Imagine a droplet of water, in equilibrium with its vapor, placed on a wire frame that can stretch the surface area of the droplet, keeping the temperature fixed. Assume that the whole system, droplet, frame, and vapor is contained in a fixed total volume V and kept at temperature T. The grand potential of the system can be written No+, where 2, = A is the surface grand potential, is the surface tension, A is the surface area of the liquid, and no is the grand potential of the remainder of the system. Neglect contributions from the frame and changes in the volume of the water droplet as it is stretched. The surface tension of water can be written

where = 75.5 dynes/cm is the surface tension at temperature, 1 = 0C, n = 1.2, and t' 368 C.

(a) Compute the internal energy per unit area of the surface assuming that the number of surface atoms, N, = 0.

(b) Plot the surface area and the surface internal energy per unit area for the temperature interval t = 0C to 1 = t'.

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