A practical vapor pressure equation for helium-3 from 0.01 K to the critical point

A saturation vapor pressure equation, p(T), is an essential component in the ³He state equation currently under development. The state equation is valid over the range 0.01-20 K with pressures from 0 to the melting pressure or 15 MPa. The vapor pressure equation consequently must be valid from 0.01 K to the critical temperature. This paper surveys available ³He critical temperature and pressure measurements, leading to new recommended critical values of 3.3157 K and 114603.91 Pa. The ITS-90 temperature scale is defined by the ³He vapor pressure from 0.65 to 3.2 K. A new vapor pressure equation is developed for the interval from the upper end of the T₉₀ scale to this newly defined critical point, employing a mathematical form in which the second derivative d²p/dT² diverges in agreement with scaling laws at the critical point. Below 0.65 K, an empirical vapor pressure expression is adopted, consistent with a theoretical expression valid in the limit T → 0. These two new components are fitted to be piecewise continuous with the EPT-76 p(T) scale rather than the ITS-90 T(p) scale between 0.65 and 3.2 K. Probable deviations between this vapor pressure scale and PLTS-2000 melting pressure-temperature scale are recognized, but not reconciled.