Some thermodynamic relations of rigid hygroscopic gels

Abstract

In studying the absorption of liquids by rigid gels, certain thermodynamic relations are required in terms of stress components and generalized co-ordinates. These have been derived using the analytical methods of Gibbs as developed by Guggenheim, and the conditions under which they hold are clearly defined. The analysis includes a new derivation of Kirchhoff's relation for the heat of absorption, in which it is shown to be an exact relation between the isopiestic and isothermal heat of absorption and the isopiestic and isosteric variation of equilibrium humidity with temperature, where the pressures concerned are the external pressures on the gel-liquid phase. The effect of internal stresses existing in a homogeneous gel-liquid phase due to the absorption of the liquid is obtained by assuming that the energy of expansion of the gel is the same for expansion due to absorption as for expansion due to external forces. The effect of external shear stresses on vapour pressure is considered, although it is not required in the case of homogeneous gels, since the analysis is similar to that for the internal energy of expansion, and the effect of such stresses is required when dealing with more complex structures such as wool cells.