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As your diaphragm or intercoastal muscles contract the size of the lungs increases. This creates a pressure difference between your lungs and the surrounding atmosphere. By increasing the size of the lungs you create a low pressure environment in the lungs by expanding the same amount of gas to a larger area. this pressure difference doesn't have to be much 1mmhg is more then enough, the main thing is just that you need a difference in preasure. Air flows from high preasure to low preasure, so by decreasing the preasure in the lungs air flows into the lungs. as you breath out you make the lungs smaller by relaxing the muscles and diaphragm, making the volume in the lungs decrease, thus increasing the preasure and moving the air from inside the lungs out to the surrounding atmosphere.