Question

The wreck of the RMS Titanic is located at a depth of 4.2km, where the pressure is 380atm and the temperature is about 1.7∘C. Like most shipwrecks, the Titanic likely sank with some air pockets trapped inside. Suppose a cabin,1.2m×2.4m×2.6m, sank in such a way that water could enter but air could not escape. If the cabin were initially filled with air at 1atm, 20∘C, what would the final volume of the air bubble have been after reaching thermal and mechanical equilibrium on the seabed? You may assume that air behaves as an ideal gas at all relevant states.

Final Volume: m^3

Note: Due to the extremely high final pressure, air is not actually an ideal gas at the final state; using the ideal gas law introduces an error of about 20%. The official answer above expects you to ignore this detail.

Answer 1