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The viscosity of gaseous hd below 80°K
Coremans, J. NL J. V a n Itterbeek, A. Beenakker, J. J. M.
Physica XXIV
1102-1104
Knaap, H. F. P. Zandbergen, P.
THE VISCOSITY OF GASEOUS HD BELOW 80°K by J. M. J. COREMANS, A. VAN I T T E R B E E K , J. J. M. B E E N A K K E R , H. F. P. KNAAP and P. Z A N D B E R G E N Communication No. 312d from the Kamerlingh Onnes Laboratorium, Leiden, Nederland Synopsis Data are given for the coefficient of viscosity of HD below 80°K. These results are compared with predictions based on a quantum-mechanical modification of the law of corresponding states.
1. Introduction. In an earher paper l) on the coefficient of viscosity of gases between 20 and 80°K we have already mentioned that HD gas was measured together with He, Ne, H2 and D~. However, there were difficulties ill analysing its purity, caused by decomposition of HD in the mass-spectrometer to a mixture of HD, D2 and H2. After some improvements the analysis of HD showed it to be 95 4- 2 ~ pure, the impurity consisting of roughly equal parts of H2 and D2. Thus, we are able at present to give measured •values of the coefficient of viscosity of HD as a function of temperature. We do not correct for the impurity of H2 and D2 since the effects of H2 and D2 on the coefficient of viscosity of HD are opposite, and approximately equal. The magnitude of the corrections is at the most 1~/o. (The viscosity of such a mixture is practically linear in the concentration). The HD was prepared by the action of D20 on LiA1H4 2). 2. Experimental results. For the method and the description we refer to our previous paper 1). T A B L E IThe coefficient of viscosity of HD as a function of temperature, Constant of the apparatus: 2 I D C / ~ R 4 = 1367 × 10-~. Zero-damping:A0/T0 = 134 x 10 -6. T °K
(AIx
-
-
Ao/zo
20.41 26.09 82.57 41.35 48.06 60.30 70.32
-
-
Adz.)
x
l0s
Mirror- and bar-damping: For H D : z]s/'r8 :
1102
~P
12.0 15.8 20. I 24.9 28.8 34.9 39.0
879 1155 1467 1824 2104 2555 2849
--
~HD
--
1.9 × 10 -6.
THE VISCOSITY OF GASEOUS H D BELOW 8 0 ° K
1103
Table I gives the experimental data. In fig. 1 the results of the measurements are plotted together with those of B e c k e r 8). The agreement is fairly good.
/
I~P 40
20
0
T__~
SO
20
8C°K
F i g . 1. C o e f f i c i e n t o f v i s c o s i t y of g a s e o u s H D a s a f u n c t i o n o f t e m p e r a t u r e . (D o w n m e a s u r e m e n t s , [] B e c k e t a n d M i s e n t a 8).
The smoothed values derived from fig. 1 are given in table II. T A B L E II Smoothed values of r/ obtained from fig. 1. T °K
r/HD /~P
20 30 40 50 60 70
11.9 18.1 24.0 29.5 34.7 39.7
We will compare these values with predictions based on a quantummechanical modification of the law of corresponding states. We assumed the molecular constants of HD to be equal to those of H2, with the exception, of course, of the mass. We used the values for a LennardJones (I2-6)potential as derived from the second virial coefficient data 1) s = 51.08 × 10-is erg, a = 2.928 A and ~/k = 37.00°K. From these values
1104
THE VISCOSITY OF GASEOUS
H D BELOW 80°K
we can derive e~'/a/me = 5.355 × 103 and the reduced length: A* -- h/(l~/ms = 1.413. Fig. 2 gives ~*/a/T* as reduced temperature for the three hydrogen isotopes: Curve 4 is the corresponding states curve derived from in our earlier mentioned paper 1).
De Broghe wave a function of the Hg., De and HD. the data of fig. 6
O.16
S
O.12
0.08 O. 5
T"
~
1.O
2.O
Fig. 2. *1"/~/T* as a f u n c t i o n of t h e - r e d u c e d t e m p e r a t u r e . 1. h y d r o g e n 3. H D 2. d e u t e r i u m 4. c o r r e s p o n d i n g s t a t e s c u r v e of H D .
The deviations from the law of corresponding states are probably caused b y the a s y m m e t r y of the H D molecule which can not be described by a Lennard-Jones potential model using the same constants as in the case of H2 and Dg..
Ackno~dedgement. This work is part of the research program of the group for molecular physics of the "Stichting voor Fundamenteel Onderzoek der Materie (F.O.M.)" and has been made possible b y financial support from the "Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek (Z.W.O.)". Received 5- I0-58 REFERENCES l) C o r e m a n s , J. M. J., V a n I t t e r b e e k , A., B e e n a k k e r , J. J. M., K n a a p , H. F . P . and Z a n d b e r g e n , P., Commun. Kamerlingh Onnes Lab., Leiden No. 31 la; Physica 24 (1958) 557. 2) Fookson,-A., P o m e r a n t z , P. and Rick, E. H., Science I12 (1950) 748. 3) B e c k e r , E. W. and M i s e n t a , R., Z. Phys. 140 (1955) 535.
Physica XXIV
1102-1104
Knaap, H. F. P. Zandbergen, P.
THE VISCOSITY OF GASEOUS HD BELOW 80°K by J. M. J. COREMANS, A. VAN I T T E R B E E K , J. J. M. B E E N A K K E R , H. F. P. KNAAP and P. Z A N D B E R G E N Communication No. 312d from the Kamerlingh Onnes Laboratorium, Leiden, Nederland Synopsis Data are given for the coefficient of viscosity of HD below 80°K. These results are compared with predictions based on a quantum-mechanical modification of the law of corresponding states.
1. Introduction. In an earher paper l) on the coefficient of viscosity of gases between 20 and 80°K we have already mentioned that HD gas was measured together with He, Ne, H2 and D~. However, there were difficulties ill analysing its purity, caused by decomposition of HD in the mass-spectrometer to a mixture of HD, D2 and H2. After some improvements the analysis of HD showed it to be 95 4- 2 ~ pure, the impurity consisting of roughly equal parts of H2 and D2. Thus, we are able at present to give measured •values of the coefficient of viscosity of HD as a function of temperature. We do not correct for the impurity of H2 and D2 since the effects of H2 and D2 on the coefficient of viscosity of HD are opposite, and approximately equal. The magnitude of the corrections is at the most 1~/o. (The viscosity of such a mixture is practically linear in the concentration). The HD was prepared by the action of D20 on LiA1H4 2). 2. Experimental results. For the method and the description we refer to our previous paper 1). T A B L E IThe coefficient of viscosity of HD as a function of temperature, Constant of the apparatus: 2 I D C / ~ R 4 = 1367 × 10-~. Zero-damping:A0/T0 = 134 x 10 -6. T °K
(AIx
-
-
Ao/zo
20.41 26.09 82.57 41.35 48.06 60.30 70.32
-
-
Adz.)
x
l0s
Mirror- and bar-damping: For H D : z]s/'r8 :
1102
~P
12.0 15.8 20. I 24.9 28.8 34.9 39.0
879 1155 1467 1824 2104 2555 2849
--
~HD
--
1.9 × 10 -6.
THE VISCOSITY OF GASEOUS H D BELOW 8 0 ° K
1103
Table I gives the experimental data. In fig. 1 the results of the measurements are plotted together with those of B e c k e r 8). The agreement is fairly good.
/
I~P 40
20
0
T__~
SO
20
8C°K
F i g . 1. C o e f f i c i e n t o f v i s c o s i t y of g a s e o u s H D a s a f u n c t i o n o f t e m p e r a t u r e . (D o w n m e a s u r e m e n t s , [] B e c k e t a n d M i s e n t a 8).
The smoothed values derived from fig. 1 are given in table II. T A B L E II Smoothed values of r/ obtained from fig. 1. T °K
r/HD /~P
20 30 40 50 60 70
11.9 18.1 24.0 29.5 34.7 39.7
We will compare these values with predictions based on a quantummechanical modification of the law of corresponding states. We assumed the molecular constants of HD to be equal to those of H2, with the exception, of course, of the mass. We used the values for a LennardJones (I2-6)potential as derived from the second virial coefficient data 1) s = 51.08 × 10-is erg, a = 2.928 A and ~/k = 37.00°K. From these values
1104
THE VISCOSITY OF GASEOUS
H D BELOW 80°K
we can derive e~'/a/me = 5.355 × 103 and the reduced length: A* -- h/(l~/ms = 1.413. Fig. 2 gives ~*/a/T* as reduced temperature for the three hydrogen isotopes: Curve 4 is the corresponding states curve derived from in our earlier mentioned paper 1).
De Broghe wave a function of the Hg., De and HD. the data of fig. 6
O.16
S
O.12
0.08 O. 5
T"
~
1.O
2.O
Fig. 2. *1"/~/T* as a f u n c t i o n of t h e - r e d u c e d t e m p e r a t u r e . 1. h y d r o g e n 3. H D 2. d e u t e r i u m 4. c o r r e s p o n d i n g s t a t e s c u r v e of H D .
The deviations from the law of corresponding states are probably caused b y the a s y m m e t r y of the H D molecule which can not be described by a Lennard-Jones potential model using the same constants as in the case of H2 and Dg..
Ackno~dedgement. This work is part of the research program of the group for molecular physics of the "Stichting voor Fundamenteel Onderzoek der Materie (F.O.M.)" and has been made possible b y financial support from the "Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek (Z.W.O.)". Received 5- I0-58 REFERENCES l) C o r e m a n s , J. M. J., V a n I t t e r b e e k , A., B e e n a k k e r , J. J. M., K n a a p , H. F . P . and Z a n d b e r g e n , P., Commun. Kamerlingh Onnes Lab., Leiden No. 31 la; Physica 24 (1958) 557. 2) Fookson,-A., P o m e r a n t z , P. and Rick, E. H., Science I12 (1950) 748. 3) B e c k e r , E. W. and M i s e n t a , R., Z. Phys. 140 (1955) 535.