A large freshwater fish has a swim bladder with a volume of 5.0 * 10^4 m^3. The

Question

A large freshwater fish has a swim bladder with a volume of 5.0 * 10^4 m^3. The fish descends from a depth where the absolute pressure is 3.0 atm to deeper water where the swim bladder is compressed to 60% of its initial volume. As the fish descends, the gas pressure in the swim bladder is always equal to the water pressure, and the temperature of the gas remains at the internal temperature of the fish's body. To adapt to its new location, the fish must add gas to
re-inflate its swim bladder to the original volume. This takes energy to accomplish. What's the minimum amount of work required to expand the swim bladder back to its original volume?

Explanation / Answer

work done=PdV P1V1 = P2V2 thus P2 = P1V1/V2 = 3 x(100/60) = 5 atm = 5.07 x 10^5 Pa volume added=0.4(5x10^-4) PdV = (5.07 x 10^5)(0.4)(5x10^-4) = 101 J

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