d for O~, t h e r e l a x a t i o n t i m e [~for t h e v i b r a t i o n a l s t a t e h a s b e e n c a l c u l a t e d a t 13.2~ a n d 101.0~ a n d also as a f u n c t i o n of p r e s s u r e . A t 13.2~ t h e l a w ~ = Pat~p,p b e i n g t h e p r e s s u r e , is n i c e l y c o n f i r m e d A t 101,0~ t h e v a l u e s o b t a i n e d for ~ are n o t i n a g r e e m e n t w i t h t h i s law. A t low t e m p e r a t u r e s , t h e v a l u e s f o u n d for t h e a b s o r p t i o n c o e f f i c i e n t s are t o o h i g h in c o m p a r i s o n w i t h t h e v a l u e s g i v e n b y t h e classical f o r m u l a . W e b e l i e v e t h a t t h e f o r m u l a for t h e classical a b s o r p t i o n m u s t b e c o r r e c t e d for t h e f a c t t h a t t h e gas is n o t ideal. As i n o u r p r e v i o u s m e a s u r e m e n t s a v e r y g r e a t a b s o r p t i o n of s o u n d i n H~ is f o u n d , w h i c h c a n n o t b e e x p l a i n e d b y t h e k n o w n t h e o r y of d i s p e r s i o n . M e a s u r e m e n t s are also m a d e in H~, in w h i c h t h e p a r a h y d r o g e n c o n c e n t r a t i o n h a s b e e n i n c r e a s e d (45 % p a r a ) . T h i s h a s n o i n f l u e n c e o n t h e a b s o r p t i o n . l ; i n a l l y , t h e m e a s u r e m e n t s w h i c h we h a v e m a d e o n CO, for w h i c h t h e v i b r a t i o n a l e n e r g y is v e r y s m a l l a t o r d i n a r y t e m p e r a t u r e s , s h o w t h a t in t h i s case too, d e v i a t i o n s o c c u r f r o m t h e k n o w n t h e o r y of t h e d i s p e r s i o n of sound.
w 1. Introduction. In continuation of our previous work on ultrasonics 1), we have now carried out new measurements on the velocity and the absorption of sound in various gases like oxygen, hydrogen and carbon oxide as a function of pressure and temperature. It is well known that such investigations are of great importance in order to obtain data concerning the temperature variation of the relaxation time for the vibrational state of the molecules. The experimental difficulty in measurements on the absorption of sound is the obtaining of an electrical system by means of which the acoustical energy is uniformly transformed into electrical energy. In --
Physica IV
6 0 9 -
39
610
A. VAN ITTERBEEK
A N D P. M A R I E N S
our previous measurements we have checked the employed system b y means of measurements on the dependence on pressure of the absorption coefficient of 02 and N 2 at the boiling point of liquid oxygen. For, at this temperature classical absorption must be found. As is well known the classical absorption is given by the formula:
A=pW.
+
--1
(I)
where A represents the absorption coefficient, p the density of the gas, W the velocity of sound, ~ the viscosity, Cv and Cp the specific heats, and K the heat conductivity. At ordinary temperatures a check for the electrical system was supplied b y comparison with some measurements made by P i e 1 em e i e r "). In our new measurements we have completed this check as follows; firstly some measurements were made on argon, for which classical absorption must also be found; secondly the diffraction pictures caused by secondary reflection of the waves on the walls of the resonator tube were examined. For that reason the dimensions of the resonator tube were completely changed. The diameter of the new resonator tube is 5.5 cm. and the length 14.5 cm., so that in the new measurements reflections could be observed at a great distance from the acoustic source. In our previous measurements we found a very great absorption for the acoustic energy in H2. This was also found by A b e 11 o 3). We have now examined this question again. Measurements are also made with hydrogen in which the parahydrogen concentration is increased (45% para). These new measurements have not contributed to an explanation of the great absorption occurring in H 2. We believe that in order to obtain some explanation, systematic measurements with other frequencies (the frequency used in our measurements was 304.4 Kc.) and also measurements on deuterium must be made. Finally we have also carried out some measurements on CO; the variation was studied of the absorption coefficient as a function of the pressure at ordinary temperatures. The results obtained for CO show that, in this case also, there occur some deviations from the known theory of the dispersion of sound. *) W h e n t h e r e is also a l a g for t h e r o t a t i o n a l s t a t e , ~ m u s t be r e p l a c e d b y ' q ' = ~ (1.146) (J. H . J e a n s, D y n a m i c a l T h e o r y of gases, p. 302, 1904).
•
VELOCITY OF SOUND IN GASES BETWEEN + '100~ AND - 100~
611
w 2. Measurements on ox3~ge~. As we h a v e said in tile introduction, check m e a s u r e m e n t s were m a d e with argon gas. The velocity was found to be 320.6 m/sec at 19.4~ (reduced to 0~ " 309.8 m/sec) which agrees c o m p a r a t i v e l y well with the values o b t a i n e d b y R ichards4) (308.8 m/sec at 0~ and b y C a m p b e l l and D i x o n 5) (308.5 m/sec at 0~ W h e n we calculate Cp/'C~ from our m e a s u r e m e n t s we obtain t.686 in stead of 1.666. This deviation m u s t be a t t r i b u t e d to impurities of the Ar. 1"he results obtained for the absorption of sound, and the absorption calculated f r o m the classical formula (1) are given in table I. In these calculations the average value f r o m d a t a given b y L a ndolt-B6rnstein were used f o r ~ a n d K . TABLE
I
M e a s u r e m e n t s o n t h e a b s o r p t i o n of s o u n d in argon at ordinary temperatures
~
pressure at.
A . 104 c m observ,
A . 104 c m ealenl.
18.1 20.0
0.289 0.304
14.9 12.0
13.2 12.5
2O C/t
o~
| I # ### ~o
'JC
~
,d, @.~176
T 0
-fO0
L ~,
-50
0
50
tO0'
Fig. 1. Absorption coefficient of sound for oxygen as a function of the temperature for about one atm. W e see from this table t h a t the a g r e e m e n t is good. A n o t h e r check on the electrical s y s t e m is applied b y m e a n s of a verification whether the intensity of the sound as a function of the distance from the source is of the form of an e-function. This check was also applied in our previous measurements.
612
A. VAN ITTERBEEK
AND P. MARI~;NS
The results obtained for oxygen are shown in Table II. T A B L E II Measurements on the v e l o c i t y and the absorption of sound as a function of the pressure and the temperature temp. @C
101.0
51,7 13.2
--16.3 --44.6 --96.4
I
pressm'e at.
Velocity of s o u n d m/sec
0.989 0.695 0.464 0.249 0.975 0.963 0.683 0.629 0.401 0.357 0.216 0.969 0.861
370.9
1.415
344.7 323.5
1.408 1.406
304.7 287.7 253.4
1.393 1.397 1.403
0.986
0.605 0.361 0.142
(cNcvb
0 I
A . 10 4 c m exper,
A . 10 4 c m class.
16.8 18,1 20.6 27.8 11.0 9.0 9.6 9.3 10.7 11.6 16.7 8.0 6.7 4.5 4.3 5.8 9.4
4.8 6.0 10.3 19.2 4.1 3.5 5.0 5.4 8.4 9.4 15.7 3.0 2.6 1.8 2.9 4.9 12.4
The results obtained for the absorption of sound as a function of the temperature and for a pressure of about one atmosphere (first values of column 2, of table II) are drawn in fig. 1. Also the results obtained for the absorption of sound at 13.2~ are drawn as a function of pressure, together with the curve for classical absorption (fig. 2). As shown in table II, even at low temperatures, where we have to deal with very small values of the vibrational energy, the experimental absorption is still much greater than the absorption calculated from formula (1). In our opinion the formula (1), which has been established for an ideal gas does not hold for such low temperatures. We will shortly examine this question by carrying out measurements using argon and neon gas.
w 3. Measurements on the velocity and lhe absorplion o~ sound in hydrogen. From preliminary measurements on H 2 we have observed that the velocity and the absorption coefficient of sound is strongly influenced by impurities *). For this reason we have taken great care to obtain pure hydrogen. We have used two kinds of H 2. Our first investigations were carried out with H 2 purified by diffusion through *) In practice, this would be in our opinion a v e r y accurate m e t h o d for checking the purity of hydrogen.
VELOCITY OF SOUND IN GASES B E T W E E N + 100~
AND - l C 0 ~
613
palladium. We are greatly indebted to Dr. C a p r o n for his helpful assistance in this experiment. The value obtained for the velocity of sound with this kind of hydrogen (denoted) by H-pall.) is 131 t m/sec at 15.0~ (reduced to 0~ 1276 m/sec.). The average value obtained from audible sound, taken from the literature is 1267 m/sec 6) at 0~ The difference between our value and the value of the literature must be attributed to the dispersion effect. 20 CM
02
~3.2'c 15
[
| qO
~._...e_. e ....
,07'
q.
I0
,P
q2
0.4
Qa
O.8
Io A r
Fig. 2. Absorptioncoefficient of oxygen, at 13.2~ as a function of the pressure. (The dashed line represents experimental absorption - - t h e other classical absorption).
A second series of measurements was carried out with H2 obtained by electrolysis and purified by slowly conducting the hydrogen over reduced copper, heated to a temperature of 500~ The value obtained from these measurements is 1329 m/sec at 20.9~ (reduced at 0~ 9 1281 m/sec), which is in good agreement with the value obtained for H-pall. The results obtained for these two kinds of hydrogen (pressure of about 1 at), and also for H2 in which the para-hydrogen concentration is increased (45~ by means of adsorption on charcoal at liquid air temperatures are given in table III. In table III are also given a few measurements on not very pure commercial hydrogen *). 9) In our opinion the impurities of this commercial hydrogen are hydro-carbons, because we have tried to purify this H~ by conducting it over heated Cu; this operation produced no change in the velocity of sound.
614
A. VAN
ITTERBEEK
AND
TABLE
P. IVIARIENS
III
M e a s u r e m e n t s o n the v e l o c i t y a n d t h e a b s o r p t i o n of s o u n d i n H 2 at o r d i n a r y a n d low temperatures temp,
K i n d of H~
~
H-pall ,
H-elect . . . . . H - e l e c t 45~ p a r a . H-conamerc.,
15.0 --84.5 '
" '
] I
Velocity
m/see
A . 10 4 c m exper.
0.916 0.887 0.900
1311 1077
5 . 5 . 102 2 . 3 . 102
presgure at.
I
I
I ;
20.9 21.0
1329
6.1 . I 0 2
0.574
1328
[
16.0
0.967
1118
6.1 . 10 ~3 . 3 . 10 2
From the results in table III it can firstly be concluded that the absorption in H2 is very great, even at low temperatures, which is in agreement with our previous measurements. Impurities seem to decrease the absorption coefficient; on the other hand the absorption (A/~7) is not so much influenced. An increase of the para-hydrogen concentration seems to have no influence on the absorption coefficient. In our opinion the difference found between the new values obtained at ordinary temperatures for the absorption coefficient of hydrogen and our previous measurements must be explained by the fact that the new measurements are more accurate, but a possible influence of the walls cannot be completely excluded. The agreement between our new values and the result obtained by A b e 11 o 7) is much better. Finally we have also made some measurements on the absorption and the velocity of hydrogen as a function of the pressure; no influence, either on the velocity or on the absorption, was found.
w 4. Measurements on the velocity and the absorption o[ sound in CO at ordinary temperatures. In preparing the CO we have taken care to obtain it very pure. The CO investigated was prepared in the following manner. We let formic acid act on concentrated H2SO4. The gas developed by this reaction passes first through a KOH-solution, and then successively through P205 and a liquid air trap. The CO-gas obtained in this manner is subsequently solidified. The final purifying consists in applying fractional distillation to the solid CO. The apparatus is then filledwith the middle fraction of the CO, obtained in this way. The results obtained for CO are given in table IV.
VELOCITY OF SOUND IN GASES BETWEEN
+ 100~
A N D -- 1 0 0 ~
615
T A B L E IV M e a s u r e m e n t s on the v e l o c i t y a n d a b s o r p t i o n of s o u n d in CO at o r d i n a r y t e m p e r a t u r e temp. ~
pressure at.
18.7 18.9 19.0 19.1
0.850 0.700 0.591 0.337
[
Velocity m/sec
Velocity a t 0~ m/sec
A . 104 c m exper,
A . 104 c m class.
348.9
337.6
14.1 12.8 12.3 12.7
3.6 4.5 5.3 9.3
The value of column 4 of table IV, has been calculated from the experimental value of the preceding column. It agrees very well with the result obtained by other investigators: W ii 11 n e r 8) (337.1 m/sec); S c h w e i k e r t 9) (337.8m/sec); S c h e e l and H e u s e 10) (337.4 m/sec.). As can be observed from table IV, the absorption coefficient of sound in CO is much greater than the classical value. The same as for H2, this fact cannot be interpreted by the known theory for the dispersion of sound, because the vibrational energy at ordinary temperatures is too small to explain this difference.
w5 . Calculation o/the relaxation time/or the vibrational energy o/ oxygen at ordinary temperatures. As is well known the relaxation time for the vibrations can be calculated by using the following formulas: !
1
C
with v~o= v/n, v being the accoustic frequency used and ~ being calculated from the following formula: = 2= ( Q 2 1) n 1 + ~22n 2 with ~ = A/X, X: wavelength in the gas, and A absorption coefficient. Further
Q2_ 1 + R/Co 1 -- R/C where R is the gasconstant, C the total specific heat of the molecule, and Ca the specific heat apart from the vibrational energy. The specific heat corresponding to the vibrational energy can be determined from the tables 11).
616
VELOCITY
OF SOUND IN GASES BETWEEN
+
100~
A N D --
100~
We have calculated ~ at various pressures and temperatures for oxygen, using the experimental results of table II. It was of importance to check whether ~ is inverselTABLE V y proportional to the pressure, as R e l a x a t i o n time corresponding to the had been found by other investivibrations of o x y g e n gators ( R i c h a r d s and R e i d 12) pressure ~ . 106 eat. 10~ at. see sec and W a l l m a n n 1 3 ) . The results obtained by calculation for 13.2~ are given in table V. 1.0 1.6 1.6 Pat is the relaxation time re1.5 0.9 1.7 1.9 1.5 0.8 duced to one atmosphere if we 0.7 2.1 1.5 suppose that ~ is inversely pro0.6 2.5 1.5 0.5 1.5 3.0 portional to the pressure. 0.4 4.2 1.7 1.8 0.3 6.0 As is seen from table V at 13.2~ the law ~ = ~at/P is very sarisI01.0 factorily confirmed. This is also 1.0 3.4 3.4 a nice indirect check on the good 0.9 3.5 3.2 0.8 3.6 2.9 working of our electrical system. 0.7 3.7 2.6 At 101.0~ the law ~ = ~t/P 0.6 2.3 3.8 0.5 3.9 2.0 would seem not to bevalid.But this 0.4 4.2 1.7 last question must be further investigated, because it may be possible that foreign gases, such as water vapour, deriving from the walls of the resonator tube when heated, spoil the measurements. But on the other hand it may be observed that thevalues for the absorption at 101.0~ appear to lie on a smooth curve. Received
June ll,
Louvain, 9th June 1937.
1937. REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
A. v a n Itterbeek andP. Mari~ns, P h y s i c a 4, 207, 1937. ~V.H. P!elemeier, P h y s . R e v . 36, 1005, 1930. T.P. Abello, P h y s . R e v . 32, 1089, 1928. W.T. Riehards, C h e m . P h y s . J . 2, 199, 1934. H.B. Dixon, C. C a m p b e l l andA. Parker, Proc. Roy. Sot. London(A 1 0 0 , 1, 1921. P h y s i k . Tabell., L a n d o l t B6rnstein, 2, 1631, 1923. T. P. A b e l l o , loe. eit. A. W i i l l n e r , W i e d . A n n . 4 , 3 2 1 , 1878. G. S c h w e i k e r t , A n n . P h y s i k . 4 . 8 , 5 9 3 , 1915. K. S e h e e l andW. Heuse, A n n . Physik. 37,79, 1912. P h y s i k . Tabell., L a n d o l t BSrnstein E I , 702, 1927. W . T . R i c h a r d s a n d C. D. R e i d, C h e m . P h y s J . 2, 199, 1934. H. Wallmann, A n n . P h y s i k . 21, 671, 1934.
A u g u s t u s 1937
MEASUREMENTS ON THE VELOCITY AND ABSORPTION OF SOUND IN VARIOUS GASES B E T W E E N + 100~ A N D - - lC0~ - - I N F L U E N C E O F P R E S S U R E ON T H E A B S O R P T I O N by A. VAN ITTERBEEK and P. MARIENS Natuurkundig Laboratorium, Leuven (Belgi6)
Summary \Ve h a v e c a r r i e d o u t n e w m e a s u r e m e n t s o n t h e v e l o c i t y a n d a b s o r p t i o n of s o u n d i n gases like 02, H2 a n d CO as a f u n c t i o n of t e m p e r a t u r e a n d pressure. F r o m t h e r e s u l t s o b t a i n e d for O~, t h e r e l a x a t i o n t i m e [~for t h e v i b r a t i o n a l s t a t e h a s b e e n c a l c u l a t e d a t 13.2~ a n d 101.0~ a n d also as a f u n c t i o n of p r e s s u r e . A t 13.2~ t h e l a w ~ = Pat~p,p b e i n g t h e p r e s s u r e , is n i c e l y c o n f i r m e d A t 101,0~ t h e v a l u e s o b t a i n e d for ~ are n o t i n a g r e e m e n t w i t h t h i s law. A t low t e m p e r a t u r e s , t h e v a l u e s f o u n d for t h e a b s o r p t i o n c o e f f i c i e n t s are t o o h i g h in c o m p a r i s o n w i t h t h e v a l u e s g i v e n b y t h e classical f o r m u l a . W e b e l i e v e t h a t t h e f o r m u l a for t h e classical a b s o r p t i o n m u s t b e c o r r e c t e d for t h e f a c t t h a t t h e gas is n o t ideal. As i n o u r p r e v i o u s m e a s u r e m e n t s a v e r y g r e a t a b s o r p t i o n of s o u n d i n H~ is f o u n d , w h i c h c a n n o t b e e x p l a i n e d b y t h e k n o w n t h e o r y of d i s p e r s i o n . M e a s u r e m e n t s are also m a d e in H~, in w h i c h t h e p a r a h y d r o g e n c o n c e n t r a t i o n h a s b e e n i n c r e a s e d (45 % p a r a ) . T h i s h a s n o i n f l u e n c e o n t h e a b s o r p t i o n . l ; i n a l l y , t h e m e a s u r e m e n t s w h i c h we h a v e m a d e o n CO, for w h i c h t h e v i b r a t i o n a l e n e r g y is v e r y s m a l l a t o r d i n a r y t e m p e r a t u r e s , s h o w t h a t in t h i s case too, d e v i a t i o n s o c c u r f r o m t h e k n o w n t h e o r y of t h e d i s p e r s i o n of sound.
w 1. Introduction. In continuation of our previous work on ultrasonics 1), we have now carried out new measurements on the velocity and the absorption of sound in various gases like oxygen, hydrogen and carbon oxide as a function of pressure and temperature. It is well known that such investigations are of great importance in order to obtain data concerning the temperature variation of the relaxation time for the vibrational state of the molecules. The experimental difficulty in measurements on the absorption of sound is the obtaining of an electrical system by means of which the acoustical energy is uniformly transformed into electrical energy. In --
Physica IV
6 0 9 -
39
610
A. VAN ITTERBEEK
A N D P. M A R I E N S
our previous measurements we have checked the employed system b y means of measurements on the dependence on pressure of the absorption coefficient of 02 and N 2 at the boiling point of liquid oxygen. For, at this temperature classical absorption must be found. As is well known the classical absorption is given by the formula:
A=pW.
+
--1
(I)
where A represents the absorption coefficient, p the density of the gas, W the velocity of sound, ~ the viscosity, Cv and Cp the specific heats, and K the heat conductivity. At ordinary temperatures a check for the electrical system was supplied b y comparison with some measurements made by P i e 1 em e i e r "). In our new measurements we have completed this check as follows; firstly some measurements were made on argon, for which classical absorption must also be found; secondly the diffraction pictures caused by secondary reflection of the waves on the walls of the resonator tube were examined. For that reason the dimensions of the resonator tube were completely changed. The diameter of the new resonator tube is 5.5 cm. and the length 14.5 cm., so that in the new measurements reflections could be observed at a great distance from the acoustic source. In our previous measurements we found a very great absorption for the acoustic energy in H2. This was also found by A b e 11 o 3). We have now examined this question again. Measurements are also made with hydrogen in which the parahydrogen concentration is increased (45% para). These new measurements have not contributed to an explanation of the great absorption occurring in H 2. We believe that in order to obtain some explanation, systematic measurements with other frequencies (the frequency used in our measurements was 304.4 Kc.) and also measurements on deuterium must be made. Finally we have also carried out some measurements on CO; the variation was studied of the absorption coefficient as a function of the pressure at ordinary temperatures. The results obtained for CO show that, in this case also, there occur some deviations from the known theory of the dispersion of sound. *) W h e n t h e r e is also a l a g for t h e r o t a t i o n a l s t a t e , ~ m u s t be r e p l a c e d b y ' q ' = ~ (1.146) (J. H . J e a n s, D y n a m i c a l T h e o r y of gases, p. 302, 1904).
•
VELOCITY OF SOUND IN GASES BETWEEN + '100~ AND - 100~
611
w 2. Measurements on ox3~ge~. As we h a v e said in tile introduction, check m e a s u r e m e n t s were m a d e with argon gas. The velocity was found to be 320.6 m/sec at 19.4~ (reduced to 0~ " 309.8 m/sec) which agrees c o m p a r a t i v e l y well with the values o b t a i n e d b y R ichards4) (308.8 m/sec at 0~ and b y C a m p b e l l and D i x o n 5) (308.5 m/sec at 0~ W h e n we calculate Cp/'C~ from our m e a s u r e m e n t s we obtain t.686 in stead of 1.666. This deviation m u s t be a t t r i b u t e d to impurities of the Ar. 1"he results obtained for the absorption of sound, and the absorption calculated f r o m the classical formula (1) are given in table I. In these calculations the average value f r o m d a t a given b y L a ndolt-B6rnstein were used f o r ~ a n d K . TABLE
I
M e a s u r e m e n t s o n t h e a b s o r p t i o n of s o u n d in argon at ordinary temperatures
~
pressure at.
A . 104 c m observ,
A . 104 c m ealenl.
18.1 20.0
0.289 0.304
14.9 12.0
13.2 12.5
2O C/t
o~
| I # ### ~o
'JC
~
,d, @.~176
T 0
-fO0
L ~,
-50
0
50
tO0'
Fig. 1. Absorption coefficient of sound for oxygen as a function of the temperature for about one atm. W e see from this table t h a t the a g r e e m e n t is good. A n o t h e r check on the electrical s y s t e m is applied b y m e a n s of a verification whether the intensity of the sound as a function of the distance from the source is of the form of an e-function. This check was also applied in our previous measurements.
612
A. VAN ITTERBEEK
AND P. MARI~;NS
The results obtained for oxygen are shown in Table II. T A B L E II Measurements on the v e l o c i t y and the absorption of sound as a function of the pressure and the temperature temp. @C
101.0
51,7 13.2
--16.3 --44.6 --96.4
I
pressm'e at.
Velocity of s o u n d m/sec
0.989 0.695 0.464 0.249 0.975 0.963 0.683 0.629 0.401 0.357 0.216 0.969 0.861
370.9
1.415
344.7 323.5
1.408 1.406
304.7 287.7 253.4
1.393 1.397 1.403
0.986
0.605 0.361 0.142
(cNcvb
0 I
A . 10 4 c m exper,
A . 10 4 c m class.
16.8 18,1 20.6 27.8 11.0 9.0 9.6 9.3 10.7 11.6 16.7 8.0 6.7 4.5 4.3 5.8 9.4
4.8 6.0 10.3 19.2 4.1 3.5 5.0 5.4 8.4 9.4 15.7 3.0 2.6 1.8 2.9 4.9 12.4
The results obtained for the absorption of sound as a function of the temperature and for a pressure of about one atmosphere (first values of column 2, of table II) are drawn in fig. 1. Also the results obtained for the absorption of sound at 13.2~ are drawn as a function of pressure, together with the curve for classical absorption (fig. 2). As shown in table II, even at low temperatures, where we have to deal with very small values of the vibrational energy, the experimental absorption is still much greater than the absorption calculated from formula (1). In our opinion the formula (1), which has been established for an ideal gas does not hold for such low temperatures. We will shortly examine this question by carrying out measurements using argon and neon gas.
w 3. Measurements on the velocity and lhe absorplion o~ sound in hydrogen. From preliminary measurements on H 2 we have observed that the velocity and the absorption coefficient of sound is strongly influenced by impurities *). For this reason we have taken great care to obtain pure hydrogen. We have used two kinds of H 2. Our first investigations were carried out with H 2 purified by diffusion through *) In practice, this would be in our opinion a v e r y accurate m e t h o d for checking the purity of hydrogen.
VELOCITY OF SOUND IN GASES B E T W E E N + 100~
AND - l C 0 ~
613
palladium. We are greatly indebted to Dr. C a p r o n for his helpful assistance in this experiment. The value obtained for the velocity of sound with this kind of hydrogen (denoted) by H-pall.) is 131 t m/sec at 15.0~ (reduced to 0~ 1276 m/sec.). The average value obtained from audible sound, taken from the literature is 1267 m/sec 6) at 0~ The difference between our value and the value of the literature must be attributed to the dispersion effect. 20 CM
02
~3.2'c 15
[
| qO
~._...e_. e ....
,07'
q.
I0
,P
q2
0.4
Qa
O.8
Io A r
Fig. 2. Absorptioncoefficient of oxygen, at 13.2~ as a function of the pressure. (The dashed line represents experimental absorption - - t h e other classical absorption).
A second series of measurements was carried out with H2 obtained by electrolysis and purified by slowly conducting the hydrogen over reduced copper, heated to a temperature of 500~ The value obtained from these measurements is 1329 m/sec at 20.9~ (reduced at 0~ 9 1281 m/sec), which is in good agreement with the value obtained for H-pall. The results obtained for these two kinds of hydrogen (pressure of about 1 at), and also for H2 in which the para-hydrogen concentration is increased (45~ by means of adsorption on charcoal at liquid air temperatures are given in table III. In table III are also given a few measurements on not very pure commercial hydrogen *). 9) In our opinion the impurities of this commercial hydrogen are hydro-carbons, because we have tried to purify this H~ by conducting it over heated Cu; this operation produced no change in the velocity of sound.
614
A. VAN
ITTERBEEK
AND
TABLE
P. IVIARIENS
III
M e a s u r e m e n t s o n the v e l o c i t y a n d t h e a b s o r p t i o n of s o u n d i n H 2 at o r d i n a r y a n d low temperatures temp,
K i n d of H~
~
H-pall ,
H-elect . . . . . H - e l e c t 45~ p a r a . H-conamerc.,
15.0 --84.5 '
" '
] I
Velocity
m/see
A . 10 4 c m exper.
0.916 0.887 0.900
1311 1077
5 . 5 . 102 2 . 3 . 102
presgure at.
I
I
I ;
20.9 21.0
1329
6.1 . I 0 2
0.574
1328
[
16.0
0.967
1118
6.1 . 10 ~3 . 3 . 10 2
From the results in table III it can firstly be concluded that the absorption in H2 is very great, even at low temperatures, which is in agreement with our previous measurements. Impurities seem to decrease the absorption coefficient; on the other hand the absorption (A/~7) is not so much influenced. An increase of the para-hydrogen concentration seems to have no influence on the absorption coefficient. In our opinion the difference found between the new values obtained at ordinary temperatures for the absorption coefficient of hydrogen and our previous measurements must be explained by the fact that the new measurements are more accurate, but a possible influence of the walls cannot be completely excluded. The agreement between our new values and the result obtained by A b e 11 o 7) is much better. Finally we have also made some measurements on the absorption and the velocity of hydrogen as a function of the pressure; no influence, either on the velocity or on the absorption, was found.
w 4. Measurements on the velocity and the absorption o[ sound in CO at ordinary temperatures. In preparing the CO we have taken care to obtain it very pure. The CO investigated was prepared in the following manner. We let formic acid act on concentrated H2SO4. The gas developed by this reaction passes first through a KOH-solution, and then successively through P205 and a liquid air trap. The CO-gas obtained in this manner is subsequently solidified. The final purifying consists in applying fractional distillation to the solid CO. The apparatus is then filledwith the middle fraction of the CO, obtained in this way. The results obtained for CO are given in table IV.
VELOCITY OF SOUND IN GASES BETWEEN
+ 100~
A N D -- 1 0 0 ~
615
T A B L E IV M e a s u r e m e n t s on the v e l o c i t y a n d a b s o r p t i o n of s o u n d in CO at o r d i n a r y t e m p e r a t u r e temp. ~
pressure at.
18.7 18.9 19.0 19.1
0.850 0.700 0.591 0.337
[
Velocity m/sec
Velocity a t 0~ m/sec
A . 104 c m exper,
A . 104 c m class.
348.9
337.6
14.1 12.8 12.3 12.7
3.6 4.5 5.3 9.3
The value of column 4 of table IV, has been calculated from the experimental value of the preceding column. It agrees very well with the result obtained by other investigators: W ii 11 n e r 8) (337.1 m/sec); S c h w e i k e r t 9) (337.8m/sec); S c h e e l and H e u s e 10) (337.4 m/sec.). As can be observed from table IV, the absorption coefficient of sound in CO is much greater than the classical value. The same as for H2, this fact cannot be interpreted by the known theory for the dispersion of sound, because the vibrational energy at ordinary temperatures is too small to explain this difference.
w5 . Calculation o/the relaxation time/or the vibrational energy o/ oxygen at ordinary temperatures. As is well known the relaxation time for the vibrations can be calculated by using the following formulas: !
1
C
with v~o= v/n, v being the accoustic frequency used and ~ being calculated from the following formula: = 2= ( Q 2 1) n 1 + ~22n 2 with ~ = A/X, X: wavelength in the gas, and A absorption coefficient. Further
Q2_ 1 + R/Co 1 -- R/C where R is the gasconstant, C the total specific heat of the molecule, and Ca the specific heat apart from the vibrational energy. The specific heat corresponding to the vibrational energy can be determined from the tables 11).
616
VELOCITY
OF SOUND IN GASES BETWEEN
+
100~
A N D --
100~
We have calculated ~ at various pressures and temperatures for oxygen, using the experimental results of table II. It was of importance to check whether ~ is inverselTABLE V y proportional to the pressure, as R e l a x a t i o n time corresponding to the had been found by other investivibrations of o x y g e n gators ( R i c h a r d s and R e i d 12) pressure ~ . 106 eat. 10~ at. see sec and W a l l m a n n 1 3 ) . The results obtained by calculation for 13.2~ are given in table V. 1.0 1.6 1.6 Pat is the relaxation time re1.5 0.9 1.7 1.9 1.5 0.8 duced to one atmosphere if we 0.7 2.1 1.5 suppose that ~ is inversely pro0.6 2.5 1.5 0.5 1.5 3.0 portional to the pressure. 0.4 4.2 1.7 1.8 0.3 6.0 As is seen from table V at 13.2~ the law ~ = ~at/P is very sarisI01.0 factorily confirmed. This is also 1.0 3.4 3.4 a nice indirect check on the good 0.9 3.5 3.2 0.8 3.6 2.9 working of our electrical system. 0.7 3.7 2.6 At 101.0~ the law ~ = ~t/P 0.6 2.3 3.8 0.5 3.9 2.0 would seem not to bevalid.But this 0.4 4.2 1.7 last question must be further investigated, because it may be possible that foreign gases, such as water vapour, deriving from the walls of the resonator tube when heated, spoil the measurements. But on the other hand it may be observed that thevalues for the absorption at 101.0~ appear to lie on a smooth curve. Received
June ll,
Louvain, 9th June 1937.
1937. REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.
A. v a n Itterbeek andP. Mari~ns, P h y s i c a 4, 207, 1937. ~V.H. P!elemeier, P h y s . R e v . 36, 1005, 1930. T.P. Abello, P h y s . R e v . 32, 1089, 1928. W.T. Riehards, C h e m . P h y s . J . 2, 199, 1934. H.B. Dixon, C. C a m p b e l l andA. Parker, Proc. Roy. Sot. London(A 1 0 0 , 1, 1921. P h y s i k . Tabell., L a n d o l t B6rnstein, 2, 1631, 1923. T. P. A b e l l o , loe. eit. A. W i i l l n e r , W i e d . A n n . 4 , 3 2 1 , 1878. G. S c h w e i k e r t , A n n . P h y s i k . 4 . 8 , 5 9 3 , 1915. K. S e h e e l andW. Heuse, A n n . Physik. 37,79, 1912. P h y s i k . Tabell., L a n d o l t BSrnstein E I , 702, 1927. W . T . R i c h a r d s a n d C. D. R e i d, C h e m . P h y s J . 2, 199, 1934. H. Wallmann, A n n . P h y s i k . 21, 671, 1934.