Some thermodynamic relationships for soils at or below the freezing point: 1. Freezing point depression and heat capacity

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Abstract
An extended equation was derived relating the relative partial molar free energy of water in a soil to its freezing point depression and relative partial molar heat content. The equation was used to prepare a table from which each of these three quantities can be ascertained if the other two are known. The table was used with experimental data to obtain a curve of freezing point depression versus water content for Na‐Wyoming bentonite. Provided the activity of the liquid water in the clay is a single‐valued function of the liquid water content, and that the ice has the properties of pure bulk ice, this curve also represents the relationship between freezing point depression and unfrozen water in the partially frozen clay. An equation for the heat capacity of a partially frozen soil was also derived. This equation was employed to calculate the heat capacities of the clay at different water contents and sub‐zero temperatures. A comparison of the calculated unfrozen water contents and heat capacities of the partially frozen Na‐Wyoming bentonite with the available experimental data indicated satisfactory agreement, especially as regards the unfrozen water contents.