The thermodynamics of the⁴He and³He vapour-pressure equations in the ITS-90 and the EPT-76

Abstract

The vapour-pressure versus temperature equations for liquid He and He that define the International Temperature Scale of 1990 (ITS-90) in the range 0,65 K to 5,0 K have been derived from earlier equations in the Échelle Provisoire de Température de 1976 (EPT-76), which span the wider range 0,2 K to 5,2 K. This paper investigates the extent to which, i.e. to within what uncertainty, the equations can be obtained from thermodynamic calculations using the most recent and thermal data for the liquid and gas phases of He and He. Regarding the He vapour-pressure equation, the paper is an extension to higher temperatures of the paper by Fellmuth and Schuster which treated the important region below 1,5 K. The paper also deals with vapour pressures near the He λ-transition and near the critical points.

A new3He vapour-pressure based temperature scale from 0.65 K to 3.2 K consistent with the PLTS-2000

“…First, within the combined standard uncertainty the PTB realization of the 3 He vapour-pressure scale agrees with a copy of the scale T X1 in the region below 1 K. Second, the uncertainty estimates are realistic for the transfer of the magnetic scale T X1 maintained on RIRTs to the 3 He vapour pressure presented in [6], on which the 3 He vapour-pressure polynomial of the ITS-90 is based. Third, the results obtained at the PTB support the suspected thermodynamic inconsistency of the ITS-90 below 1.2 K [3,4,[8][9][10].…”

“…to obtain internal consistency of the calculated scales. For the vapour-pressure scale calculations carried out in [10], an extrapolation to saturation outside the experimental range was necessary for the entropy data deduced from Greywall's specific heat capacity data at higher temperatures.…”

“…the ITS-90 is not based on primary thermodynamic principles in this temperature range [8]. The existence of the deviation was supported by calculations applying the thermodynamic vapour-pressure equation (TVPE) [8][9][10].…”

The status of thermodynamic thermometry

“…They show that by making reasonable choices for the second and third virial coefficients of the vapour, and for the heat capacity of the liquid, good agreement is obtained between a calibrated vapour-pressure scale and the results from new low-temperature scales at the PTB [25] and the NIST [26]. Reesink and Durieux [27] have made calculations of both 3 He and 4 He vapour pressures, and for 3 He the results are similar to those in [24].…”