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In this problem we will consider a vapor fluid interface on top of a solid surface. A schematic is shown below:
This is a zoomed-in picture of the edge of a liquid droplet sitting on a surface. The change in the Helmholtz energy due to a change in the position of the vapor-liquid interface along the surface is:
Where are the interaction energies (in N/m, analogous to the intermolecular potential but for macroscopic substances) between the three phases and are material-dependant constants. L is the length of the interface in-and-out of the figure (in-and-out of the page) and θ is the contact angle (a) Compute the work (W) required to move the liquid-vapor interface from x0 to a distance x at constant T, L and θ
(b) Find dU for this system for a given T (for constant T).
(c) You perform an experiment and find that the change in temperature as a function of distance (x) under adiabatic conditions is 10 Kelvin/mm. Find how the contact angle would change as a function of applied heat under isothermal conditions at constant x (and constant L).
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