Moran inflates a helium balloon to a diameter of 10 inches (25.4 cm) and decides to see what happens when it is submerged underwater. You may assume (1) helium behaves as an ideal gas, (2) the helium...

Extracted text: Moran inflates a helium balloon to a diameter of 10 inches (25.4 cm) and decides to see what happens when it is submerged underwater. You may assume (1) helium behaves as an ideal gas, (2) the helium mass is constant (no leaks), (3) the balloon is a perfect sphere, (4) at any time, the pressure of the helium is the same as the ambient pressure (in actuality, the pressure inside the balloon is slightly higher than the ambient to balance the tension in the balloon's skin), (5) the specific heats of helium can be evaluated at 300 K. These can be found, along with the gas constant, from Table A-2: R = 2.0769 kJ/kg-K, c, = 3.1156 kJ/kg-K, c, = 5.1926 kJ/kg-K. The volume of a sphere is V = ar³ : , r= radius, d= diameter. (a) Calculate the mass of helium required to inflate the balloon so that its diameter is 10 inches when the absolute pressure of the helium is P = 100 kPa and everything is at room temperature (298 K). (b) Prof. Moran now submerges the balloon just beneath the surface of a nearby lake, which is at a temperature of T, = 288 K. The gas quickly attains thermal equilibrium with the lake water. If the pressure remains the same (P2 = P1 = 100 kPa), by how much does the balloon diameter change? Wearing an ultra-insulating wetsuit developed in his lab (along with proper SCUBA gear), Prof. Moran submerges himself and the balloon deeper underwater. He submerges very slowły so that the balloon is always in mechanical equilibrium with the surrounding water. He and the balloon eventually stop at 10 m below the surface, where the water pressure is P3 = 200 kPa. The water temperature remains constant at 288 K during this descent. (c) Taking the helium gas as the system, calculate the work transfer during the descent, process 2->3. (d) While Prof. Moran remains submerged, a wave of cold water causes the ambient temperature to drop to T4 = 283 K (while the pressure remains constant at 200 kPa). Determine the heat transfer experienced by the helium. (Hint: what property is relevant for determining the heat added or removed at constant pressure?)