The Analysis of⁴He Isotherms: Density and Dielectric Virial Coefficients, and the Accuracy of NPL-75

Abstract

The highly accurate conventional isotherms of Berry and dielectric constant isotherms of Gugan and Michel have been analysed in a mutually consistent way between 2.6 K and 27 K by the method of surface-fitting. Semi-empirical expressions are presented for the variation of the virial Coefficients C ( T ) and D(T). A variety of expressions which conform to the expected theoretical constraints have been examined for B(T): the best of these agrees closely down to about 9 K with values recently calculated by Feltgen et al. using a potential derived from scattering experiments. The second dielectric virial coefficient b(T) shows a temperature dependence reasonably close to that calculated from the pair-polarizability given by Dacre, and the internal consistency of these results suggests that the values obtained for B ( T ) have an uncertainty of about f 0.05 cm3 mol-' down to 6 K, rising to perhaps f 0.2 cm3 mol-' below this. The temperature scale NPL-75 is assessed against several recent experiments: while there are indications of minor discrepancies the evidence is not conclusive and NPL-75 appears to be accurate at very close to the level originally claimed.

Direct Measurements of the Dielectric Virial Coefficients of4He between 3 K and 18 K

“…(i) Our experiments confirm that the apparent variation of b between 4 K and 27 K [4] is an artefact of the method of analysis used arising from an inadequate representation of the second density virial coefficient B(T). In the present direct measurements of b between 3 K and 18 K no temperature dependence is seen at the level of about f 0,008 cm3 mol-' (Table 4).…”

“…The second virial coefficient which is effective in DCGT can be seen from ( 5) to be (Bb), and in [4] an attempt was made to combine this with the values of B ( T ) from the work of Berry [17] so as to give b by difference. For this purpose b was assumed to be temperature dependent and for several different parametrized forms used in the surface-fitting analysis it showed an apparent variation between the limits of -0,05 and -0,25cm3 mol-' between 4 K and 27 K ( [4], Figure 2), however it is now known that this anomalous temperature dependence (cf. the expected variation of less than 0,01cm3 mol-', above) arose from the use of an inadequately flexible expression to represent B ( T ) , as is discussed in [18].…”

Improved Virial Coefficients of4He from Dielectric Constant Measurements

“…The dielectric constant gas thermometry (DCGT) of 'He described by Gugan and Michel [l, 21 is related to the isotherm thermometry of Berry [3] and also to the familiar constant volume gas thermometry (CVGT) of Berry the virial expansion (1). A detailed comparison between DCGT and Berry's work was presented by Gugan [7,8] and this gave an independent confirmation that NPL-75 is accurate at very close to the level originally estimated by Berry. DCGT analysis is based on the dielectric virial expansion of the Clausius-Mossotti function…”

“…The final procedure adopted in [8] was to use for B ( T ) what appeared to be the best three-term expression which could be obtained by surface fitting to the isotherm work of Berry [3]* and to fit a variety of three-term expressions for b ( T ) to the difference B ( T ) -B ' ( T ) of (3). This empirical procedure established that between 4,2 K and 27,l K, b was everywhere very small, so that the DCGT data provided strong independent evidence that the values of B(T) obtained from Berry's work were highly accurate.…”

“…New evidence on several points has emerged since [8] was completed, and this allows better analysis of the DCGT data which is presented here. (iii) further information from CVGT on the deviations of NPL-75 from thermodynamic temperature [4, 5 , 61; (iv) evidence that the assigned value of the reference point of NPL-75, 20,2712 K, is systematically low by about 0,5 mK [5, 61.…”