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An open container, exposed to the atmosphere, contains water of density ρw. A “L-shaped” tube is inserted into it as shown in the figure below. The diameter of the vertical part of the tube is negligible while the horizontal part of the tube has a uniform cross-sectional area and length l. Initially, the tube is motionless such that the water level is completely flat at equilibrium. Subsequently, the tube is rotated at a constant angular velocity ω about the vertical column such that the water level in the tube is a height Δh above the water level in the container at equilibrium. If the atmospheric pressure and temperature are pa and T and if the molar mass of the gas inside the tube is μ, determine Δh. Assume that the gas in the tube undergoes an isothermal process