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Submitted on 1 Jan 1978
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DIELECTRIC CONSTANT GAS THERMOMETRY
AND THE EQUATION OF STATE OF HELIUM
D. Gugan, G. Michel
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplPment au no 8, Tome 39, aotit 1978, page C6-1171
DIELECTRIC CONSTANT GAS THERMOMETRY AND THE EQUATION OF STATE OF HELIUM
D. Gugan and G.W. Michel
H.H. Wills Physics Laboratory, RoyaZ Fort, BristoZ BS8 ITL, U.K.
RQsum6.- On prdsente des mesures prdliminaires de thermomgtrie prgcise au moyen de la constante diglectrique de 11h61ium gazeux entre 4 et 27 K. On donne les valeurs du troisizme coefficient du viriel de la densitd, du deuxisme coefficient de la constante dislectrique, et de la polarisibilitd pour l'hdlium.
Abstract.- Preliminary measurements are reported of precision Dielectric Constant Gas Thermometry using helium between 4 and 27 K. Values are given for the third density virial coefficient, for the second dielectric virial coefficient, and for the polarizability of helium.
The relative change of capacitance of a sui- tably designed capacitor containing gas of dielec-
tric constant E at pressure p can be written
-
C(p)
-
C(O)/C(O) = y = (€-I) + K E p, where K is, the 20.2703 K (NPL 7 5 ) (zopo~nts, 3 t e r m t ~ t Jeffective linear compressibility of the capacitor.
-
If we combine the dielectric virlal expanslon of a A 540
-
the Clauslus-Mossotti function,
-
2 PE-1
- - - - ( 1 +
-
bE + -4 + "')&+2
v2
32,50C-
with the ordinary vlrial expansion of the equationof state,
we can eliminate V and obata2n a relatlvely si'mple expansion for the pressure i'n terms of the polariza- tion parameter )1(= y/y+3), such that the virial coefficients have their simplest form :
4
4
,
'0.8- ', b a s e d on 6 C = 0.1 a F:-
E 6 p / p = lo-' 5'0.4-
-
0- - -
- - -_ _ _ _ _
--- 0-e---
W n 0 O--.--- - ---- - X - - - --- -0.4--
I -0 8 I I I I IFig.
-
1 : DCGT isotherm of helium at 20.2703 K.We have measured p and 1-1 along isotherms between 4 Weighted, least-squares fit of equation (1) up to and 27 K. The measurements were made using terms in p2, the next term was not
dlfferent from zero. The r.m.s. deviation around t k a C.E..C. pressure balance and an M.K.S. Baratron fltted line corresponds to 0.31 mK uncertainty in T. diaphragm gauge
(cf.
B~~~~ 1.11, w2th (6p/p) ,,, 10-5 ; The dashed lines show the scatter expected from theinstrumental resolution the capacitance measurements were made with a Gene-
ral Radio Bridge, GR 1621, with & % 0.1 aF, giving
The values of the coefficients are not much depen-
6)1 2. 3 x
lo-'.
The temperature was monitored withdent on the details of the fitting, the weighting, ~hodium-1ron and Germanium resis tance ttiermome ters
or the number of data points included. The preci- (Calibrated against NPL 75) with a precision of
slon of DCGT isotherm thermometry is at the level
% 0.5 mK.
of 0.3 mK, but the yalues of AE (and of K) depend Welghted, least-squares, polynomial fits
on the accuracy of the temperature scale being used.
have been made to and the deviations for One We shall discuss this thoroughly elsewhere when the such fit up to terms in p2 are shown i.n the figure. intercomparison of our eight isotherms, together
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786518
with measurements using the di'electric constant analogue of CVGT, will allow us to assess the smo- othness of the NPL 75 temperature scale. The proce- dure is similar to the test of smoothness using ma- gnetic thermometry (Cf. Duri'eux / 2 h , but more sa- tisfactory since the correcti'ng terms are relative- ly well known and since they can be extrapolated to zero.
Our provisional value for the polari'zability AE is 5175 f 1 x
lo-'
cm3 mole-', while the varia-tional calculations of Buckingham and Hibbard 131) and of Weinhold 141) give 5170.33 f 0.05 and 5170.21 x lo-* cm3
mole-I
respectively. An experi-3
mental value of 5210 f2x 10-4 cm mole-1 has recent- ly been reported by Kirouac and Bose 151 but this value is inconsistent with all other precise values, which are in the range 5160
-
5190 x cm3 mole-l, with a typical uncertainty of t 10xcm3 mole-]. Our value indicates a small but genuine discrepancy in the calculation of this fundamental atomic property of helium.
The second dielectric virial coefficient is -.06 cm3 mole-' at room temperature /5/ but its change at low temperatures 2s not known. We find by difference from the ordinary virial coefficients of Berry / I / that bE is not signi'fi'cantly different from zero between 4 and 27 K, = -0.03 + 0.1 cm3
E
mole-'.
The coefficfent of p21n ( I ) yi'elds the value of the third virial coeffi'cient, since b is negli-
E
gible ; we find C = 80 + 4000/T cm6 molem2 to within about f 100 cm6 mole-2 between 4 and 27 K. These values considerably extend' the experimental know-
ledge of C, see e.g. the discussion of Berry /I/. We are grateful to the D.O.I. for financial support and to many ind2vi'duals at Bristol and at the N.P.L. for their help.
References
111 Berry, K.H., Temperature Measurement
,
(1975) (The Institute of Physics, London and Bristol, Conference Series number 26) 1975, p. 32 ; Metrologia, in press/ 2 / Duri'eux, M., i'bid., p. 17
/3/ Buckingham, R.A. and Hibbard, P.G., Symp. Farad. SOC.
2
(1968) 41141 Weinhold, F., Proc. Roy. Soc. A
