Serway & Jewett — Temperature: Problem 28

You are applying for a position with a sea rescue unit and are taking the qualifying exam. One question on the exam is about the use of a diving bell. The diving bell is in the shape of a cylinder with a vertical length of \(L = 2.50 \text{ m}\). It is closed at the upper circular end and open at the lower circular end. The bell is lowered from air into seawater (\(\rho = 1.025 \text{ g/cm}^3\)) and kept in its upright orientation as it is lowered. The air in the bell is initially at temperature \(T_i = 20.0^\circ\text{C}\). The bell, with two humans inside, is lowered to a depth (measured to the bottom of the bell) of \(27.0 \text{ fathoms}\), or \(h = 49.4 \text{ m}\). At this depth the water temperature is \(T_f = 4.0^\circ\text{C}\), and the bell is in thermal equilibrium with the water. The exam question asks you to compare two situations: (i) No additional gas is added to the interior of the bell as it is submerged. Therefore, water enters the open bottom of the bell and the volume of the enclosed air decreases. (ii) The bell is fitted with pressurized air tanks, which deliver high-pressure air into the interior of the bell to keep the level of water at the bottom edge of the bell. This choice requires money and effort to attach the tanks. The exam question asks: Which scenario is better?