SaturatedHe4near Its Critical Temperature

Abstract

Measurements of the refractive index $n$ of saturated ${\mathrm{He}}^{4}$ liquid and vapor have been made at $\ensuremath{\lambda}=5462.27$ \AA{} from 4.2\ifmmode^\circ\else\textdegree\fi{}K nearly to the critical temperature (${T}_{c}=5.1994$\ifmmode^\circ\else\textdegree\fi{}K). Careful determinations of $n$ and $\frac{\mathrm{dn}}{\mathrm{dT}}$ as a function of temperature were made using a metal optical cryostat and a Jamin interferometer modified to produce a chart record of the interference fringes. The measurements extended to within 50 mdeg of ${T}_{c}$ for saturated vapor, and to within 36 mdeg of ${T}_{c}$ for saturated liquid. These results, combined with the Lorenz-Lorentz equation, then give the density $\ensuremath{\rho}$ of both saturated liquid and saturated vapor, and the expansion coefficient ${\ensuremath{\beta}}_{s}$ of the saturated liquid. These $n$, $\ensuremath{\rho}$, and ${\ensuremath{\beta}}_{s}$ measurements are the first ever made above 4.4\ifmmode^\circ\else\textdegree\fi{}K except for two early measurements of density at 4.6 and 4.7\ifmmode^\circ\else\textdegree\fi{}K. The critical density is found to be ${\ensuremath{\rho}}_{c}=(0.06948\ifmmode\pm\else\textpm\fi{}0.00030$ g ${\mathrm{cm}}^{\ensuremath{-}3}$, or the critical molar volume, ${V}_{c}=(57.628\ifmmode\pm\else\textpm\fi{}0.25)$ ${\mathrm{cm}}^{3}$ ${\mathrm{mole}}^{\ensuremath{-}1}$.We have modified and extended the Landau-Lifshitz theory of the properties of a substance "near" the critical point, and then find excellent agreement with our experimental values of the molar volumes of saturated ${\mathrm{He}}^{4}$ within about 110 mdeg of ${T}_{c}$. This agreement is taken as evidence that ${(\frac{{\ensuremath{\partial}}^{3}P}{\ensuremath{\partial}{V}^{3}})}_{T}$ is negative at the critical point---in clear contradiction to theories which suggest that this third derivative is zero at ${T}_{c}$. In terms of the "reduced" parameters ${V}^{\ensuremath{'}}=\frac{V}{{V}_{c}}$ and ${P}^{\ensuremath{'}}=\frac{P}{{P}_{c}}$, we find ${(\frac{{\ensuremath{\partial}}^{3}{P}^{\ensuremath{'}}}{\ensuremath{\partial}{V}^{\ensuremath{'}3}})}_{{T}_{c}}=\ensuremath{-}(10.4\ifmmode\pm\else\textpm\fi{}1.8)$ for ${\mathrm{He}}^{4}$. In addition, we can then calculate saturated vapor and liquid molar volumes, and liquid coefficient of expansion values right up to the critical temperature, assuming the continued validity of the modified Landau-Lifshitz theory.