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

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.

Step-by-step explanation:

Pressure at depth of 500 m =
`p_1=\rho* g* 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* g* 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* g* 500 m* 0.12 L=\rho* g* h* 0.34 L`

`h=(\rho* g* 500 m* 0.12 L)/(\rho* g* 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.