A Statistical Theory of Liquids. II

In continuation of Part I, vapor pressure, surface tension, and the neighborhood of the critical point are discussed. Section IX deals with the vapor pressure law. A comparison with experimental data shows that the experimental values of the heat of vaporization are, on the average, 55 percent higher than the calculated values for the ten liquids studied. This suggests association in the liquid phase. However, even for the noble gases and mono-atomic metal vapors there remains a discrepancy, though of less degree. In Section X the previously established expression for the surface tension is developed. The "number of molecules per sq. cm of surface" can be defined by the aid of integrals involving the potential of molecular interaction. If, then, a "molar surface $S^{*}$," is defined as a surface containing one mole of the liquid, the equation of state for the surface phase assumes the form $\gamma S^{*}=RT$. The value for mercury can be calculated quantitatively from the potential as established in Part I. In the case of the other nine liquids the potential has to be "cut off" at a distance of the order ${\sigma }_1$. Eötvös' law follows as a limiting law for sufficiently high temperatures.—In Section XI the potential in the surface layer is supplemented for the case that the density in the vapor phase becomes comparable with that in the liquid phase. Then the proof of the coexistence of the two phases (Section IV) is extended to the neighborhood of the critical point. For that neighborhood the rule of Cailletet and Mathias is deduced. Finally the Kamerlingh Onnes constant is deduced from the special form of potential introduced in Section VII. It comes out 25 to 33 percent too low.