An autonomous research probe operates in a subglacial liquid brine reservoir on a day when the atmospheric pressure at the surface is 102 kPa102\text{ kPa}102 kPa and the density of the brine is 1150 kg/m31150\text{ kg/m}^31150 kg/m3.
The probe uses compressed nitrogen gas for buoyancy control.
1800 litres1800\text{ litres}1800 litres of nitrogen gas from the surface atmosphere is compressed into a 12-litre12\text{-litre}12-litre internal ballast tank.
The compressed gas quickly cools back to its original temperature.
Calculate the pressure of the nitrogen in the ballast tank.
State the equation linking pressure difference, depth, density and ggg.
Calculate the increase in pressure when the probe descends from the surface to a depth of 24 m24\text{ m}24 m.
Calculate the total pressure on the probe at a depth of 24 m24\text{ m}24 m.
Assume that the atmospheric pressure at the surface remains at 102 kPa102\text{ kPa}102 kPa.
During its ascent, the probe releases small bubbles of nitrogen gas to adjust its buoyancy.
As the gas bubbles rise to the surface, they increase in volume.
Explain this increase in volume.
