A frictionless and leak-proof piston with a de (in kg) and negligible thickness, is in equilibrium as shown in the figure with gas below it and water above it till the top. The cross-sectional area of the cylinder is A (in m) and the total length is L (in m). A linear spring with a stiffness K (in N/m) is placed inside the cylinder, which is initially uncompressed, with a length of H/2 (H in meters). Water is slowly poured such that no water spills from the top of the cylinder and the piston moves down slowly to accommodate the additional water that is being added. The process of adding water is stopped when the spring is compressed by a length of H/4 Neglect the volume of the spring and take the atmospheric pressure as Patm (in Pa). Using the given variables, obtain relations for the following quantity. (a) Initial and final pressures of the gas. wh (b) Expressions for intermediate pressures of the gas bottom, for the ranges H/ 2 L D4 } Patm Water Gas H/4 H/4