Werk gedaan tijdens volumeverandering

Consider an inflated soccer ball having a volume of V. The pressure acting on the ball is the atmospheric pressure.

Suppose the ball falls off the cliff and gets punctured; the air inside the ball releases. Assuming uniform deflation, let its radius be reduced by a distance of dr.

The magnitude of the force acting on the ball depends on the atmospheric pressure and the surface area of the ball.

Therefore, the work done by the surroundings on the ball equals the negative product of the atmospheric pressure, the ball's surface area, and the change in its radius.

However, the product of surface area and dr is the change in the volume of the ball.

Therefore, during a finite change in volume from V₁ to V₂, work done can be expressed as the integral of the product of pressure and change in volume.

Here the negative sign indicates that the work is done on the system by the surroundings. Conversely, the work done by the system is considered positive.