³He Vapor Pressure near Its Critical Point

Abstract

Between 0.65 K and 3.2 K, the temperature dependence of the vapor pressure P of ³He is defined by the International Temperature Scale of 1990 (ITS-90). However, the ITS-90 vapor pressure equation was not designed to be consistent with the scaling law required for the second temperature derivative of the vapor pressure in the vicinity of the liquid-vapor critical point. In this paper, two scaling-type equations are used to describe the ³He vapor pressure in the region near the critical point. The first scaling equation contains two unknown coefficients which are obtained by taking as reference the temperature $\bar{T}$ at which the product (T _c −T)P presents a maximum ( $\bar{T}=2.56736$  K). The second scaling equation contains three unknown coefficients which are obtained by using as references $\bar{T}$ and T _up=3.2 K, the upper value of the ITS-90 interval. In both equations we take for the critical temperature and pressure the values T _c =3.31554 K and P _c =114 632.7 Pa. The proposed equations, specially the second one, are satisfactorily compared with experimental data for P and dP/dT within the temperature range (T _c −T)/T _c ≤0.065 and with semiempirical data for d ² P/dT ² within the temperature range 0.0001≤(T _c −T)/T _c ≤0.03.