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 = [tex]p_1=\rho\times g\times 500 m[/tex]
Volume of gas hold by fish's swim bladder = [tex]V_1=0.12 L[/tex]
Pressure at dept h where fish's swim bladder can hold maximum gas = [tex]P_2=\rho\times g\times h[/tex]
Maximum volume of the gas in fish's swim bladder = [tex]V_2=0.34 L[/tex]
Applying Boyle's law:
[tex]P_1V_1=P_2V_2[/tex] ( at constant temperature)
[tex]\rho\times g\times 500 m\times 0.12 L=\rho\times g\times h\times 0.34 L[/tex]
[tex]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[/tex]
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.
