We've seen that fish can control their buoyancy through the use of a swim bladder, a gas-filled organ inside the body. You can assume that the gas pressure inside the swim bladder is roughly equal to the external water pressure. A fish swimming at a particular depth adjusts the volume of its swim bladder to give it neutral buoyancy. If the fish swims upward or downward, the changing water pressure causes the bladder to expand or contract. Consequently, the fish must adjust the quantity of gas to restore the original volume and thus reestablish neutral buoyancy. Consider a large, \(7.0 \mathrm{~kg}\) striped bass with a volume of \(7.0 \mathrm{~L}\). When neutrally buoyant, \(7.0 \%\) of the fish's volume is taken up by the swim bladder. Assume a body temperature of \(15^{\circ} \mathrm{C}\).

a. How many moles of air are in the swim bladder when the fish is at a depth of \(80 \mathrm{ft}\) ?

b. What will the volume of the swim bladder be if the fish ascends to a \(50 \mathrm{ft}\) depth without changing the quantity of gas?

c. To return the swim bladder to its original size, how many moles of gas must be removed?

Long-distance balloon flights are usually made using a hot-airballoon/helium-balloon hybrid. The balloon has a sealed, flexible chamber of helium gas that expands or contracts to keep the helium pressure approximately equal to the air pressure outside. The helium chamber sits on top of an open (that is, air can enter or leave), constant-volume chamber of propane-heated air. Assume that the hot air and the helium are kept at a constant temperature by burning propane.