Determination of the thermodynamics of He II from sound-velocity data

Abstract

Recently measured sound-velocity data were used to completely determine the thermodynamics of superfluid helium at all temperatures above 1.2 K and at all pressures in the He II phase. The sound-velocity data consisted of first-, second-, and fourth-sound velocities measured simultaneously at more than 400 points in the $P$-$T$ plane. Equations of two-fluid hydrodynamics and a small amount of published data were used to convert the sound velocities to thermodynamic quantities. Because of the high precision of the data (0.2%) and the fine mesh of data points, it was possible to obtain continuous functions (of the variables $P$ and $T$) for the density, thermal-expansion coefficient, normal-fluid fraction, entropy, specific heats, and compressibility of He II. As an additional feature the correct asymptotic behavior near the $\ensuremath{\lambda}$ line was incorporated into the thermodynamic functions. These functions were used to generate tables of the thermodynamic quantities and smoothed values of the sound velocities. The precision of the results, typically 0.3%, represents an order-of-magnitude improvement over a significant portion of the existing data and has eliminated some discrepancies as large as (10-15)%.