We\'ve seen that fish can control their buoyancy through the use of a swim bladd

Question

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 kg striped bass with a volume of 7.0 L. When neutrally buoyant, 7.0% of the fish's volume is taken up by the swim bladder. Assume a body temperature of 15 degrees C. What will the volume of the swim bladder be if the fish ascends to a 49 depth without changing the quantity of gas? Express your answer to two significant figures and include the appropriate units. *Please show work

Explanation / Answer

Volume of the bladder = 7 x (7/100) = 0.49 L Temperature = 15°C = 288 K Gauge Pressure (at 97 ft) = ?gh = (1000)(9.8)(29.5) = 289100 Pa = 2.89 x 10^5 Pa Total pressure = P(atm) + (2.89 x 10^5) = 1.01 x 10^5 + 2.89 x 10^5 = 3.9 x 10^5 Pa = 3.86 atm Using PV = nRT, n = PV / RT = (3.86)(0.49) / (0.0821)(288) = 0.08 moles When the fish ascends to 44 ft without changing temperature and number of moles, we can assume it to be isothermal process. In an isothermal process, PV = constant Total pressure at 44 ft = 1 atm + (1000)(9.8)(13.4) / 101325 = 1 + 1.29 = 2.29 atm Pi x Vi = Pf x Vf 3.86 x 0.49 = 2.29 x Vf Vf = 0.82 L

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