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When we are tired,feel sleepy,drowsy,bored, we breathe slowly and don't take much oxygen to make energy.So we open our mouth wide open and take more oxygen to fulfil our requirement of breathing.
When you feel is actually the brain cells which are in a sense of saying..going to fall asleep for lack of oxygen (hypoxia or hypoxemia). Also when we feel drowsy, our respiratory rate being controlled by reflex centres in our brain falls. This is a vicious cycle. The yawn breaks this cycle.
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