Study of the Specific Heat of aHe3-He4Mixture near Its Gas-Liquid Critical Point

We present measurements of the specific heat $C_{\mathrm{vx}}$ of a mixture of ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ with a nominal concentration of ${\mathrm{He}}^3$, $X_3=0.80\mathrm{}$. Data were taken with a flat calorimeter cell in the vicinity of the gas-liquid critical point of the mixture, which is characterized (at a given $X_3$) by its density ${\rho }_c$ and temperature $T_c$. The data consist of nine isochores within the approximate density range $0.52<\mathrm{}\frac{\rho }{{\rho }_c}<1.20\mathrm{}$ and in the temperature range $-0.1\mathrm{}\le t\le 0.1$, where $t=\frac{(T-T_c)}{T_c}$. Data were taken to within 0.4 mK of the transition temperature on all but one of the isochores. We find that the behavior of the specific heat in the mixture for a given reduced density $\frac{\rho }{{\rho }_c}$ is in general very similar to that seen in pure ${\mathrm{He}}^3$. In particular, the behavior of $C_{\mathrm{vx}}$ along the critical isochore is the same as that for pure ${\mathrm{He}}^3$ in the range ${10}^{-4\mathrm{}}\le t\le {10}^{-2\mathrm{}}$. There the apparent weak divergence is characterized by an exponent $\alpha \approx 0.1$. From thermodynamic considerations of the upper bound of $C_{\mathrm{vx}}$ along a line of singularities in mixtures, the apparent weak divergence we observe does not, however, represent the asymptotic behavior. This question is discussed in the light of the paper by Griffiths and Wheeler and of new calculations by Leung and Griffiths for a binary fluid. The thermal-equilibrium times in the two-phase region were found to be much longer than in the pure ${\mathrm{He}}^3$ fluid, and these are briefly discussed. The thermal diffusivity in this region is found to have a maximum at a density approximately 20% lower than ${\rho }_c$, in rough correspondence to the density of the temperature extremum of the two-phase-region boundary.