Thermodynamics of Solid and Fluid Surfaces

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Entry by Emily Redston, AP 226, Spring 2012

Work in Progress


Thermodynamics of Solid and Fluid Surfaces by J. W. Cahn. Segregation to Interfaces, ASM Seminar Series (1978) pp. 3-23.



In this paper, Cahn provides a slightly different take on Gibbs' original development of the thermodynamics of fluid and solid surfaces. His goal was to develop a mathematical system that was physically equivalent to Gibbs' formulation while being more easily applicable. The key change he made is that he concentrated on the system rather than defining excess quantities by comparing the actual system to a hypothetical system not containing the surface. This avoids problems with the identification of the location of the dividing surface.

Plane Fluid Interfaces - Area Work Term

For surfaces between fluids, Gibbs defined surface tension <math>\sigma</math> in a work term. The quantity <math>\sigma</math> is taken as a force per unit length of surface perimeter. When a portion of the perimeter moves an infinitesimal distance in the place of the surface, the area change <math>dA</math> is the product of perimeter length and distance moved. Thus <math>\sigma dA</math> is a forces-times-distance work term, and it appears in the combined first and second laws of thermodynamics as follows:

<math>dU = TdS - PdV + \displaystyle \sum_{i} \mu_i dN_i + \sigma dA </math>

Strictly speaking, <math>\sigma</math> is defined as the change in internal energy when the area is reversibly increase at constant entropy and volume in a closed system.