Pressure Coefficient and Compressibility of LiquidHe4Very Close to theλCurve

Abstract

Measurements of the pressure coefficient ${\beta }_V={\left(\frac{\partial p}{\partial T}\right)}_V$ and the compressibility ${\kappa }_T=-\left(\frac{1}{V}\right){\left(\frac{\partial V}{\partial p}\right)}_T$ in the immediate vicinity of the point $p_{\lambda }=13.04\mathrm{}$ atm, $V_{\lambda }=24.20\mathrm{}$ ${\mathrm{cm}}^3$/mole, $T_{\lambda }=2.023\mathrm{}°$K are described. For ${\beta }_V$ the smallest increments were $\Delta T\simeq 2\times {10}^{-5\mathrm{}}°$K and for ${\kappa }_T$ they were $\Delta p\simeq 1\times {10}^{-3\mathrm{}}$ atm corresponding to $\frac{\Delta V}{V}\simeq 8\times {10}^{-6\mathrm{}}$. From about 2×${10}^{-2\mathrm{}}$°K to within ${10}^{-5\mathrm{}}$°K of $T_{\lambda }$, ${\beta }_V$ is given by relations ${\beta }_{V=V_{\lambda }}=3.5+3.4\mathrm{} {log}_{10}|T-T_{\lambda }| \left(\mathrm{He}\mathrm{I}\right),$ ${\beta }_{V=V_{\lambda }}=-6.0+2.3\mathrm{} {log}_{10}|T-T_{\lambda }| \left(\mathrm{He}\mathrm{II}\right).\mathrm{}$ ${\kappa }_T$, from ${10}^{-2\mathrm{}}$ to ${10}^{-3\mathrm{}}$ atm of $p_{\lambda }$, may be represented by equations ${\kappa }_T=0.0079-0.02(p-p_{\lambda })-1.5(T-T_{\lambda }) \left(\mathrm{He}\mathrm{I}\right),$ ${\kappa }_T=0.0089+0.11(p-p_{\lambda })+8.4(T-T_{\lambda }) \left(\mathrm{He}\mathrm{II}\right).\mathrm{}$ In these relations $T$ is expressed in °K, $p$ in atm, ${\beta }_V$ in atm/°K, and ${\kappa }_T$ in ${\mathrm{atm}}^{-1\mathrm{}}$. Close to the $\lambda$ curve ${\beta }_V$ is thus a linear function of $log|T-T_{\lambda }|$ and ${\kappa }_T$ has a discontinuity at the transition point amounting to about 10% of its value. The results are discussed on the basis of thermodynamic equations derived recently by Buckingham and Fairbank.