A water tank has one rigid wall and one movable wall that acts like a massless piston. The tank contains a volume of water initially at height, ho, and length, Lo, with width, w, into the page. In its final state, the water tank is 4Lo in length. The force on the movable wall, pushing against the contained water, is F. (1a) If the system evolves from its initial to final state slowly, determine the amount of work by the water on the movable wall from an appropriate F-dx integral if the water pressure exerted is Pavg = pgh. (16) Calculate the change in potential energy as the water evolves from its initial to final state. Is this change in potential energy the same or different from the magnitude of work you found above? Why is that so? (1c) If the wall is rapidly moved such that the process between the initial and final states is highly non- equilibrium, is the change in the potential energy the same as in the above quasi-equilibrium process? h water