Thermodynamically consistent equilibrium properties of normal-liquid Helium-3

TL;DR

This paper provides a comprehensive, thermodynamically consistent set of equilibrium properties for normal-liquid Helium-3, derived from high-precision experimental data, enabling detailed analysis of its thermodynamic behavior across various conditions.

Contribution

It introduces the first complete, thermodynamically consistent dataset of equilibrium properties of normal-liquid Helium-3 based on experimental data, including calculations of entropy, specific heat, volume, and compressibility.

Findings

Alpha(T,P) exhibits intricate pressure dependence at low temperatures.

Alpha(T,P) vs T curves do not cross at a single temperature for all pressures.

The dataset enables detailed thermodynamic analysis of Helium-3 in zero magnetic field.

Abstract

The high-precision data for the specific heat C_{V}(T,V) of normal-liquid Helium-3 obtained by Greywall, taken together with the molar volume V(T_0,P) at one temperature T_0, are shown to contain the complete thermodynamic information about this phase in zero magnetic field. This enables us to calculate the T and P dependence of all equilibrium properties of normal-liquid Helium-3 in a thermodynamically consistent way for a wide range of parameters. The results for the entropy S(T,P), specific heat at constant pressure C_P(T,P), molar volume V(T,P), compressibility kappa(T,P), and thermal expansion coefficient alpha(T,P) are collected in the form of figures and tables. This provides the first complete set of thermodynamically consistent values of the equilibrium quantities of normal-liquid Helium-3. We find, for example, that alpha(T,P) has a surprisingly intricate pressure dependence at low temperatures, and that the curves alpha(T,P) vs T do not cross at one single temperature for all pressures, in contrast to the curves presented in the comprehensive survey of helium by Wilks. Corrected in cond-mat/9906222v3: The sign of the coefficient d_0 was misprinted in Table I of cond-mat/9906222v1 and v2. It now correctly reads d_0=-7.1613436. All results in the paper were obtained with the correct value of d_0. (We would like to thank for E. Collin, H. Godfrin, and Y. Bunkov for finding this misprint.)