Pressure Coefficient and Phase Diagram ofHe4near the Upper Lambda Point

Abstract

Measurements are reported of the derivatives ${\left(\frac{\mathrm{dP}}{\mathrm{dT}}\right)}_{\lambda }$, ${\left(\frac{d\rho }{\mathrm{dT}}\right)}_{\lambda }$, and ${\left(\frac{d\rho }{\mathrm{dP}}\right)}_{\lambda }$ on the lambda curve, of ${\left(\frac{\mathrm{dP}}{\mathrm{dT}}\right)}_m$ on the melting curve, and of the pressure coefficient ${\beta }_v={\left(\frac{\partial P}{\partial T}\right)}_v$ of the liquid very close to the upper lambda point ($T_{{\lambda }^{\prime }},P_{{\lambda }^{\prime }},V_{{\lambda }^{\prime }}$). The measurements are well represented by the equations $\{{\left(\frac{\mathrm{dP}}{\mathrm{dT}}\right)}_{\lambda },=-55.54-96(T_{\lambda }-T_{{\lambda }^{\prime }}), T_{\lambda }-T_{{\lambda }^{\prime }}<~12.5\times {10}^{-3\mathrm{}}{}_{}{}^{\circ }{}_{}{}^{}\mathrm{K};\}\{{\left(\frac{d\rho }{\mathrm{dT}}\right)}_{\lambda },=-43.7-230(T_{\lambda }-T_{{\lambda }^{\prime }}), T_{\lambda }-T_{{\lambda }^{\prime }}<~12.5\times {10}^{-3\mathrm{}}{}_{}{}^{\circ }{}_{}{}^{}\mathrm{K};\}\{{\left(\frac{d\rho }{\mathrm{dP}}\right)}_{\lambda },=0.7868+2.8(T_{\lambda }-T_{{\lambda }^{\prime }}), T_{\lambda }-T_{{\lambda }^{\prime }}<~12.5\times {10}^{-3\mathrm{}}{}_{}{}^{\circ }{}_{}{}^{}\mathrm{K};\}\{{\left(\frac{\mathrm{dP}}{\mathrm{dT}}\right)}_m,=29.43+326(T_m-T_{{\lambda }^{\prime }}), 0<~T_{{\lambda }^{\prime }}-T_m<17\mathrm{}\times {10}^{-3\mathrm{}}{}_{}{}^{\circ }{}_{}{}^{}\mathrm{K};\}\{{\left(\frac{\partial P}{\partial T}\right)}_v,=9.39+7.69\mathrm{} {log}_{10}( T-T_{\lambda }), V=V_{{\lambda }^{\prime }}, 6\times {10}^{-5\mathrm{}}{}_{}{}^{\circ }{}_{}{}^{}\mathrm{K}<~T-T_{\lambda }<~6\times {10}^{-3\mathrm{}} {}_{}{}^{\circ }{}_{}{}^{}\mathrm{K};\}$ where $P$ is in atm, $T$ is in °K, and $\rho$ is in mg/${\mathrm{cm}}^3$. The temperature and pressure of the upper lambda point are $T_{{\lambda }^{\prime }}=1.7633\mathrm{}\pm 0.0001{}_{}{}^{\circ }{}_{}{}^{}\mathrm{K}, P_{{\lambda }^{\prime }}=29.84\mathrm{}\pm 0.02 \mathrm{atm}.$ There is no evidence of a first-order transition in the solid in the temperature range $-17\mathrm{}\times {10}^{-3\mathrm{}}{}_{}{}^{\circ }{}_{}{}^{}\mathrm{K}<T-T_{{\lambda }^{\prime }}<4.3\mathrm{}\times {10}^{-3\mathrm{}}{}_{}{}^{\circ }{}_{}{}^{}\mathrm{K}$.