An air rifle shoots a lead pellet by allowing high-pressure air to expand, propelling the pellet down the rifle barrel. Because this process happens very quickly, no appreciable thermal conduction occurs and the expansion is essentially adiabatic. Suppose the rifle starts with 11.5 cm^3 of compressed air, which behaves as an ideal gas with γ = 1.40. The expanding air pushes a 1.25-g pellet as a piston with cross-sectional area 0.0175 cm^2 along the 49.0-cm-long gun barrel.
1. What initial pressure is required to eject the pellet with a muzzle speed of 110 m/s? Ignore the effects of the air in front of the bullet and friction with the inside walls of the barrel.