A sealed vertical cylinder of height 0.80m contains an ideal gas at uniform temperature T and initial pressure P0 while the cylinder is at rest. The cylinder is then given a constant upward acceleration of 3.0m/s2 for several seconds, long enough for the gas to re-establish equilibrium in the accelerating frame. Derive an expression for the pressure difference ΔP between the bottom and the top of the cylinder in terms of the gas density ρ, the acceleration due to gravity g, and the given acceleration.