Measurements on the velocity of sound in helium gas at liquid helium temperatures

Measurements on the velocity of sound in helium gas at liquid helium temperatures

Van Itterbeek, A F o r r e z , G. Physica XX 767-772 1954 MEASUREMENTS ON T H E VELOCITY OF SOUND IN HELIUM GAS AT LIQUID HELIUM T E M P E R A T U ...

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Van Itterbeek, A F o r r e z , G.

Physica XX 767-772

1954

MEASUREMENTS ON T H E VELOCITY OF SOUND IN HELIUM GAS AT LIQUID HELIUM T E M P E R A T U R E S b y A. V A N I T T E R B E E K

a n d G. F O R R E Z

Instituut voor lage temperaturen en technische physica, Leuven, Belgi~

Synopsis From measurements on the velocity of sound in helium gas as a function of pressure at fixed temperatures between 4.22 °K and 3.60 °K we calculated the ratio of the specific heats and the specific heats self. Nearly straight lines are obtained for Cp/Co as a function of pressure. The values are between 2.00 and 1.67. For C,, as a iunction of pressure a minimum is found. The values for Co lie between 2.92 cal/°mol and 3.62 cal/°mol.

§ 1. Introduction. Continuing our previous m e a s u r e m e n t s on the v e l o c i t y of s o u n d at liquid helium t e m p e r a t u r e s , we m e a s u r e d the v e l o c i t y of s o u n d in helium gas at different pressures a n d t e m p e r a t u r e s b e t w e e n 4.22 °K a n d 3.60 °K. F r o m these e x p e r i m e n t a l results we calculated, with the use of the second virial coefficients d e t e r m i n e d b y K e e s o m a n d W a 1 s t r a (1), t h e ratio of the specific h e a t s Gp/Co a n d also the specific h e a t s self as a function of pressure. As it was a l r e a d y f o u n d b y one of us (2) and which was l a t e r on also c o n f i r m e d b y W a 1 s t r a (3) a m i n i m u m a p p e a r s in the specific h e a t Co as a function of pressure. § 2. Experimental technique and cryostat. T h e e x p e r i m e n t a l t e c h n i q u e which we h a v e used at present is b a s e d on the acoustical i n t e r f e r o m e t e r . The a p p a r a t u s is the s a m e as t h a t which we h a v e used in our m e a s u r e m e n t s on liquid helium (4), e x c e p t e d t h a t the vessel c o n t a i n i n g the q u a r t z c r y s t a l is closed a n d is s e p a r a t e d f r o m the liquid, so t h a t it can be e v a c u a t e d a n d filled w i t h helium gas u n d e r different pressures. T h e f u n d a m e n t a l f r e q u e n c y of the q u a r t z c r y s t a l used is a p p r o x i m a t e l y 510 kc, b u t this f r e q u e n c y is d e t e r m i n e d at each m e a s u r e m e n t b y m e a n s of an a c c u r a t e f r e q u e n c y m e t e r (Philco C o r p o r a t i o n t y p e B.C. 221-E). E a c h m e a s u r e m e n t is e x t e n d e d o v e r !0 half w a v e l e n g t h s f r o m which the a v e r a g e is calculated. T h e pressure of the helium gas inside the i n t e r f e r o m e t e r is r e a d b y m e a n s of a precision c a t h e t o m e t e r of the Soci6t6 G6n6voise. T h e t e m p e r a t u r e of the liquid h e l i u m b a t h is d e t e r m i n e d f r o m the v a p o u r pressure, using the tables of V a n Dyk-Schoenberg. - - 767 - -

768

A. VAN ITTERBEEK AND G. FORREZ

§ 3. Experimental Results. The values obtained for the velocity as a function of pressure and different temperatures are given in table I. TABLE I Velocity of sound in helium gas at liquid helium temperatureas a function of pressure Temp. W P °K m/sec n]nl 4.208 120,9 *) 0 97,20 120,5 132,24 119,8 120,82 Ii9,5 243,94 117,9 304,76 114,1 316,82 114,5 I 14,0 354,10 474,88 109,0 494,66 I I0,5 531,84 110, I 610,90 105,8 691,0 105,7 710,00 I03,8 104,1 731,00 738,14 I02,0 727,60 I02,6 734,32 104,3 736,86 I04,4 3.978

0 132,30 181,72 226,06 284,34 345,38 404,00 455,36

l 17,3 *) 116,0 l 14,7

3,780

0 133,76 211,74 293,80 367,30 427,02

114,4 *) l 12,0 I I0,5 107,6 I05,0 I03,2

3.582

0 96,90 125,66 162,90 191,32 243,64 294,60 328,20 395,54

112,5 111,3 109,5 108,0 I07,7

111,3 109,1 108,8 108,2 106,5 105,6 104, I 102,5 i 100,0

*) Calculated from the expression W2 = 5RM.T/3M.

MEASUREMENTS ON THE VELOCITY OF SOUND IN HELIUM GAS

769

Measurements could not be made to pressures below 7 cm Hg, because the sound absorption in the helium gas becomes to large and our oscillator was not adapted for this strong absorption. A new oscillator is now under construction so that the measurements will be continued at still lower temperatures and pressures. The values of table I are graphically drawn in fig. 1 together with the values obtained with audible sound by Keesom and Van Itterbeek (5) see Table II. TABLE II Velocity data of Keesom and Van Itterbeek (7) corrected to

4.192 °K p

W

atm.

m/sec

0 120,88 0,0736 119,85 0,1373 I19,14 0,1966 I17,93 0,2648 I 16,70 0,3981 114,47 0,6282 llO,19 0,9121 I 0 3 , 6 9

q2C ~

• ••

11c

.

IN

x~

1o5

,~



\\

\

%

P. a it,,.

100

od

0.2

o,s

o,4

~"

q5

0,6

0,7

--I

o.a

o,9

~.o

Fig. I. Velocity of sound in helium gas at liquid helium temperatures. Physica XX

49

770

A. VAN I T T E R B E E K A N D G. F O R R E Z

§ 4. Specific heats. Calculations. One of us together with W. H. K e e s o m (5) established the equations to calculate respectively the ratio of the specific heats Cp/C, and the specific heats from measurements of the velocity of sound as a function of pressure for the case that the second and third virial coefficients are known as a function of temperature. If we use Kamerlingh Onnes' equation of state p V = RT(1 + B / V + C/V 2)

(1)

3700o£'~

4~.~08 ° K.

/

/•1582"K

¢P/Ov '1.90

/~

"

1.80

I.zo

1.66

f

p.a,;,.

o

q2

0.4

0.6

0.8

to

F i g . 2. V a l u e s of C p / C v a s a f u n c t i o n of p r e s s u r e .

(R = 1/273,15, B and C the second-and third virial coefficient, p expressed in atmospheres) in combination with classical thermodynamic equations we obtain the following expressions

Cp _ M W 2 [ 1 -

c-7

2BR_Pf+ 3 ( 2 B 2 _ C) [email protected] ]

2 dB Cp -- C~ = R~.l { 1Jr- -R- -dT - "p+

[B2--4TB--d-f--tdB dB 2

-~- T 2 _ _

dT

_

c+

2r dC7 dr_J" R--~}

(2)

771

MEASUREMENTS ON THE VELOCITY OF SOUND IN HELIUM GAS"

W i t h M = 4,0024; Ru=8,315 × 107(erg°CMol) Rc,z = 1,986 (cal/°C Mol). T o calculate the values of B and by Keesom and Walstra(6) 103B = 0,8873

dB/dT we used the equation o b t a i n e d 19,476

5,93 + T---i -

(4)

and also their values of C. The values of dC/dT we calculated from t h e i r values of C as a function of t e m p e r a t u r e . In table I I I the values for B, dB/dT, C and dC/dT are given which we used. TABLE III T°K 4,208 3,582

B'I0"

dTdB'10a ] C.10"

--3,406 . --4,088

0,941 1,260

--0,300 --0,253

dC. 106 dT 1,5 9,5

Table IV contains the values which we obtained for Cp/Co, Co and for C~ The values of table IV are graphically drawn in fig. 2 and fig. 3 respectively. 4.0

C,Cal/'mot b

3.5

3.0

L

P. a ~ m

2.5 0

0.2

0,4

0.6

0.8

t.0

Fig. 3. Values of Cv as a function of pressure. As we see nearly straight lines are found for the values of Cp/Co with a small deviation however at the highest pressures. This m a y be due to t h e fact t h a t the f o u r t h virial coefficient has not been considered. F o r C o a small m i n i m u m appears, as has already been mentioned.

772

" M E A S U R E M E N T S ON T H E V E L O C I T Y OF S O U N D IN H E L I U M GAS

We take the opportunity to express our thanks to Mr De Win, Lic. in Physics for his help during the measurements. This work has been done with the finantial aid of the Belgian Department of Education. TABLEIV T °K

p atm

Cp/Cv

4.208

0, I 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

1,717 1,763 1,805 1,844 1,890 1,932 1,976 2,013 2,037

3.978

0,1 0,2 0,3 0,4 0,5

1,727 1,781 1,833 1,880 1,926

3.780

0,1 0,2 0,3 0,4 0,5

1,736 1,795 1,852

3.582

0, I 0,2 0,3 0,4 0,5

Co

cal/°Mol, 2,92 2,91 2,94

Cp

cal/°Mol.

3,03 3,09 3,16 3,26 3,42 •

5,02 5,13 5,30 5,51 5,72 5,97 6,25 6,57 6,96

2,88 2,88 2,95 3,04 3,20

5,02 5,23 5,53 5,91 6,39

2,99

1,902 1,947 1,745 1,812 1,877 1,943

1,998

Received 4-8-54.

Louvain, July 30th, 1954.

REFERENCES 1) K e e s o m , W. H. and W a l s t r a , W. K., Physica 7 (1940) 985; Comm. Leiden 260c. - Physica 13 (1947) 225 - - Comm. Leiden 271a. 2) V a n I t t e r b e e k , A., Doctorate Theses, Ghent, 1932. 3) W a 1 s t r a, W. K., Doctorate Theses, Leiden, 1946. 4) V a n I t t e r b e e k , A. and F o r r e z , G., Physica 20 (1984) 133. 5) K e e s o m , W. H. and V a n I t t e r b e e k , A.,Proc. roy. Ac. Amst. 34 (1931), 204; Comm. Leiden 213b. 6) V a n I t t e r b e e k , A. and K e e s o m , W. H . , C o m m . Leiden no. 209a. 7) K e e s o m , W. H. and V a n I t t e r b e e k , A.,loc. cit.