Many fish maintain buoyancy with a gas-filled swim bladder. The pressure inside the swim bladder is the same as the outside water pressure, so when a fish descends to a greater depth, the gas compresses. Adding gas to restore the original volume requires energy. A fish at a depth where the absolute pressure is 3.0 atm has a swim bladder with the desired volume of 5.0×10^−4m^3. The fish now descends to a depth where the absolute pressure is 5.0 atm. Required:
a. The gas in the swim bladder is always the same temperature as the fish's body. What is the volume of the swim bladder at the greater depth?
b. The fish remains at the greater depth, slowly adding gas to the swim bladder to return it to its desired volume. How much work is required?