Study of the Specific-Heat Singularity ofHe3near Its Critical Point

Abstract

We present measurements of the specific heat $C_v$ of ${\mathrm{He}}^3$ with an impurity of 250-ppm ${\mathrm{He}}^4$ near its critical point, characterized by its density ${\rho }_c$ and temperature $T_c$. The sample cell had a vertical height of 0.5 mm to reduce the effect of gravity on the singularity. Data were taken along five isochores within the density range $-0.17<\Delta \rho <+0.11\mathrm{}$, where $\Delta \rho =\frac{(\rho -{\rho }_c)}{{\rho }_c}$, and in the temperature range $3\times {10}^{-5\mathrm{}}<\left|t\right|<{10}^{-1\mathrm{}}$, where $t=\frac{(T-T_c)}{T_c}$. The data are compared with previous $P-V-T$ measurements on this system and good consistency is shown between the two sets of data. An adequate description of the data along the critical isochore is found to be given by the extended scaling formulation of Green, Cooper, and Sengers, based on a generalized parametric equation of state. Within experimental error, the critical exponent describing the divergence of $C_v$ is the same for $t>\mathrm{}0\mathrm{}$ and $t<\mathrm{}0\mathrm{}$ and its value is $\alpha =0.105\mathrm{}\pm 0.015$. Scaled behavior of the specific heat as a function of temperature and density is exhibited by the data. This scaling is then related to the linear model of Schofield, Litster, and Ho. Good agreement is found between the calculated and the experimentally measured parameters for the linear model. Small systematic deviations will be discussed. We also present an account of the calorimeter relaxation times encountered in the vicinity of $T_c$. In the two-phase region, these relaxation times are much longer than in the one-phase region and diverge as the transition temperature is approached. This behavior is empirically described and tentatively attributed to processes at the boundary between the phases.