(Solved) : Container Pressurised Gas Small Hole Gas Escapes Results Decrease Internal Pressure Rate P Q32729541 . . . .

A container of pressurised gas has a small hole so that gasescapes. THis results in a decrease of internal pressure at a rateproportional to the difference between the internal pressure andthe pressure outside of the container. The outside pressure isconstant.

i.

Define the variables required and write out a differentialequation for the rate of change of the internal pressure.

ii.

Solve the differential equation to find a general solution forthe internal pressure in terms of time.

iii.

Find the exact solution given that the outside pressure is 1N/m^2 and the internal pressure was 201N/m^2 when leak started and41 N/m^2 after 1 hour.

Expert Answer

An