An air pump has a cylinder 0.280 m long with a movable piston. The pump is used to compress air from the atmosphere (at

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An air pump has a cylinder 0.280 m long with a movable piston.
The pump is used to compress air from the atmosphere (at absolute
pressure 1.01×105Pa) into a very large tank at 4.00×105
Pa gauge pressure. (For air,
CV=20.8J/(mol⋅K.)
The piston begins the compression stroke at the open end of the
cylinder. How far down the length of the cylinder has the piston
moved when air first begins to flow from the cylinder into the
tank? Assume that the compression is adiabatic.
If the air is taken into the pump at 25.0 ∘C, what is the
temperature of the compressed air? How much work does the pump do
in order to compress 22.0 mol of air into the tank?