What is the fractional change in the volume of the hagfish when it is brought to the surface?

Question

Various species of hagfish, or slime eels, live on the ocean floor, where they burrow inside other fish, eating them from the inside out and secreting copious amounts of slime. Their skins are widely used to make eelskin wallets and accessories. Suppose a hagfish is caught in a trap at a depth of 200 m below the ocean surface, where the water temperature is 10°C, then brought to the surface where the temperature is 15°C. If the isothermal compressibility and volume expansivity are assumed constant and equal to the values for water,



the specific volume, isothermal compressibility, and volume expansivity of several liquids at 20°C and 1 bar25, where ? and ? may be assumed constant.

Answer 1

If the isothermal compressibility and volume expansivity are taken to be constant, then we can integrate



From the initial state to the final state, to get



The change in temperature is = 5 K. The pressure changes with height in a column (or ocean) of fluid as ?P = ?gh. So, if we take the density of water to be 1000 (actually, for sea water it is more like 1030), and g = 9.8 and h = -200 m (the fish ends up at the surface, where the pressure is lower), then ?P = 1000*9.8*-200 = Pa = -20 bar (about 20 atmopheres, or 300 psi). Thus, we have



Thus, = 1.0015. The hagfish expands by about 0.15%.