An increase in the volume of the alveoli would directly result in

Air moves into the lungs from atmosphere

Explanation:

As per the gas law, pressure of a gas is indirectly proportional to the volume of the gas. Thus, if volume increases pressure decreases.  

Here, the volume of alveoli has increased due to which the pressure within the alveolar space reduces such that the atmospheric pressure outside alveoli becomes higher than the alveolar pressure within the alveoli. Due to this difference in pressure, the air gushes into the lungs.