Question

A particular deep-sea fish has a swim bladder that can hold a maximum to 0.34 L of gas. It lives at 500m depth. If the fish's swim bladder currently holds 0.12 L of gas, about how high could researchers safely raise it before rupturing ("popping") the swim bladder? (Show your work)

Answer 1

Answer:

At the height of the 176 meter fish's swim bladder will hold the gas without rupturing its swim badder, at this height researchers can safely raise it.

Explanation:

Pressure at depth of  500 m = $p_1=\rho\times g\times 500 m$

Volume of gas hold by fish's swim bladder = $V_1=0.12 L$

Pressure at dept h where fish's swim bladder can hold maximum gas = $P_2=\rho\times g\times h$

Maximum volume of the gas in fish's swim bladder = $V_2=0.34 L$

Applying Boyle's law:

$P_1V_1=P_2V_2$  ( at constant temperature)

$\rho\times g\times 500 m\times 0.12 L=\rho\times g\times h\times 0.34 L$

$h=\frac{\rho\times g\times 500 m\times 0.12 L}{\rho\times g\times 0.34 L}=176.5 m\approx 176 m$

At the height of the 176 meter fish's swim bladder will hold the gas without rupturing its swim badder, at this height researchers can safely raise it.