FYKOS Year 26 Series 2 Problem 5 — the U tube · FYKOS 26 #26.2.5
Physics · thermodynamics
Problem
Imagine a U-tube filled with mercury, and a bubble of height h0 that floats inside (see the attached picture). Describe what would happen if we changed the surrounding atmosphere in the following ways. Assume that the density of mercury is independent of temperature. The same is valid for the glass the tube is made of. Also assume that the surrounding air behaves as an ideal gas. The initial state of the atmosphere is described by temperature T0=300K, and pressure pa=10⋅105Pa. Furthermore, assume that the system is in a thermodynamic equilibrium at all times, and that the bubble has a cylindrical shape.
Both ends of the tube are open, and the temperature doubles.
Both ends of the tube are closed, and the temperature doubles.
Only one of the ends of the tube is closed, and the temperature doubles. For each of these cases, determine the new size of the bubble, and the height difference between the mercury columns in the two branches.