Problem 4 (25 points) - A Spring-Loaded Piston-Cylinder An unknown gas is contained in a well-sealed piston-cylinder device. There is a spring on the backside of the piston that changes the force exerted on the piston as the gas volume changes. The spring is initially uncompressed. The initial pressure of the gas is Po. a) Draw a general schematic of this device. b] Draw two free body diagrams (FBDsl of the piston: one at the initial state with the spring in its equilibrium position, and one at some later state when the gas has expanded to some larger volume. c) Recall that force of a typical Spring is F5 = Inc, where x is measured from the equilibrium position of the spring. Knowing this, how does the pressure of the gas vary as a function of its specic volume for this system? You may assume any processes for this system occur quasi-statically, and so the pressure is always well-dened and uniform throughout the gas