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Pumping pushes more air molecules into the ball. That makes more molecules moving around inside of the ball and more molecules colliding with the inside of the ball. All of those collisions (trillions and trillions) push the inside of the ball out. When the temperature is increased, the molecules move faster. Faster molecules collide with the inside walls more frequently, which also increases the pressure. You can test this by pumping up a ball then putting it into the freezer and see what happens to the pressure.

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Q: Why does pumping a soccer ball with an air pump increase the pressure inside the ball?
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