As a rough approximation, blowing up the balloon is like stretching a spring. In particular, we can approximate the force of the air required to keep the balloon stretched to a diameter D as F ≈ KD, where K is a proportionality constant determined by the properties of the balloon. Then the work required to change the diameter a small amount dD is dW_b = KDdD. Integrating from the initial diameter D₀ to the final diameter we find the total work required to blow up the balloon as