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During exhalation, the primary mechanism that increases pressure in the lungs is the relaxation of the intercostal muscles. When these muscles relax, the ribcage moves downward and inward, which reduces the volume of the thoracic cavity. According to Boyle's Law, as the volume of a container decreases, the pressure within that container increases. Therefore, the reduction in thoracic volume caused by the relaxing intercostal muscles leads to an increase in lung pressure, allowing air to be expelled from the lungs.

The other processes mentioned would not lead to increased pressure during exhalation. For instance, an increase in thorax volume or expansion of the ribcage would actually lower the pressure in the lungs, facilitating inhalation rather than exhalation. Similarly, contraction of the diaphragm occurs during inhalation, where it moves downwards to increase thoracic volume and reduce pressure, thus drawing air into the lungs. Understanding these mechanics is crucial for grasping how breathing cycles function.