Second-Order Transformations in Two-Component Systems. Application to Solutions ofHe3inHe4

Abstract

A thermodynamic treatment has been made of a second-order transformation in two-component systems. In addition to the requirement that there be no heat of transformation and no volume change, it turns out that the composition is equal in the two phases. Equations have been developed for ${\left(\frac{\mathrm{dT}}{\mathrm{dx}}\right)}_P$, ${\left(\frac{\mathrm{dx}}{\mathrm{dP}}\right)}_T$, and ${\left(\frac{\mathrm{dP}}{\mathrm{dT}}\right)}_x$ along the equilibrium curves. If we assume that the transformation of liquid helium remains second-order on the addition of a mole fraction $x$ of ${\mathrm{He}}^3$ to a ${\mathrm{He}}^4$ solution, then for the limit of very dilute solutions