This question is concerned with the energy required to

This question is concerned with the energy required to inflate the lung. Specifically, we wish to know what fraction of the total inflation energy is used to overcome alveolar surface tension forces, and what fraction is used to overcome parenchymal elasticity.

(a) How much energy is required to inflate a spherical bubble from radius R1 to radius R2? The surface tension coefficient is constant and equal to σ. Hint: think in terms of a pressure-volume relationship.

(b) Considering surface tension effects only, how much energy is required to inflate all 300 million alveoli in the lungs? Assume that the total alveolar volume before inspiration is 2.5 liters, that the tidal volume is 500 ml, that all alveoli are identically sized spheres, and that the effective surface tension coefficient during inspiration is constant and equal to 35 dynes/cm.