According to the regulation bounce of a basketball, when the ball is dropped at the full extension of the arm the ball should bounce to shoulder level. In order to inflate my slightly deflated ball, I needed to do work to move the pump. The work allowed air to be pushed into the ball. Unlike a heat engine where air currents do work, the pump required work and resulted in air change. The volume of the pump is compressed (isobaric) so that air flows out. The ball remained isochoric as the volume never changed.
The ball bounces higher once air is pumped in because the impact with the ground becomes more of an elastic collision with more air in the ball.
By using work to push the handle in, air flows out of the nozzle and into the ball creating more pressure.
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