The external inter costal and diaphragm muscles contract.
This causes the rib cage to move upwards and outwards and the diaphragm to flatten, increasing the volume of the thoracic cavity.
As the volume of the thoracic cavity increases, the lung pressure decreases.
Air will always flow from an area of high pressure to an area of lower pressure so air flows down the trachea and into the lungs.
Inspiration is an active process-it requires energy.
Expiration
The external inter costal and diaphragm muscles relax.
The internal inter costal muscles contract pulling the rib cage further down and in. During this time the movement of two sets of intercostal muscles are said to be antagonastic.
The volume of the thoracic cavity decreases, causing the air pressure to increase.
Air is forced down the pressure gradient and out of the lungs.
Normal expiration is a passive process - it doesn't require energy.