Slope of theλCurve of Liquid Helium

Abstract

Landau's theory of liquid helium is developed to give an approximate value of the slope of the $\lambda$ curve in terms of the quantities $\left(\frac{\rho }{\Delta }\right)\frac{\partial \Delta }{\partial \rho }$, $\left(\frac{\rho }{p_0}\right)\frac{\partial p_0}{\partial \rho }$, and $\left(\frac{\rho }{\mu }\right)\frac{\partial \mu }{\partial \rho }$. From the experimental data on the coefficient of expansion and the pressure variation of the velocities of first and second sound, the following numerical values are derived for these quantities: $\frac{\rho }{\Delta }\frac{\partial \Delta }{\partial \rho }=-0.57, \frac{\rho }{p_0}\frac{\partial p_0}{\partial \rho }=+0.26, \frac{\rho }{\mu }\frac{\partial \mu }{\partial \rho }=-\mathrm{1.8.}\mathrm{}$ The negative slope of the $\lambda$ curve can then be explained and its magnitude predicted with an accuracy of about 15 percent.